| Battaglia M, Kontar EP, Fletcher L and MacKinnon AL (2012), "Numerical Simulations of Chromospheric Hard X-Ray Source Sizes in Solar Flares", The Astrophysical Journal. Vol. 752, pp. 4. |
| Abstract: X-ray observations are a powerful diagnostic tool for transport, acceleration, and heating of electrons in solar flares. Height and size measurements of X-ray footpoint sources can be used to determine the chromospheric density and constrain the parameters of magnetic field convergence and electron pitch-angle evolution. We investigate the influence of the chromospheric density, magnetic mirroring, and collisional pitch-angle scattering on the size of X-ray sources. The time-independent Fokker-Planck equation for electron transport is solved numerically and analytically to find the electron distribution as a function of height above the photosphere. From this distribution, the expected X-ray flux as a function of height, its peak height, and full width at half-maximum are calculated and compared with RHESSI observations. A purely instrumental explanation for the observed source size was ruled out by using simulated RHESSI images. We find that magnetic mirroring and collisional pitch-angle scattering tend to change the electron flux such that electrons are stopped higher in the atmosphere compared with the simple case with collisional energy loss only. However, the resulting X-ray flux is dominated by the density structure in the chromosphere and only marginal increases in source width are found. Very high loop densities (>1011 cm–3) could explain the observed sizes at higher energies, but are unrealistic and would result in no footpoint emission below about 40 keV, contrary to observations. We conclude that within a monolithic density model the vertical sizes are given mostly by the density scale height and are predicted smaller than the RHESSI results show. |
BibTeX:
@article{BattagliaKontarFletcherMacKinnon2012,
author = {Battaglia, M. and Kontar, E. P. and Fletcher, L. and MacKinnon, A. L.},
title = {Numerical Simulations of Chromospheric Hard X-Ray Source Sizes in Solar Flares},
journal = {The Astrophysical Journal},
year = {2012},
volume = {752},
pages = {4},
url = {http://adsabs.harvard.edu/abs/2012ApJ...752....4B}
}
|
| Hannah IG and Kontar EP (2012), "Differential emission measures from the regularized inversion of Hinode and SDO data", Astronomy and Astrophysics. Vol. 539, pp. 146. |
| Abstract: Aims: To demonstrate the capabilities of regularized inversion to recover differential emission measures (DEMs) from multi-wavelength observations provided by telescopes such as Hinode and SDO. Methods: We develop and apply an enhanced regularization algorithm, used in RHESSI X-ray spectral analysis, to constrain the ill-posed inverse problem that is determining the DEM from solar observations. We demonstrate this computationally fast technique applied to a range of DEM models simulating broadband imaging data from SDO/AIA and high resolution line spectra from Hinode/EIS, as well as actual active region observations with Hinode/EIS and XRT. As this regularization method naturally provides both vertical and horizontal (temperature resolution) error bars we are able to test the role of uncertainties in the data and response functions. Results: The regularization method is able to successfully recover the DEM from simulated data of a variety of model DEMs (single Gaussian, multiple Gaussians and CHIANTI DEM models). It is able to do this, at best, to over four orders of magnitude in DEM space but typically over two orders of magnitude from peak emission. The combination of horizontal and vertical error bars and the regularized solution matrix allows us to easily determine the accuracy and robustness of the regularized DEM. We find that the typical range for the horizontal errors is Δlog T ≈ 0.1-0.5 and this is dependent on the observed signal to noise, uncertainty in the response functions as well as the source model and temperature. With Hinode/EIS an uncertainty of 20% greatly broadens the regularized DEMs for both Gaussian and CHIANTI models although information about the underlying DEMs is still recoverable. When applied to real active region observations with Hinode/EIS and XRT the regularization method is able to recover a DEM similar to that found via a MCMC method but in considerably less computational time. Conclusions: Regularized inversion quickly determines the DEM from solar observations and provides reliable error estimates (both horizontal and vertical) which allows the temperature spread of coronal plasma to be robustly quantified. |
BibTeX:
@article{HannahKontar2012,
author = {Hannah, I. G. and Kontar, E. P.},
title = {Differential emission measures from the regularized inversion of Hinode and SDO data},
journal = {Astronomy and Astrophysics},
year = {2012},
volume = {539},
pages = {146},
url = {http://adsabs.harvard.edu/abs/2012A%26A...539A.146H}
}
|
| Kontar EP, Ratcliffe H and Bian NH (2012), "Wave-particle interactions in non-uniform plasma and the interpretation of hard X-ray spectra in solar flares", Astronomy and Astrophysics. Vol. 539, pp. 43. |
| Abstract: Context. High-energy electrons accelerated during solar flares are abundant in the solar corona and in interplanetary space. Commonly, the number and energy of non-thermal electrons at the Sun is estimated through hard X-ray (HXR) spectral observations (e.g. RHESSI) and a single-particle collisional approximation. Aims: We aim to investigate the role of the spectrally evolving Langmuir turbulence on the population of energetic electrons in the solar corona. Methods: We numerically simulated the relaxation of a power-law non-thermal electron population in a collisional inhomogeneous plasma, including wave-particle and wave-wave interactions. Results: The numerical simulations show that the long-time evolution of electron population above 20 keV deviates substantially from the collisional approximation when wave-particle interactions in non-uniform plasma are taken into account. The evolution of the Langmuir wave spectrum towards smaller wavenumbers, caused by large-scale density fluctuations and wave-wave interactions, leads to an effective acceleration of electrons. Furthermore, the time-integrated spectrum of non-thermal electrons, which is normally observed with HXR above 20 keV, is noticeably increased because of acceleration of non-thermal electrons through Langmuir waves. Conclusions: The results show that the observed HXR spectrum, when interpreted in terms of collisional relaxation, can lead to an overestimated number and energy of energetic electrons accelerated in the corona. |
BibTeX:
@article{KontarRatcliffeBian2012,
author = {Kontar, E. P. and Ratcliffe, H. and Bian, N. H.},
title = {Wave-particle interactions in non-uniform plasma and the interpretation of hard X-ray spectra in solar flares},
journal = {Astronomy and Astrophysics},
year = {2012},
volume = {539},
pages = {43},
url = {http://adsabs.harvard.edu/abs/2012A%26A...539A..43K}
}
|
| Matthews SA, Williams DR, Klein K-L, Kontar EP, Smith DM, Lagg A, Krucker S, Hurford GJ, Vilmer N, MacKinnon AL, Zharkova VV, Fletcher L, Hannah IG, Browning PK, Innes DE, Trottet G, Foullon C, Nakariakov VM, Green LM, Lamoureux H, Forsyth C, Walton DM, Mathioudakis M, Gandorfer A, Martinez-Pillet V, Limousin O, Verwichte E, Dalla S, Mann G, Aurass H and Neukirch T (2012), "Solar Particle Acceleration Radiation and Kinetics (SPARK). A mission to understand the nature of particle acceleration", Experimental Astronomy. Vol. 33, pp. 237-269. |
| Abstract: Energetic particles are critical components of plasma populations found throughout the universe. In many cases particles are accelerated to relativistic energies and represent a substantial fraction of the total energy of the system, thus requiring extremely efficient acceleration processes. The production of accelerated particles also appears coupled to magnetic field evolution in astrophysical plasmas through the turbulent magnetic fields produced by diffusive shock acceleration. Particle acceleration is thus a key component in helping to understand the origin and evolution of magnetic structures in, e.g. galaxies. The proximity of the Sun and the range of high-resolution diagnostics available within the solar atmosphere offers unique opportunities to study the processes involved in particle acceleration through the use of a combination of remote sensing observations of the radiative signatures of accelerated particles, and of their plasma and magnetic environment. The SPARK concept targets the broad range of energy, spatial and temporal scales over which particle acceleration occurs in the solar atmosphere, in order to determine how and where energetic particles are accelerated. SPARK combines highly complementary imaging and spectroscopic observations of radiation from energetic electrons, protons and ions set in their plasma and magnetic context. The payload comprises focusing-optics X-ray imaging covering the range from 1 to 60 keV; indirect HXR imaging and spectroscopy from 5 to 200 keV, γ-ray spectroscopic imaging with high-resolution LaBr3 scintillators, and photometry and source localisation at far-infrared wavelengths. The plasma environment of the regions of acceleration and interaction will be probed using soft X-ray imaging of the corona and vector magnetography of the photosphere and chromosphere. SPARK is designed for solar research. However, in addition it will be able to provide exciting new insights into the origin of particle acceleration in other regimes, including terrestrial gamma-ray flashes (TGF), the origin of γ-ray bursts, and the possible existence of axions. |
BibTeX:
@article{MatthewsWilliamsKleinKontarSmithLaggKruckerHurfordVilmerMacKinnonZharkovaFletcherHannahBrowningInnesTrottetFoullonNakariakovGreenLamoureuxForsythWaltonMathioudakisGandorferMartinez-PilletLimousinVerwichteDallaMannAurassNeukirch2012,
author = {Matthews, Sarah A. and Williams, David R. and Klein, Karl-Ludwig and Kontar, Eduard P. and Smith, David M. and Lagg, Andreas and Krucker, Sam and Hurford, Gordon J. and Vilmer, Nicole and MacKinnon, Alexander L. and Zharkova, Valentina V. and Fletcher, Lyndsay and Hannah, Iain G. and Browning, Philippa K. and Innes, Davina E. and Trottet, Gerard and Foullon, Clare and Nakariakov, Valery M. and Green, Lucie M. and Lamoureux, Herve and Forsyth, Colin and Walton, David M. and Mathioudakis, Mihalis and Gandorfer, Achim and Martinez-Pillet, Valentin and Limousin, Olivier and Verwichte, Erwin and Dalla, Silvia and Mann, Gottfried and Aurass, Henri and Neukirch, Thomas},
title = {Solar Particle Acceleration Radiation and Kinetics (SPARK). A mission to understand the nature of particle acceleration},
journal = {Experimental Astronomy},
year = {2012},
volume = {33},
pages = {237--269},
url = {http://adsabs.harvard.edu/abs/2012ExA....33..237M}
}
|
| Battaglia M and Kontar EP (2011), "Height structure of X-ray, EUV, and white-light emission in a solar flare", Astronomy and Astrophysics. Vol. 533, pp. L2. |
| Abstract: Context. The bulk of solar flare emission originates from very compact sources located in the lower solar atmosphere and observable at a broad range of wavelengths such as near optical, UV, EUV, soft and hard X-rays, and gamma-rays. Nevertheless, very few spatially resolved imaging observations have been performed to determine the structure of these compact regions. Aims: We investigate the above-the-photosphere heights of hard X-ray (HXR), EUV, and white-light (6173 Å) continuum sources in the low atmosphere and the corresponding densities at these heights. By considering the collisional transport of solar energetic electrons, we also determine where and how much energy is deposited and compare these values with the emissions observed in HXR, EUV, and the continuum. Methods: Simultaneous EUV/continuum images from AIA/HMI on-board SDO and HXR RHESSI images are compared to study a well-observed gamma-ray limb flare. Using RHESSI X-ray visibilities, we determine the height of the HXR sources as a function of energy above the photosphere. Co-aligning AIA/SDO and HMI/SDO images with RHESSI, we infer, for the first time, the heights and characteristic densities of HXR, EUV, and continuum (white-light) sources in the flaring footpoint of the magnetic loop. Results: We find 35-100 keV HXR sources at heights of between 1.7 and 0.8 Mm above the photosphere, below the 6173 Å continuum emission that appears at heights 1.5-3 Mm and the peak of EUV emission originating near 3 Mm. Conclusions: The EUV emission locations are consistent with energy deposition from low energy electrons of ~12 keV occurring in the top layers of the fully ionized chromosphere/low corona and not by ≳ 20 keV electrons that produce HXR footpoints in the lower neutral chromosphere. The maximum of white-light continuum emission appears between the HXR and EUV emission, presumably in the transition between ionized and neutral atmospheres, implying that it consists of free-bound and free-free continuum emission. We note that the energy deposited by low energy electrons is sufficient to explain the energetics of both the optical and UV emissions. Two movies are available in electronic form at |
BibTeX:
@article{BattagliaKontar2011,
author = {Battaglia, M. and Kontar, E. P.},
title = {Height structure of X-ray, EUV, and white-light emission in a solar flare},
journal = {Astronomy and Astrophysics},
year = {2011},
volume = {533},
pages = {L2},
url = {http://adsabs.harvard.edu/abs/2011A%26A...533L...2B}
}
|
| Battaglia M and Kontar EP (2011), "Hard X-Ray Footpoint Sizes and Positions as Diagnostics of Flare Accelerated Energetic Electrons in the Low Solar Atmosphere", The Astrophysical Journal. Vol. 735, pp. 42. |
| Abstract: The hard X-ray (HXR) emission in solar flares comes almost exclusively from a very small part of the flaring region, the footpoints of magnetic loops. Using RHESSI observations of solar flare footpoints, we determine the radial positions and sizes of footpoints as a function of energy in six near-limb events to investigate the transport of flare accelerated electrons and the properties of the chromosphere. HXR visibility forward fitting allows us to find the positions/heights and the sizes of HXR footpoints along and perpendicular to the magnetic field of the flaring loop at different energies in the HXR range. We show that in half of the analyzed events, a clear trend of decreasing height of the sources with energy is found. Assuming collisional thick-target transport, HXR sources are located between 600 and 1200 km above the photosphere for photon energies between 120 and 25 keV, respectively. In the other events, the position as a function of energy is constant within the uncertainties. The vertical sizes (along the path of electron propagation) range from 1.3 to 8 arcsec which is up to a factor four larger than predicted by the thick-target model even in events where the positions/heights of HXR sources are consistent with the collisional thick-target model. Magnetic mirroring, collisional pitch-angle scattering, and X-ray albedo are discussed as potential explanations of the findings. |
BibTeX:
@article{BattagliaKontar2011a,
author = {Battaglia, M. and Kontar, E. P.},
title = {Hard X-Ray Footpoint Sizes and Positions as Diagnostics of Flare Accelerated Energetic Electrons in the Low Solar Atmosphere},
journal = {The Astrophysical Journal},
year = {2011},
volume = {735},
pages = {42},
url = {http://adsabs.harvard.edu/abs/2011ApJ...735...42B}
}
|
| Battaglia M, Kontar EP and Hannah IG (2011), "The influence of albedo on the size of hard X-ray flare sources", Astronomy and Astrophysics. Vol. 526, pp. 3. |
| Abstract: Context. Hard X-rays from solar flares are an important diagnostic of particle acceleration and transport in the solar atmosphere. However, any observed X-ray flux from on-disc sources is composed of direct emission plus Compton backscattered photons (albedo). This affects both the observed spectra and images and the physical quantities derived from them, such as the spatial and spectral distributions of accelerated electrons or characteristics of the solar atmosphere (e.g. density). the directivity of X-rays in imaging using RHESSI data. We describe this method and demonstrate its application to a compact disc event observed with RHESSI. Methods: Visibility forward fitting is used to determine the size (second moment) of a disc event observed by RHESSI as a function of energy. Using a Monte Carlo simulation code of photon transport in the chromosphere, maps for different degrees of downward directivity and true source sizes are computed. The resulting sizes from the simulated maps are compared with the sizes from the observations to find limits on the true source size and the directivity. Results: The observed full width half maximum of the source varies in size between 7.4 arcsec and 9.1 arcsec with the maximum between 30 and 40 keV. Such behaviour is expected in the presence of albedo and is found in the simulations. The uncertainties in the data are not small enough to make unambiguous statements about the true source size and the directivity simultaneously. However, a source size smaller than 6 arcsec is improbable for modest directivities, and the true source size is likely to be around 7 arcsec for small directivities. Conclusions: While it is difficult to image the albedo patch directly, the effect of backscattered photons on the observed source size can be estimated. This is demonstrated here on observations for the first time. The increase in source size caused by albedo has to be accounted for when computing physical quantities that include the size as a parameter, such as flare energetics. At the same time, studying the albedo signature provides vital information about the directivity of X-rays and related electrons. |
BibTeX:
@article{BattagliaKontarHannah2011,
author = {Battaglia, M. and Kontar, E. P. and Hannah, I. G.},
title = {The influence of albedo on the size of hard X-ray flare sources},
journal = {Astronomy and Astrophysics},
year = {2011},
volume = {526},
pages = {3},
url = {http://adsabs.harvard.edu/abs/2011A%26A...526A...3B}
}
|
| Bian NH and Kontar EP (2011), "Parallel electric field amplification by phase mixing of Alfven waves", Astronomy and Astrophysics. Vol. 527, pp. 130. |
| Abstract: Context. Several numerical studies have identified phase mixing of low-frequency Alfven waves as a means of parallel electric field amplification and acceleration of electrons in a collisionless plasma. Aims: Theoretical explanations are given of how phase mixing amplifies the parallel electric field and, as a consequence, also leads to enhanced collisionless damping of the wave by energy transfer to the electrons. Methods: Our results are based on the properties of the Alfven waves in a warm plasma. These results are obtained within the framework of drift-kinetic theory. Results: Phase mixing in a collisionless low-β plasma proceeds in a manner very similar to the resistive case, except that electron Landau damping is the primary energy dissipation channel. The time and length scales involved are evaluated. We also focus on the evolution of the parallel electric field and calculate its maximum value in the course of its amplification |
BibTeX:
@article{BianKontar2011,
author = {Bian, N. H. and Kontar, E. P.},
title = {Parallel electric field amplification by phase mixing of Alfven waves},
journal = {Astronomy and Astrophysics},
year = {2011},
volume = {527},
pages = {130},
url = {http://adsabs.harvard.edu/abs/2011A%26A...527A.130B}
}
|
| Bian NH, Kontar EP and MacKinnon AL (2011), "Turbulent cross-field transport of non-thermal electrons in coronal loops: theory and observations", Astronomy and Astrophysics. Vol. 535, pp. 18. |
| Abstract: Context. A fundamental problem in astrophysics is the interaction between magnetic turbulence and charged particles. It is now possible to use Ramaty High Energy Solar Spectroscopic Imager (RHESSI) observations of hard X-rays (HXR) emitted by electrons to identify the presence of turbulence and to estimate the magnitude of the magnetic field line diffusion coefficient at least in dense coronal flaring loops. Aims: We discuss the various possible regimes of cross-field transport of non-thermal electrons resulting from broadband magnetic turbulence in coronal loops. The importance of the Kubo number K as a governing parameter is emphasized and results applicable in both the large and small Kubo number limits are collected. Methods: Generic models, based on concepts and insights developed in the statistical theory of transport, are applied to the coronal loops and to the interpretation of hard X-ray imaging data in solar flares. The role of trapping effects, which become important in the non-linear regime of transport, is taken into account in the interpretation of the data. Results: For this flaring solar loop, we constrain the ranges of parallel and perpendicular correlation lengths of turbulent magnetic fields and possible Kubo numbers. We show that a substantial amount of magnetic fluctuations with energy ~1% (or more) of the background field can be inferred from the measurements of the magnetic diffusion coefficient inside thick-target coronal loops. |
BibTeX:
@article{BianKontarMacKinnon2011,
author = {Bian, N. H. and Kontar, E. P. and MacKinnon, A. L.},
title = {Turbulent cross-field transport of non-thermal electrons in coronal loops: theory and observations},
journal = {Astronomy and Astrophysics},
year = {2011},
volume = {535},
pages = {18},
url = {http://adsabs.harvard.edu/abs/2011A%26A...535A..18B}
}
|
| Fleishman GD, Kontar EP, Nita GM and Gary DE (2011), "A Cold, Tenuous Solar Flare: Acceleration Without Heating", The Astrophysical Journal Letters. Vol. 731, pp. L19. |
| Abstract: We report the observation of an unusual cold, tenuous solar flare, which reveals itself via numerous and prominent non-thermal manifestations, while lacking any noticeable thermal emission signature. RHESSI hard X-rays and 0.1-18 GHz radio data from OVSA and Phoenix-2 show copious electron acceleration (1035 electrons s-1 above 10 keV) typical for GOES M-class flares with electrons energies up to 100 keV, but GOES temperatures not exceeding 6.1 MK. The imaging, temporal, and spectral characteristics of the flare have led us to a firm conclusion that the bulk of the microwave continuum emission from this flare was produced directly in the acceleration region. The implications of this finding for the flaring energy release and particle acceleration are discussed. |
BibTeX:
@article{FleishmanKontarNitaGary2011,
author = {Fleishman, Gregory D. and Kontar, Eduard P. and Nita, Gelu M. and Gary, Dale E.},
title = {A Cold, Tenuous Solar Flare: Acceleration Without Heating},
journal = {The Astrophysical Journal Letters},
year = {2011},
volume = {731},
pages = {L19},
url = {http://adsabs.harvard.edu/abs/2011ApJ...731L..19F}
}
|
| Guo J, Liu S, Fletcher L and Kontar EP (2011), "Relationship Between Hard and Soft X-ray Emission Components of a Solar Flare", The Astrophysical Journal. Vol. 728, pp. 4. |
| Abstract: X-ray observations of solar flares routinely reveal an impulsive high-energy and a gradual low-energy emission component, whose relationship is one of the key issues of solar flare study. The gradual and impulsive emission components are believed to be associated with, respectively, the thermal and nonthermal components identified in spectral fitting. In this paper, a prominent ~50 s hard X-ray (HXR) pulse of a simple GOES class C7.5 flare on 2002 February 20 is used to study the association between high-energy, non-thermal, and impulsive evolution, and low-energy, thermal, and gradual evolution. We use regularized methods to obtain time derivatives of photon fluxes to quantify the time evolution as a function of photon energy, obtaining a break energy between impulsive and gradual behavior. These break energies are consistent with a constant value of ~11 keV in agreement with those found spectroscopically between thermal and non-thermal components, but the relative errors of the former are greater than 15% and much greater than the few percent errors found from the spectral fitting. These errors only weakly depend on assuming an underlying spectral model for the photons, pointing to the current data being inadequate to reduce the uncertainties rather than there being a problem associated with an assumed model. The time derivative method is used to test for the presence of a "pivot energy" in this flare. Although these pivot energies are marginally consistent with a constant value of ~9 keV, its values in the HXR rise phase appear to be lower than those in the decay phase. Assuming that electrons producing the high-energy component have a power-law distribution and are accelerated from relatively hot regions of a background plasma responsible for the observed thermal component, a low limit is obtained for the low-energy cutoff. This limit is always lower than the break and pivot energies and is located in the tail of the Maxwellian distribution of the thermal component. |
BibTeX:
@article{GuoLiuFletcherKontar2011,
author = {Guo, Jingnan and Liu, Siming and Fletcher, Lyndsay and Kontar, Eduard P.},
title = {Relationship Between Hard and Soft X-ray Emission Components of a Solar Flare},
journal = {The Astrophysical Journal},
year = {2011},
volume = {728},
pages = {4},
url = {http://adsabs.harvard.edu/abs/2011ApJ...728....4G}
}
|
| Hannah IG and Kontar EP (2011), "The spectral difference between solar flare HXR coronal and footpoint sources due to wave-particle interactions", Astronomy and Astrophysics. Vol. 529, pp. 109. |
| Abstract: Aims: We investigate the spatial and spectral evolution of hard X-ray (HXR) emission from flare accelerated electron beams subject to collisional transport and wave-particle interactions in the solar atmosphere. Methods: We numerically follow the propagation of a power-law of accelerated electrons in 1D space and time with the response of the background plasma in the form of Langmuir waves using the quasilinear approximation. Results: We find that the addition of wave-particle interactions to collisional transport for a transient initially injected electron beam flattens the spectrum of the footpoint source. The coronal source is unchanged and so the difference in the spectral indices between the coronal and footpoint sources is Δγ > 2, which is larger than expected from purely collisional transport. A steady-state beam shows little difference between the two cases, as has been previously found, as a transiently injected electron beam is required to produce significant wave growth, especially at higher velocities. With this transiently injected beam the wave-particle interactions dominate in the corona whereas the collisional losses dominate in the chromosphere. The shape of the spectrum is different with increasing electron beam density in the wave-particle interaction case whereas with purely collisional transport only the normalisation is changed. We also find that the starting height of the source electron beam above the photosphere affects the spectral index of the footpoint when Langmuir wave growth is included. This may account for the differing spectral indices found between double footpoints if asymmetrical injection has occurred in the flaring loop. |
BibTeX:
@article{HannahKontar2011,
author = {Hannah, I. G. and Kontar, E. P.},
title = {The spectral difference between solar flare HXR coronal and footpoint sources due to wave-particle interactions},
journal = {Astronomy and Astrophysics},
year = {2011},
volume = {529},
pages = {109},
url = {http://adsabs.harvard.edu/abs/2011A%26A...529A.109H}
}
|
| Holman GD, Aschwanden MJ, Aurass H, Battaglia M, Grigis PC, Kontar EP, Liu W, Saint-Hilaire P and Zharkova VV (2011), "Implications of X-ray Observations for Electron Acceleration and Propagation in Solar Flares", Space Science Reviews. Vol. 159, pp. 107-166. |
| Abstract: High-energy X-rays and γ-rays from solar flares were discovered just over fifty years ago. Since that time, the standard for the interpretation of spatially integrated flare X-ray spectra at energies above several tens of keV has been the collisional thick-target model. After the launch of the Reuven Ramaty High Energy Solar Spectroscopic Imager ( RHESSI) in early 2002, X-ray spectra and images have been of sufficient quality to allow a greater focus on the energetic electrons responsible for the X-ray emission, including their origin and their interactions with the flare plasma and magnetic field. The result has been new insights into the flaring process, as well as more quantitative models for both electron acceleration and propagation, and for the flare environment with which the electrons interact. In this article we review our current understanding of electron acceleration, energy loss, and propagation in flares. Implications of these new results for the collisional thick-target model, for general flare models, and for future flare studies are discussed. |
BibTeX:
@article{HolmanAschwandenAurassBattagliaGrigisKontarLiuSaint-HilaireZharkova2011,
author = {Holman, G. D. and Aschwanden, M. J. and Aurass, H. and Battaglia, M. and Grigis, P. C. and Kontar, E. P. and Liu, W. and Saint-Hilaire, P. and Zharkova, V. V.},
title = {Implications of X-ray Observations for Electron Acceleration and Propagation in Solar Flares},
journal = {Space Science Reviews},
year = {2011},
volume = {159},
pages = {107--166},
url = {http://adsabs.harvard.edu/abs/2011SSRv..159..107H}
}
|
| Inglis AR, Zimovets IV, Dennis BR, Kontar EP, Nakariakov VM, Struminsky AB and Tolbert AK (2011), "Instrumental oscillations in RHESSI count rates during solar flares", Astronomy and Astrophysics. Vol. 530, pp. 47. |
| Abstract: Aims: We seek to illustrate the analysis problems posed by RHESSI spacecraft motion by studying persistent instrumental oscillations found in the lightcurves measured by RHESSI's X-ray detectors in the 6-12 keV and 12-25 keV energy range during the decay phase of the flares of 2004 November 4 and 6. Methods: The various motions of the RHESSI spacecraft which may contribute to the manifestation of oscillations are studied. The response of each detector in turn is also investigated. correspond to the nutation period of the RHESSI instrument. These oscillations are of greatest amplitude for detector 5, while in the lightcurves of many other detectors the oscillations are small or undetectable. We also find that the variation in detector pointing is much larger during this flare than the counterexample of 2004 November 4. Conclusions: Sufficiently large nutation motions of the RHESSI spacecraft lead to clearly observable oscillations in count rates, posing a significant hazard for data analysis. This issue is particularly problematic for detector 5 due to its design characteristics. Dynamic correction of the RHESSI counts, accounting for the livetime, data gaps, and the transmission of the bi-grid collimator of each detector, is required to overcome this issue. These corrections should be applied to all future oscillation studies. |
BibTeX:
@article{InglisZimovetsDennisKontarNakariakovStruminskyTolbert2011,
author = {Inglis, A. R. and Zimovets, I. V. and Dennis, B. R. and Kontar, E. P. and Nakariakov, V. M. and Struminsky, A. B. and Tolbert, A. K.},
title = {Instrumental oscillations in RHESSI count rates during solar flares},
journal = {Astronomy and Astrophysics},
year = {2011},
volume = {530},
pages = {47},
url = {http://adsabs.harvard.edu/abs/2011A%26A...530A..47I}
}
|
| Jeffrey NLS and Kontar EP (2011), "Spatially resolved hard X-ray polarization in solar flares: effects of Compton scattering and bremsstrahlung", Astronomy and Astrophysics. Vol. 536, pp. 93. |
| Abstract: Aims: We study the polarization of hard X-ray (HXR) sources in the solar atmosphere, including Compton backscattering of photons in the photosphere (the albedo effect) and the spatial distribution of polarization across the source. Methods: HXR photon polarization and spectra produced via electron-ion bremsstrahlung emission are calculated from various electron distributions typical for solar flares. Compton scattering and photoelectric absorption are then modelled using Monte Carlo simulations of photon transport in the photosphere to study the observed (primary and albedo) sources. Polarization maps across HXR sources (primary and albedo components) for each of the modelled electron distributions are calculated at various source locations from the solar centre to the limb. Results: We show that Compton scattering produces a distinct polarization variation across the albedo patch at peak albedo energies of 20-50 keV for all anisotropies modelled. The results show that there are distinct spatial polarization changes in both the radial and perpendicular to radial directions across the extent of the HXR source at a given disk location. In the radial direction, the polarization magnitude and direction at specific positions along the HXR source will either increase or decrease with increased photon distribution directivity towards the photosphere. We also show how high electron cutoff energies influence the direction of polarization at above ~100 keV. Conclusions: Spatially resolved HXR polarization measurements can provide important information about the directivity and energetics of the electron distribution. Our results indicate the preferred angular resolution of polarization measurements required to distinguish between the scattered and primary components. We also show how spatially resolved polarization measurements could be used to probe the emission pattern of an HXR source, using both the magnitude and the direction of the polarization. |
BibTeX:
@article{JeffreyKontar2011,
author = {Jeffrey, N. L. S. and Kontar, E. P.},
title = {Spatially resolved hard X-ray polarization in solar flares: effects of Compton scattering and bremsstrahlung},
journal = {Astronomy and Astrophysics},
year = {2011},
volume = {536},
pages = {93},
url = {http://adsabs.harvard.edu/abs/2011A%26A...536A..93J}
}
|
| Kontar EP, Brown JC, Emslie AG, Hajdas W, Holman GD, Hurford GJ, Kašparová J, Mallik PCV, Massone AM, McConnell ML, Piana M, Prato M, Schmahl EJ and Suarez-Garcia E (2011), "Deducing Electron Properties from Hard X-ray Observations", Space Science Reviews. Vol. 159, pp. 301-355. |
| Abstract: X-radiation from energetic electrons is the prime diagnostic of flare-accelerated electrons. The observed X-ray flux (and polarization state) is fundamentally a convolution of the cross-section for the hard X-ray emission process(es) in question with the electron distribution function, which is in turn a function of energy, direction, spatial location and time. To address the problems of particle propagation and acceleration one needs to infer as much information as possible on this electron distribution function, through a deconvolution of this fundamental relationship. This review presents recent progress toward this goal using spectroscopic, imaging and polarization measurements, primarily from the Reuven Ramaty High Energy Solar Spectroscopic Imager ( RHESSI). Previous conclusions regarding the energy, angular (pitch angle) and spatial distributions of energetic electrons in solar flares are critically reviewed. We discuss the role and the observational evidence of several radiation processes: free-free electron-ion, free-free electron-electron, free-bound electron-ion, photoelectric absorption and Compton backscatter (albedo), using both spectroscopic and imaging techniques. This unprecedented quality of data allows for the first time inference of the angular distributions of the X-ray-emitting electrons and improved model-independent inference of electron energy spectra and emission measures of thermal plasma. Moreover, imaging spectroscopy has revealed hitherto unknown details of solar flare morphology and detailed spectroscopy of coronal, footpoint and extended sources in flaring regions. Additional attempts to measure hard X-ray polarization were not sufficient to put constraints on the degree of anisotropy of electrons, but point to the importance of obtaining good quality polarization data in the future. |
BibTeX:
@article{KontarBrownEmslieHajdasHolmanHurfordKasparovaMallikMassoneMcConnellPianaPratoSchmahlSuarez-Garcia2011,
author = {Kontar, E. P. and Brown, J. C. and Emslie, A. G. and Hajdas, W. and Holman, G. D. and Hurford, G. J. and Kašparová, J. and Mallik, P. C. V. and Massone, A. M. and McConnell, M. L. and Piana, M. and Prato, M. and Schmahl, E. J. and Suarez-Garcia, E.},
title = {Deducing Electron Properties from Hard X-ray Observations},
journal = {Space Science Reviews},
year = {2011},
volume = {159},
pages = {301--355},
url = {http://adsabs.harvard.edu/abs/2011SSRv..159..301K}
}
|
| Kontar EP, Hannah IG and Bian NH (2011), "Acceleration, Magnetic Fluctuations, and Cross-field Transport of Energetic Electrons in a Solar Flare Loop", The Astrophysical Journal Letters. Vol. 730, pp. L22. |
| Abstract: Plasma turbulence is thought to be associated with various physical processes involved in solar flares, including magnetic reconnection, particle acceleration, and transport. Using RHESSI observations and the X-ray visibility analysis, we determine the spatial and spectral distributions of energetic electrons for a flare (GOES M3.7 class, 2002 April 14, 23:55 UT), which was previously found to be consistent with a reconnection scenario. It is demonstrated that because of the high density plasma in the loop, electrons have to be continuously accelerated about the loop apex of length ~2 × 109 cm and width ~7 × 108 cm. Energy-dependent transport of tens of keV electrons is observed to occur both along and across the guiding magnetic field of the loop. We show that the cross-field transport is consistent with the presence of magnetic turbulence in the loop, where electrons are accelerated, and estimate the magnitude of the field line diffusion coefficient for different phases of the flare. The energy density of magnetic fluctuations is calculated for given magnetic field correlation lengths and is larger than the energy density of the non-thermal electrons. The level of magnetic fluctuations peaks when the largest number of electrons is accelerated and is below detectability or absent at the decay phase. These hard X-ray observations provide the first observational evidence that magnetic turbulence governs the evolution of energetic electrons in a dense flaring loop and is suggestive of their turbulent acceleration. |
BibTeX:
@article{KontarHannahBian2011,
author = {Kontar, E. P. and Hannah, I. G. and Bian, N. H.},
title = {Acceleration, Magnetic Fluctuations, and Cross-field Transport of Energetic Electrons in a Solar Flare Loop},
journal = {The Astrophysical Journal Letters},
year = {2011},
volume = {730},
pages = {L22},
url = {http://adsabs.harvard.edu/abs/2011ApJ...730L..22K}
}
|
| Krucker S, Hudson HS, Jeffrey NLS, Battaglia M, Kontar EP, Benz AO, Csillaghy A and Lin RP (2011), "High-resolution Imaging of Solar Flare Ribbons and Its Implication on the Thick-target Beam Model", The Astrophysical Journal. Vol. 739, pp. 96. |
| Abstract: We report on high-resolution optical and hard X-ray observations of solar flare ribbons seen during the GOES X6.5 class white-light flare of 2006 December 6. The data consist of imaging observations at 430 nm (the Fraunhofer G band) taken by the Hinode Solar Optical Telescope with the hard X-rays observed by the Reuven Ramaty High Energy Solar Spectroscopic Imager. The two sets of data show closely similar ribbon structures, strongly suggesting that the flare emissions in white light and in hard X-rays have physically linked emission mechanisms. While the source structure along the ribbons is resolved at both wavelengths (length ~ 30''), only the G-band observations resolve the width of the ribbon, with values between ~0farcs5 and ~1farcs8. The unresolved hard X-ray observations reveal an even narrower ribbon in hard X-rays (the main footpoint has a width perpendicular to the ribbon of <1farcs1 compared to the G-band width of ~1farcs8) suggesting that the hard X-ray emission comes from the sharp leading edge of the G-band ribbon. Applying the thick-target beam model, the derived energy deposition rate is >5 × 1012 erg s-1 cm-2 provided by an electron flux of 1 × 1020 electrons s-1 cm-2 above 18 keV. This requires that the beam density of electrons above 18 keV be at least 1 × 1010 cm-3. Even if field lines converge toward the chromospheric footpoints, the required beam in the corona has too high a density to be described as a dilute tail population on top of a Maxwellian core. We discuss this issue and others associated with this extreme event, which poses serious questions to the standard thick target beam interpretation of solar flares. |
BibTeX:
@article{KruckerHudsonJeffreyBattagliaKontarBenzCsillaghyLin2011,
author = {Krucker, Säm and Hudson, H. S. and Jeffrey, N. L. S. and Battaglia, M. and Kontar, E. P. and Benz, A. O. and Csillaghy, A. and Lin, R. P.},
title = {High-resolution Imaging of Solar Flare Ribbons and Its Implication on the Thick-target Beam Model},
journal = {The Astrophysical Journal},
year = {2011},
volume = {739},
pages = {96},
url = {http://adsabs.harvard.edu/abs/2011ApJ...739...96K}
}
|
| Krucker S, Kontar EP, Christe S, Glesener L and Lin RP (2011), "Electron Acceleration Associated with Solar Jets", The Astrophysical Journal. Vol. 742, pp. 82. |
| Abstract: This paper investigates the solar source region of supra-thermal (few keV up to the MeV range) electron beams observed near Earth by combining in situ measurements of the three-dimensional Plasma and Energetic Particles experiment on the WIND spacecraft with remote-sensing hard X-ray observations by the Reuven Ramaty High Energy Solar Spectroscopic Imager. The in situ observations are used to identify events, and the hard X-ray observations are then searched for signatures of supra-thermal electrons radiating bremsstrahlung emission in the solar atmosphere. Only prompt events detected above 50 keV with a close temporal correlation between the flare hard X-ray emission and the electrons seen near Earth are selected, limiting the number of events to 16. We show that for 7 of these 16 events, hard X-ray imaging shows three chromospheric sources: two at the footpoints of the post-flare loop and one related to an apparently open field line. The remaining events show two footpoints (seven events, four of which show elongated sources possibly hiding a third source) or are spatially unresolved (two events). Out of the 16 events, 6 have a solar source region within the field of view of the Transition Region and Corona Explorer (TRACE). All events with TRACE data show EUV jets that have the same onset as the hard X-ray emission (within the cadence of tens of seconds). After the hard X-ray burst ends, the jets decay. These results suggest that escaping prompt supra-thermal electron events observed near Earth are accelerated in flares associated with reconnection between open and closed magnetic field lines, the so-called interchange reconnection scenario. |
BibTeX:
@article{KruckerKontarChristeGlesenerLin2011,
author = {Krucker, Säm and Kontar, E. P. and Christe, S. and Glesener, L. and Lin, R. P.},
title = {Electron Acceleration Associated with Solar Jets},
journal = {The Astrophysical Journal},
year = {2011},
volume = {742},
pages = {82},
url = {http://adsabs.harvard.edu/abs/2011ApJ...742...82K}
}
|
| Reid HAS, Vilmer N and Kontar EP (2011), "Characteristics of the flare acceleration region derived from simultaneous hard X-ray and radio observations", Astronomy and Astrophysics. Vol. 529, pp. 66. |
| Abstract: We investigate the type III radio bursts and X-ray signatures of accelerated electrons in a well-observed solar flare in order to find the spatial properties of the acceleration region. Combining simultaneous RHESSI hard X-ray flare data and radio data from Phoenix-2 and the Nançay radioheliograph, the outward transport of flare accelerated electrons is analysed. The observations show that the starting frequencies of type III bursts are anti-correlated with the HXR spectral index of solar flare accelerated electrons. We demonstrate both analytically and numerically that the type III burst starting location is dependent upon the accelerated electron spectral index and the spatial acceleration region size, but weakly dependent on the density of energetic electrons for relatively intense electron beams. Using this relationship and the observed anti-correlation, we estimate the height and vertical extent of the acceleration region, giving values of around 50 Mm and 10 Mm, respectively. The inferred acceleration height and size suggest that electrons are accelerated well above the soft X-ray loop-top, which could be consistent with the electron acceleration between 40 Mm and 60 Mm above the flaring loop. |
BibTeX:
@article{ReidVilmerKontar2011,
author = {Reid, H. A. S. and Vilmer, N. and Kontar, E. P.},
title = {Characteristics of the flare acceleration region derived from simultaneous hard X-ray and radio observations},
journal = {Astronomy and Astrophysics},
year = {2011},
volume = {529},
pages = {66},
url = {http://adsabs.harvard.edu/abs/2011A%26A...529A..66R}
}
|
| Zharkova VV, Arzner K, Benz AO, Browning P, Dauphin C, Emslie AG, Fletcher L, Kontar EP, Mann G, Onofri M, Petrosian V, Turkmani R, Vilmer N and Vlahos L (2011), "Recent Advances in Understanding Particle Acceleration Processes in Solar Flares", Space Science Reviews. Vol. 159, pp. 357-420. |
| Abstract: We review basic theoretical concepts in particle acceleration, with particular emphasis on processes likely to occur in regions of magnetic reconnection. Several new developments are discussed, including detailed studies of reconnection in three-dimensional magnetic field configurations (e.g., current sheets, collapsing traps, separatrix regions) and stochastic acceleration in a turbulent environment. Fluid, test-particle, and particle-in-cell approaches are used and results compared. While these studies show considerable promise in accounting for the various observational manifestations of solar flares, they are limited by a number of factors, mostly relating to available computational power. Not the least of these issues is the need to explicitly incorporate the electrodynamic feedback of the accelerated particles themselves on the environment in which they are accelerated. A brief prognosis for future advancement is offered. |
BibTeX:
@article{ZharkovaArznerBenzBrowningDauphinEmslieFletcherKontarMannOnofriPetrosianTurkmaniVilmerVlahos2011,
author = {Zharkova, V. V. and Arzner, K. and Benz, A. O. and Browning, P. and Dauphin, C. and Emslie, A. G. and Fletcher, L. and Kontar, E. P. and Mann, G. and Onofri, M. and Petrosian, V. and Turkmani, R. and Vilmer, N. and Vlahos, L.},
title = {Recent Advances in Understanding Particle Acceleration Processes in Solar Flares},
journal = {Space Science Reviews},
year = {2011},
volume = {159},
pages = {357--420},
url = {http://adsabs.harvard.edu/abs/2011SSRv..159..357Z}
}
|
| Bian NH and Kontar EP (2010), "A gyrofluid description of Alfvénic turbulence and its parallel electric field", Physics of Plasmas. Vol. 17, pp. 2308. |
| Abstract: Anisotropic Alfvénic fluctuations with k∥/k⊥<<1 remain at frequencies much smaller than the ion cyclotron frequency in the presence of a strong background magnetic field. Based on the simplest truncation of the electromagnetic gyrofluid equations in a homogeneous plasma, a model for the energy cascade produced by Alfvénic turbulence is constructed, which smoothly connects the large magnetohydrodynamics scales and the small ``kinetic'' scales. Scaling relations are obtained for the electromagnetic fluctuations, as a function of k⊥ and k∥. Moreover, a particular attention is paid to the spectral structure of the parallel electric field which is produced by Alfvénic turbulence. The reason is the potential implication of this parallel electric field in turbulent acceleration and transport of particles. For electromagnetic turbulence, this issue was raised some time ago in Hasegawa and Mima [J. Geophys. Res. 83, 1117 (1978)]. |
BibTeX:
@article{BianKontar2010,
author = {Bian, N. H. and Kontar, E. P.},
title = {A gyrofluid description of Alfvénic turbulence and its parallel electric field},
journal = {Physics of Plasmas},
year = {2010},
volume = {17},
pages = {2308},
url = {http://adsabs.harvard.edu/abs/2010PhPl...17f2308B}
}
|
| Bian NH, Kontar EP and Brown JC (2010), "Parallel electric field generation by Alfvén wave turbulence", Astronomy and Astrophysics. Vol. 519, pp. 114. |
| Abstract: Aims: This work aims to investigate the spectral structure of the parallel electric field generated by strong anisotropic and balanced Alfvénic turbulence in relation with the problem of electron acceleration from the thermal population in solar flare plasma conditions. Methods: We consider anisotropic Alfvénic fluctuations in the presence of a strong background magnetic field. Exploiting this anisotropy, a set of reduced equations governing non-linear, two-fluid plasma dynamics is derived. The low-β limit of this model is used to follow the turbulent cascade of the energy resulting from the non-linear interaction between kinetic Alfvén waves, from the large magnetohydrodynamics (MHD) scales with k⊥ρ_s≪1 down to the small “kinetic” scales with k⊥ρs ≫1, ρ_s being the ion sound gyroradius. Results: Scaling relations are obtained for the magnitude of the turbulent electromagnetic fluctuations, as a function of k⊥ and k∥, showing that the electric field develops a component parallel to the magnetic field at large MHD scales. Conclusions: The spectrum we derive for the parallel electric field fluctuations can be effectively used to model stochastic resonant acceleration and heating of electrons by Alfvén waves in solar flare plasma conditions |
BibTeX:
@article{BianKontarBrown2010,
author = {Bian, N. H. and Kontar, E. P. and Brown, J. C.},
title = {Parallel electric field generation by Alfvén wave turbulence},
journal = {Astronomy and Astrophysics},
year = {2010},
volume = {519},
pages = {114},
url = {http://adsabs.harvard.edu/abs/2010A%26A...519A.114B}
}
|
| Fleishman GD and Kontar EP (2010), "Sub-Thz Radiation Mechanisms in Solar Flares", The Astrophysical Journal Letters. Vol. 709, pp. L127-L132. |
| Abstract: Observations in the sub-THz range of large solar flares have revealed a mysterious spectral component increasing with frequency and hence distinct from the microwave component commonly accepted to be produced by gyrosynchrotron (GS) emission from accelerated electrons. Evidently, having a distinct sub-THz component requires either a distinct emission mechanism (compared to the GS one), or different properties of electrons and location, or both. We find, however, that the list of possible emission mechanisms is incomplete. This Letter proposes a more complete list of emission mechanisms, capable of producing a sub-THz component, both well known and new in this context, and calculates a representative set of their spectra produced by (1) free-free emission, (2) GS emission, (3) synchrotron emission from relativistic positrons/electrons, (4) diffusive radiation, and (5) Cherenkov emission. We discuss the possible role of the mechanisms in forming the sub-THz emission and emphasize their diagnostics potential for flares. |
BibTeX:
@article{FleishmanKontar2010,
author = {Fleishman, Gregory D. and Kontar, Eduard P.},
title = {Sub-Thz Radiation Mechanisms in Solar Flares},
journal = {The Astrophysical Journal Letters},
year = {2010},
volume = {709},
pages = {L127-L132},
url = {http://adsabs.harvard.edu/abs/2010ApJ...709L.127F}
}
|
| Kontar EP, Hannah IG, Jeffrey NLS and Battaglia M (2010), "The Sub-arcsecond Hard X-ray Structure of Loop Footpoints in a Solar Flare", The Astrophysical Journal. Vol. 717, pp. 250-256. |
| Abstract: The newly developed X-ray visibility forward fitting technique is applied to the RHESSI data of a limb flare to investigate the energy and height dependence on sizes, shapes, and position of hard X-ray (HXR) chromospheric footpoint sources. This provides information about the electron transport and chromospheric density structure. The spatial distribution of two footpoint X-ray sources is analyzed using PIXON, Maximum Entropy Method, CLEAN, and visibility forward fit algorithms at nonthermal energies from ~20 to ~200 keV. We report, for the first time, the vertical extents and widths of HXR chromospheric sources measured as a function of energy for a limb event. Our observations suggest that both the vertical and horizontal sizes of footpoints are decreasing with energy. Higher energy emission originates progressively deeper in the chromosphere, consistent with downward flare accelerated streaming electrons. The ellipticity of the footpoints grows with energy from ~0.5 at ~20 keV to ~0.9 at ~150 keV. The positions of X-ray emission are in agreement with an exponential density profile of scale height ~150 km. The characteristic size of the HXR footpoint source along the limb decreases with energy, suggesting a converging magnetic field in the footpoint. The vertical sizes of X-ray sources are inconsistent with simple collisional transport in a single density scale height but can be explained using a multi-threaded density structure in the chromosphere. |
BibTeX:
@article{KontarHannahJeffreyBattaglia2010,
author = {Kontar, E. P. and Hannah, I. G. and Jeffrey, N. L. S. and Battaglia, M.},
title = {The Sub-arcsecond Hard X-ray Structure of Loop Footpoints in a Solar Flare},
journal = {The Astrophysical Journal},
year = {2010},
volume = {717},
pages = {250--256},
url = {http://adsabs.harvard.edu/abs/2010ApJ...717..250K}
}
|
| Kontar EP and Jeffrey NLS (2010), "Positions and sizes of X-ray solar flare sources", Astronomy and Astrophysics. Vol. 513, pp. L2. |
| Abstract: Aims: The positions and source sizes of X-ray sources taking into account Compton backscattering (albedo) are investigated. Methods: Using a Monte Carlo simulation of X-ray photon transport including photo-electric absorption and Compton scattering, we calculate the apparent source sizes and positions of X-ray sources at the solar disk for various source sizes, spectral indices and directivities of the primary source. Results: We show that the albedo effect can alter the true source positions and substantially increase the measured source sizes. The source positions are shifted by up to ~0.5” radially towards the disk centre and 5 arcsec source sizes can be two times larger even for an isotropic source (minimum albedo effect) at 1 Mm above the photosphere. The X-ray sources therefore should have minimum observed sizes, and thus their FWHM source size (2.35 times second-moment) will be as large as ~7” in the 20-50 keV range for a disk-centered point source at a height of 1 Mm (~1.4”) above the photosphere. The source size and position change is greater for flatter primary X-ray spectra, a stronger downward anisotropy, for sources closer to the solar disk centre, and between the energies of 30 and 50 keV. Conclusions: Albedo should be taken into account when X-ray footpoint positions, footpoint motions or source sizes from e.g. RHESSI or Yohkoh data are interpreted, and we suggest that footpoint sources should be larger in X-rays than in either optical or EUV ranges. |
BibTeX:
@article{KontarJeffrey2010,
author = {Kontar, E. P. and Jeffrey, N. L. S.},
title = {Positions and sizes of X-ray solar flare sources},
journal = {Astronomy and Astrophysics},
year = {2010},
volume = {513},
pages = {L2},
url = {http://adsabs.harvard.edu/abs/2010A%26A...513L...2K}
}
|
| Reid HAS and Kontar EP (2010), "Solar Wind Density Turbulence and Solar Flare Electron Transport from the Sun to the Earth", The Astrophysical Journal. Vol. 721, pp. 864-874. |
| Abstract: Solar flare accelerated electron beams propagating away from the Sun can interact with the turbulent interplanetary media, producing plasma waves and Type III radio emission. These electron beams are detected near the Earth with a double power-law energy spectrum. We simulate electron beam propagation from the Sun to the Earth in the weak turbulent regime taking into account the self-consistent generation of plasma waves and subsequent wave interaction with density fluctuations from low-frequency MHD turbulence. The rate at which plasma waves are induced by an unstable electron beam is reduced by background density fluctuations, most acutely when fluctuations have large amplitudes or small wavelengths. This suppression of plasma waves alters the wave distribution which changes the electron beam transport. Assuming a 5/3 Kolmogorov-type power-density spectrum of fluctuations often observed near the Earth, we investigate the corresponding energy spectrum of the electron beam after it has propagated 1 AU. We find a direct correlation between the spectrum of the double power-law below the break energy and the turbulent intensity of the background plasma. For an initial spectral index of 3.5, we find a range of spectra below the break energy between 1.6 and 2.1, with higher levels of turbulence corresponding to higher spectral indices. |
BibTeX:
@article{ReidKontar2010,
author = {Reid, Hamish A. S. and Kontar, Eduard P.},
title = {Solar Wind Density Turbulence and Solar Flare Electron Transport from the Sun to the Earth},
journal = {The Astrophysical Journal},
year = {2010},
volume = {721},
pages = {864--874},
url = {http://adsabs.harvard.edu/abs/2010ApJ...721..864R}
}
|
| Temmer M, Veronig AM, Kontar EP, Krucker S and Vršnak B (2010), "Combined STEREO/RHESSI Study of Coronal Mass Ejection Acceleration and Particle Acceleration in Solar Flares", The Astrophysical Journal. Vol. 712, pp. 1410-1420. |
| Abstract: Using the potential of two unprecedented missions, Solar Terrestrial Relations Observatory (STEREO) and Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI), we study three well-observed fast coronal mass ejections (CMEs) that occurred close to the limb together with their associated high-energy flare emissions in terms of RHESSI hard X-ray (HXR) spectra and flux evolution. From STEREO/EUVI and STEREO/COR1 data, the full CME kinematics of the impulsive acceleration phase up to ~4 R sun is measured with a high time cadence of <=2.5 minutes. For deriving CME velocity and acceleration, we apply and test a new algorithm based on regularization methods. The CME maximum acceleration is achieved at heights h <= 0.4 R sun, and the peak velocity at h <= 2.1 R sun (in one case, as small as 0.5 R sun). We find that the CME acceleration profile and the flare energy release as evidenced in the RHESSI HXR flux evolve in a synchronized manner. These results support the "standard" flare/CME model which is characterized by a feedback relationship between the large-scale CME acceleration process and the energy release in the associated flare. |
BibTeX:
@article{TemmerVeronigKontarKruckerVrsnak2010,
author = {Temmer, M. and Veronig, A. M. and Kontar, E. P. and Krucker, S. and Vršnak, B.},
title = {Combined STEREO/RHESSI Study of Coronal Mass Ejection Acceleration and Particle Acceleration in Solar Flares},
journal = {The Astrophysical Journal},
year = {2010},
volume = {712},
pages = {1410--1420},
url = {http://adsabs.harvard.edu/abs/2010ApJ...712.1410T}
}
|
| Brown JC, Turkmani R, Kontar EP, MacKinnon AL and Vlahos L (2009), "Local re-acceleration and a modified thick target model of solar flare electrons", Astronomy and Astrophysics. Vol. 508, pp. 993-1000. |
| Abstract: Context: The collisional thick target model (CTTM) of solar hard X-ray (HXR) bursts has become an almost “standard model” of flare impulsive phase energy transport and radiation. However, it faces various problems in the light of recent data, particularly the high electron beam density and anisotropy it involves. Aims: We consider how photon yield per electron can be increased, and hence fast electron beam intensity requirements reduced, by local re-acceleration of fast electrons throughout the HXR source itself, after injection. due to e.g. waves or local current sheet electric (E) fields are a significant fraction of collisional loss rates, electron lifetimes, and hence the net radiative HXR output per electron can be substantially increased over the CTTM values. In this local re-acceleration thick target model (LRTTM) fast electron number requirements and anisotropy are thus reduced. One specific possible scenario involving such re-acceleration is discussed, viz, a current sheet cascade (CSC) in a randomly stressed magnetic loop. Results: Combined MHD and test particle simulations show that local E fields in CSCs can efficiently accelerate electrons in the corona and and re-accelerate them after injection into the chromosphere. In this HXR source scenario, rapid synchronisation and variability of impulsive footpoint emissions can still occur since primary electron acceleration is in the high Alfvén speed corona with fast re-acceleration in chromospheric CSCs. It is also consistent with the energy-dependent time-of-flight delays in HXR features. Conclusions: Including electron re-acceleration in the HXR source allows an LRTTM modification of the CTTM in which beam density and anisotropy are much reduced, and alleviates theoretical problems with the CTTM, while making it more compatible with radio and interplanetary electron numbers. The LRTTM is, however, different in some respects such as spatial distribution of atmospheric heating by fast electrons. |
BibTeX:
@article{BrownTurkmaniKontarMacKinnonVlahos2009,
author = {Brown, J. C. and Turkmani, R. and Kontar, E. P. and MacKinnon, A. L. and Vlahos, L.},
title = {Local re-acceleration and a modified thick target model of solar flare electrons},
journal = {Astronomy and Astrophysics},
year = {2009},
volume = {508},
pages = {993--1000},
url = {http://adsabs.harvard.edu/abs/2009A%26A...508..993B}
}
|
| Hannah IG, Kontar EP and Sirenko OK (2009), "The Effect of Wave-Particle Interactions on Low-Energy Cutoffs in Solar Flare Electron Spectra", The Astrophysical Journal Letters. Vol. 707, pp. L45-L50. |
| Abstract: Solar flare hard X-ray (HXR) spectra from Reuven Ramaty High Energy Solar Spectrometer (RHESSI) are normally interpreted in terms of purely collisional electron beam propagation, ignoring spatial evolution and collective effects. In this Letter, we present self-consistent numerical simulations of the spatial and temporal evolution of an electron beam subject to collisional transport and beam-driven Langmuir wave turbulence. These wave-particle interactions represent the background plasma's response to the electron beam propagating from the corona to chromosphere and occur on a far faster timescale than Coulomb collisions. From these simulations, we derive the mean electron flux spectrum, comparable to such spectra recovered from high-resolution HXRs observations of solar flares with RHESSI. We find that a negative spectral index (i.e., a spectrum that increases with energy), or local minima when including the expected thermal spectral component at low energies, occurs in the standard thick-target model, when Coulomb collisions are only considered. The inclusion of wave-particle interactions does not produce a local minimum, maintaining a positive spectral index. These simulations are a step toward a more complete treatment of electron transport in solar flares and suggest that a flat spectrum (spectral index of 0-1) down to thermal energies maybe a better approximation instead of a sharp cutoff in the injected electron spectrum. |
BibTeX:
@article{HannahKontarSirenko2009,
author = {Hannah, I. G. and Kontar, E. P. and Sirenko, O. K.},
title = {The Effect of Wave-Particle Interactions on Low-Energy Cutoffs in Solar Flare Electron Spectra},
journal = {The Astrophysical Journal Letters},
year = {2009},
volume = {707},
pages = {L45-L50},
url = {http://adsabs.harvard.edu/abs/2009ApJ...707L..45H}
}
|
| Kontar EP and Reid HAS (2009), "Onsets and Spectra of Impulsive Solar Energetic Electron Events Observed Near the Earth", The Astrophysical Journal Letters. Vol. 695, pp. L140-L144. |
| Abstract: Impulsive solar energetic electrons are often observed in the interplanetary space near the Earth and have an attractive diagnostic potential for poorly understood solar flare acceleration processes. We investigate the transport of solar flare energetic electrons in the heliospheric plasma to understand the role of transport to the observed onset and spectral properties of the impulsive solar electron events. The propagation of energetic electrons in solar wind plasma is simulated from the acceleration region at the Sun to the Earth, taking into account self-consistent generation and absorption of electrostatic electron plasma (Langmuir) waves, effects of nonuniform plasma, collisions, and Landau damping. The simulations suggest that the beam-driven plasma turbulence and the effects of solar wind density inhomogeneity play a crucial role and lead to the appearance of (1) a spectral break for a single power-law injected electron spectrum, with the spectrum flatter below the break, (2) apparent early onset of low-energy electron injection, and (3) the apparent late maximum of low-energy electron injection. We show that the observed onsets, spectral flattening at low energies, and formation of a break energy at tens of keV is the direct manifestation of wave-particle interactions in nonuniform plasma of a single accelerated electron population with an initial power-law spectrum. |
BibTeX:
@article{KontarReid2009,
author = {Kontar, Eduard P. and Reid, Hamish A. S.},
title = {Onsets and Spectra of Impulsive Solar Energetic Electron Events Observed Near the Earth},
journal = {The Astrophysical Journal Letters},
year = {2009},
volume = {695},
pages = {L140-L144},
url = {http://adsabs.harvard.edu/abs/2009ApJ...695L.140K}
}
|
| Massone AM, Emslie AG, Hurford GJ, Prato M, Kontar EP and Piana M (2009), "Hard X-ray Imaging of Solar Flares Using Interpolated Visibilities", The Astrophysical Journal. Vol. 703, pp. 2004-2016. |
| Abstract: RHESSI produces solar flare images with the finest angular and spectral resolutions ever achieved at hard X-ray energies. Because this instrument uses indirect, collimator-based imaging techniques, the "native" output of which is in the form of "visibilities" (two-dimensional spatial Fourier components of the image), the development and application of robust, accurate, visibility-based image reconstruction techniques is required. Recognizing that the density of spatial-frequency (u, v) coverage by RHESSI is much sparser than that normally encountered in radio astronomy, we therefore introduce a method for image reconstruction from a relatively sparse distribution of sampled visibilities. The method involves spline interpolation at spatial frequencies less than the largest sampled frequency and the imposition of a positivity constraint on the image to reduce the ringing effects resulting from an unconstrained Fourier transform inversion procedure. Using simulated images consisting both of assumed mathematical forms and of the type of structure typically associated with solar flares, we validate the fidelity, accuracy, and robustness with which the new procedure recovers input images. The method faithfully recovers both single and multiple sources, both compact and extended, over a dynamic range of ~10:1. The performance of the method, which we term as uv_smooth, is compared with other RHESSI image reconstruction algorithms currently in use and its advantages summarized. We also illustrate the application of the method using RHESSI observations of four solar flares. |
BibTeX:
@article{MassoneEmslieHurfordPratoKontarPiana2009,
author = {Massone, Anna Maria and Emslie, A. Gordon and Hurford, G. J. and Prato, Marco and Kontar, Eduard P. and Piana, Michele},
title = {Hard X-ray Imaging of Solar Flares Using Interpolated Visibilities},
journal = {The Astrophysical Journal},
year = {2009},
volume = {703},
pages = {2004--2016},
url = {http://adsabs.harvard.edu/abs/2009ApJ...703.2004M}
}
|
| Prato M, Emslie AG, Kontar EP, Massone AM and Piana M (2009), "The Location of Centroids in Photon and Electron Maps of Solar Flares", The Astrophysical Journal. Vol. 706, pp. 917-922. |
| Abstract: We explore the use of centroid coordinates as a means to identify the "locations" of electron-proton bremsstrahlung hard X-ray sources in solar flares. Differences between the coordinates of the electron and photon centroids are derived and explained. For electron propagation in a collision-dominated target, with either a uniform or an exponential density profile, the position of the electron centroid can be calculated analytically. We compare these analytic forms to data from a flare event on 2002 February 20. We first spectrally invert the native photon visibility data to obtain "electron visibilities," which are in turn used to construct electron flux images at various electron energies E. Centroids of these maps are then obtained by straightforward numerical integration over the electron maps. This comparison allows us to infer the density structure in the two compact sources visible, and we discuss the (somewhat unexpected) results thus obtained. |
BibTeX:
@article{PratoEmslieKontarMassonePiana2009,
author = {Prato, Marco and Emslie, A. Gordon and Kontar, Eduard P. and Massone, Anna Maria and Piana, Michele},
title = {The Location of Centroids in Photon and Electron Maps of Solar Flares},
journal = {The Astrophysical Journal},
year = {2009},
volume = {706},
pages = {917--922},
url = {http://adsabs.harvard.edu/abs/2009ApJ...706..917P}
}
|
| Kontar EP, Dickson E and Kašparová J (2008), "Low-Energy Cutoffs in Electron Spectra of Solar Flares: Statistical Survey", Solar Physics. Vol. 252, pp. 139-147. |
| Abstract: The Reuven Ramaty High Energy Spectroscopic Imager (RHESSI) X-ray data base (February 2002 May 2006) has been searched to find solar flares with weak thermal components and flat photon spectra. Using a regularized inversion technique, we determine the mean electron flux distribution from count spectra for a selection of events with flat photon spectra in the 15 20 keV energy range. Such spectral behavior is expected for photon spectra either affected by photospheric albedo or produced by electron spectra with an absence of electrons in a given energy range ( e.g., a low-energy cutoff in the mean electron spectra of nonthemal particles). We have found 18 cases that exhibit a statistically significant local minimum (a dip) in the range of 13 19 keV. The positions and spectral indices of events with low-energy cutoff indicate that such features are likely to be the result of photospheric albedo. It is shown that if the isotropic albedo correction is applied, all low-energy cutoffs in the mean electron spectrum are removed, and hence the low-energy cutoffs in the mean electron spectrum of solar flares above ˜ 12 keV cannot be viewed as real features. If low-energy cutoffs exist in the mean electron spectra, their energies should be less than ˜ 12 keV. |
BibTeX:
@article{KontarDicksonKasparova2008,
author = {Kontar, E. P. and Dickson, E. and Kašparová, J.},
title = {Low-Energy Cutoffs in Electron Spectra of Solar Flares: Statistical Survey},
journal = {Solar Physics},
year = {2008},
volume = {252},
pages = {139--147},
url = {http://adsabs.harvard.edu/abs/2008SoPh..252..139K}
}
|
| Kontar EP, Hannah IG and MacKinnon AL (2008), "Chromospheric magnetic field and density structure measurements using hard X-rays in a flaring coronal loop", Astronomy and Astrophysics. Vol. 489, pp. L57-L60. |
| Abstract: Aims: A novel method of using hard X-rays as a diagnostic for chromospheric density and magnetic structures is developed to infer sub-arcsecond vertical variation of magnetic flux tube size and neutral gas density. Methods: Using Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) X-ray data and the newly developed X-ray visibilities forward fitting technique we find the FWHM and centroid positions of hard X-ray sources with sub-arcsecond resolution (~0.2'') for a solar limb flare. We show that the height variations of the chromospheric density and the magnetic flux densities can be found with an unprecedented vertical resolution of ~150 km by mapping 18-250 keV X-ray emission of energetic electrons propagating in the loop at chromospheric heights of 400-1500 km. Results: Our observations suggest that the density of the neutral gas is in good agreement with hydrostatic models with a scale height of around 140 ± 30 km. FWHM sizes of the X-ray sources decrease with energy suggesting the expansion (fanning out) of magnetic flux tubes in the chromosphere with height. The magnetic scale height B(z)(dB/dz)-1 is found to be of the order of 300 km and a strong horizontal magnetic field is associated with noticeable flux tube expansion at a height of ~900 km. |
BibTeX:
@article{KontarHannahMacKinnon2008,
author = {Kontar, E. P. and Hannah, I. G. and MacKinnon, A. L.},
title = {Chromospheric magnetic field and density structure measurements using hard X-rays in a flaring coronal loop},
journal = {Astronomy and Astrophysics},
year = {2008},
volume = {489},
pages = {L57-L60},
url = {http://adsabs.harvard.edu/abs/2008A%26A...489L..57K}
}
|
| Prato M, Massone AM, Piana M, Emslie AG, Hurford GJ, Kontar EP and Schwartz RA (2008), "A visibility-based approach using regularization for imaging-spectroscopy in solar X-ray astronomy", Journal of Physics Conference Series. Vol. 135, pp. 2084. |
| Abstract: The Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI) is a nine-collimators satellite detecting X-rays and γ-rays emitted by the Sun during flares. As the spacecraft rotates, imaging information is encoded as rapid time-variations of the detected flux. We recently proposed a method for the construction of electron flux maps at different electron energies from sets of count visibilities (i.e., direct, calibrated measurements of specific Fourier components of the source spatial structure) measured by RHESSI. The method requires the application of regularized inversion for the synthesis of electron visibility spectra and of imaging techniques for the reconstruction of two-dimensional electron flux maps. The method, already tested on real events registered by RHESSI, is validated in this paper by means of simulated realistic data. |
BibTeX:
@article{PratoMassonePianaEmslieHurfordKontarSchwartz2008,
author = {Prato, M. and Massone, A. M. and Piana, M. and Emslie, A. G. and Hurford, G. J. and Kontar, E. P. and Schwartz, R. A.},
title = {A visibility-based approach using regularization for imaging-spectroscopy in solar X-ray astronomy},
journal = {Journal of Physics Conference Series},
year = {2008},
volume = {135},
pages = {2084},
url = {http://adsabs.harvard.edu/abs/2008JPhCS.135a2084P}
}
|
| Sullivan JM, Lockwood M, Lanchester BS, Kontar EP, Ivchenko N, Dahlgren H and Whiter DK (2008), "An optical study of multiple NEIAL events driven by low energy electron precipitation", Annales Geophysicae. Vol. 26, pp. 2435. |
| Abstract: Optical data are compared with EISCAT radar observations of multiple Naturally Enhanced Ion-Acoustic Line (NEIAL) events in the dayside cusp. This study uses narrow field of view cameras to observe small-scale, short-lived auroral features. Using multiple-wavelength optical observations, a direct link between NEIAL occurrences and low energy (about 100 eV) optical emissions is shown. This is consistent with the Langmuir wave decay interpretation of NEIALs being driven by streams of low-energy electrons. Modelling work connected with this study shows that, for the measured ionospheric conditions and precipitation characteristics, growth of unstable Langmuir (electron plasma) waves can occur, which decay into ion-acoustic wave modes. The link with low energy optical emissions shown here, will enable future studies of the shape, extent, lifetime, grouping and motions of NEIALs. |
BibTeX:
@article{SullivanLockwoodLanchesterKontarIvchenkoDahlgrenWhiter2008,
author = {Sullivan, J. M. and Lockwood, M. and Lanchester, B. S. and Kontar, E. P. and Ivchenko, N. and Dahlgren, H. and Whiter, D. K.},
title = {An optical study of multiple NEIAL events driven by low energy electron precipitation},
journal = {Annales Geophysicae},
year = {2008},
volume = {26},
pages = {2435},
url = {http://adsabs.harvard.edu/abs/2008AnGeo..26.2435S}
}
|
| Brown JC, Kontar EP, Veronig AM and MacKinnon AL (2007), "RHESSI Results Time for a Rethink?", In Lecture Notes in Physics, Berlin Springer Verlag. Vol. 725, pp. 65. |
| Abstract: Hard X-rays and γ-rays are the most direct signatures of energetic electrons and ions in the sun’s atmosphere which is optically thin at these energies and their radiation involves no coherent processes. Being collisional they are complementary to gyro-radiation in probing atmospheric density as opposed to magnetic field and the electrons are primarily 10 100~keV in energy, complementing the (>100 keV) electrons likely responsible for microwave bursts. The pioneering results of the Ramaty High Energy Solar Spectroscopic Imager (RHESSI) are raising the first new major questions concerning solar energetic particles in many years. Some highlights of these results are discussed primarily around RHESSI topics on which the authors have had direct research involvement particularly when they are raising the need for re-thinking of entrenched ideas. Results and issues are broadly divided into discoveries in the spatial, temporal and spectral domains, with the main emphasis on flare hard X-rays/fast electrons but touching also on γ-rays/ions, non-flare emissions, and the relationship to radio bursts. |
BibTeX:
@inproceedings{BrownKontarVeronigMacKinnon2007,
author = {Brown, J. C. and Kontar, E. P. and Veronig, A. M. and MacKinnon, Alexander L.},
editor = {Klein, Karl-Ludwig},
title = {RHESSI Results Time for a Rethink?},
booktitle = {Lecture Notes in Physics, Berlin Springer Verlag},
year = {2007},
volume = {725},
pages = {65},
url = {http://adsabs.harvard.edu/abs/2007LNP...725...65B}
}
|
| Kašparová J, Kontar EP and Brown JC (2007), "Hard X-ray spectra and positions of solar flares observed by RHESSI: photospheric albedo, directivity and electron spectra", Astronomy and Astrophysics. Vol. 466, pp. 705-712. |
| Abstract: Aims:We investigate the signature of the photospheric albedo contribution in solar flare hard X-ray spectra, the effect of low energy cutoffs in electron spectra, and the directivity of hard X-ray emission. Methods: Using Ramaty High Energy Solar Spectroscopic Imager (RHESSI) flare data we perform a statistical analysis of spatially integrated spectra and positions of solar flares. Results: We demonstrate clear centre-to-limb variation of photon spectral indices in the 15-20 keV energy range and a weaker dependency in the 20-50 keV range which is consistent with photospheric albedo as the cause. The results also suggest that low-energy cutoffs sometimes inferred in mean electron spectra are an artefact of albedo. We also derive the anisotropy (ratio of downward/observer directed photons) of hard X-ray emission in the 15-20 keV range for various heliocentric angles. |
BibTeX:
@article{KasparovaKontarBrown2007,
author = {Kašparová, J. and Kontar, E. P. and Brown, J. C.},
title = {Hard X-ray spectra and positions of solar flares observed by RHESSI: photospheric albedo, directivity and electron spectra},
journal = {Astronomy and Astrophysics},
year = {2007},
volume = {466},
pages = {705--712},
url = {http://adsabs.harvard.edu/abs/2007A%26A...466..705K}
}
|
| Kontar EP, Emslie AG, Massone AM, Piana M, Brown JC and Prato M (2007), "Electron-Electron Bremsstrahlung Emission and the Inference of Electron Flux Spectra in Solar Flares", The Astrophysical Journal. Vol. 670, pp. 857-861. |
| Abstract: Although both electron-ion and electron-electron bremsstrahlung contribute to the hard X-ray emission from solar flares, the latter is normally ignored. Such an omission is not justified at electron (and photon) energies above ~300 keV, and inclusion of the additional electron-electron bremsstrahlung in general makes the electron spectrum required to produce a given hard X-ray spectrum steeper at high energies. Unlike electron-ion bremsstrahlung, electron-electron bremsstrahlung cannot produce photons of all energies up to the electron energy involved. The maximum possible photon energy depends on the angle between the direction of the emitting electron and the emitted photon, and this suggests a diagnostic for an upper cutoff energy and/or for the degree of beaming of the accelerated electrons. We analyze the large event of 2005 January 17 and show that the upward break around 400 keV in the observed hard X-ray spectrum is naturally accounted for by the inclusion of electron-electron bremsstrahlung. Indeed, the mean source electron spectrum recovered through a regularized inversion of the hard X-ray spectrum, using a cross section that includes both electron-ion and electron-electron terms, has a relatively constant spectral index δ over the range from electron kinetic energy E=200 keV to E=1 MeV. Such a spectrum is indicative of an acceleration mechanism without a characteristic energy or corresponding scale. |
BibTeX:
@article{KontarEmslieMassonePianaBrownPrato2007,
author = {Kontar, Eduard P. and Emslie, A. Gordon and Massone, Anna Maria and Piana, Michele and Brown, John C. and Prato, Marco},
title = {Electron-Electron Bremsstrahlung Emission and the Inference of Electron Flux Spectra in Solar Flares},
journal = {The Astrophysical Journal},
year = {2007},
volume = {670},
pages = {857--861},
url = {http://adsabs.harvard.edu/abs/2007ApJ...670..857K}
}
|
| Krucker S, Kontar EP, Christe S and Lin RP (2007), "Solar Flare Electron Spectra at the Sun and near the Earth", The Astrophysical Journal Letters. Vol. 663, pp. L109-L112. |
| Abstract: We compare hard X-ray (HXR) photon spectra observed by the RHESSI with the spectra of the electrons in the associated solar impulsive particle events observed near 1 AU by the WIND 3D Plasma and Energetic Particle (3DP) instrument. For prompt events, where the inferred injection time at the Sun coincides with the HXR burst, the HXR photon power-law spectral index γ and the in situ observed electron spectral index δ measured above 50 keV show a good linear fit, δ=γ+0.1(+/-0.1), with correlation coefficient of 0.83, while for delayed events (inferred injection >10 minutes after the HXR burst) only a weak correlation with a coefficient of 0.43 is seen. The observed relationship for prompt events is inconsistent, however, with both the thin target case, where the escaping electrons come from the X-ray-producing electron population, and the thick target case where some of the accelerated source population escapes to 1 AU and the rest produce the HXRs while losing all their energy to collisions. Furthermore, the derived total number of escaping electrons correlates with the number of electrons required to produce observed X-ray flux but is only about ~0.2% of the number of HXR-producing electrons. |
BibTeX:
@article{KruckerKontarChristeLin2007,
author = {Krucker, Säm and Kontar, E. P. and Christe, S. and Lin, R. P.},
title = {Solar Flare Electron Spectra at the Sun and near the Earth},
journal = {The Astrophysical Journal Letters},
year = {2007},
volume = {663},
pages = {L109-L112},
url = {http://adsabs.harvard.edu/abs/2007ApJ...663L.109K}
}
|
| Piana M, Massone AM, Hurford GJ, Prato M, Emslie AG, Kontar EP and Schwartz RA (2007), "Electron Flux Spectral Imaging of Solar Flares through Regularized Analysis of Hard X-Ray Source Visibilities", The Astrophysical Journal. Vol. 665, pp. 846-855. |
| Abstract: We introduce a new method for imaging spectroscopy analysis of hard X-ray emission during solar flares. The method avoids the ``traditional'' noise-sensitive step of stacking independent images made in different count-based energy intervals. Rather, it involves regularized inversion of the count visibility spectra (i.e., the two-dimensional spatial Fourier transforms of the spectral image) to obtain smoothed (regularized) forms of the corresponding electron visibility spectra. Application of conventional visibility-based imaging algorithms then yields images of the electron flux that vary smoothly with energy. We apply the method to a solar flare observed on 2002 February 20 by the RHESSI instrument. The event is characterized by two bright footpoints with a more diffuse emission between them. Analysis of the regularized electron flux images reveals that the electron flux spectra at the footpoints are systematically harder than those in the region between the footpoints and that the observed degree of hardening is consistent with that produced by Coulomb collisions between an acceleration site high in the corona and the dense chromospheric footpoint regions. |
BibTeX:
@article{PianaMassoneHurfordPratoEmslieKontarSchwartz2007,
author = {Piana, Michele and Massone, Anna Maria and Hurford, G. J. and Prato, Marco and Emslie, A. Gordon and Kontar, Eduard P. and Schwartz, Richard A.},
title = {Electron Flux Spectral Imaging of Solar Flares through Regularized Analysis of Hard X-Ray Source Visibilities},
journal = {The Astrophysical Journal},
year = {2007},
volume = {665},
pages = {846--855},
url = {http://adsabs.harvard.edu/abs/2007ApJ...665..846P}
}
|
| Brown JC, Emslie AG, Holman GD, Johns-Krull CM, Kontar EP, Lin RP, Massone AM and Piana M (2006), "Evaluation of Algorithms for Reconstructing Electron Spectra from Their Bremsstrahlung Hard X-Ray Spectra", The Astrophysical Journal. Vol. 643, pp. 523-531. |
| Abstract: The Ramaty High Energy Solar Spectroscopic Imager (RHESSI) has yielded solar flare hard X-ray spectra with unprecedented resolution, enabling reconstruction of mean source electron energy spectra F(E) by deconvolution of photon energy spectra I(ɛ). While various algorithms have been proposed, the strengths and weaknesses of each have yet to be explored in a systematic fashion. For real data F(E) is unknown, so these various algorithms must instead be tested on simulated data for which the ``true'' F(E) is known. Accordingly, we devised several forms of F(E) with ``interesting'' features, generated the corresponding (noise-added) I(ɛ), and recovered F(E) using a variety of algorithms, including zero- and first-order Tikhonov regularizations, triangular matrix row elimination, and forward fitting using a parametric form consisting of a double power law with low/high cutoffs plus an isothermal component. All inversion methods reconstructed the general magnitude and form of F(E) well, suffering only from (1) blurring of sharp features and (2) poor recovery at low electron energies E in cases in which F'(E) was positive and large. Addition of a steep thermal component at low E did not prevent recovery of features at higher values of E. Forward fitting did recover large-scale forms and features well but, inevitably, failed to recover local features not expressible within the parametric used. This confirms that inversions are the most dependable way to discover such features. However, examination of the pattern of I(ɛ) residuals can suggest feature locations and so help refine the parametric form used. Since quite smooth F(E) forms do reproduce the observed I(ɛ) form with relatively small residuals, it appears that sharp features may be uncommon in actual flares. |
BibTeX:
@article{BrownEmslieHolmanJohns-KrullKontarLinMassonePiana2006,
author = {Brown, John C. and Emslie, A. Gordon and Holman, Gordon D. and Johns-Krull, Christopher M. and Kontar, Eduard P. and Lin, Robert P. and Massone, Anna Maria and Piana, Michele},
title = {Evaluation of Algorithms for Reconstructing Electron Spectra from Their Bremsstrahlung Hard X-Ray Spectra},
journal = {The Astrophysical Journal},
year = {2006},
volume = {643},
pages = {523--531},
url = {http://adsabs.harvard.edu/abs/2006ApJ...643..523B}
}
|
| Kontar EP and Brown JC (2006), "Stereoscopic Electron Spectroscopy of Solar Hard X-Ray Flares with a Single Spacecraft", The Astrophysical Journal Letters. Vol. 653, pp. L149-L152. |
| Abstract: Hard X-ray (HXR) spectroscopy is the most direct method of diagnosing energetic electrons in solar flares. Here we present a technique that allows us to use a single HXR spectrum to determine an effectively stereoscopic electron energy distribution. Considering the Sun's surface to act as a ``Compton mirror'' allows us to look at emitting electrons also from behind the source, providing vital information on downward-propagating particles. Using this technique we determine simultaneously the electron spectra of downward- and upward-directed electrons for two solar flares observed by the Ramaty High Energy Solar Spectroscopic Imager (RHESSI). The results reveal surprisingly near-isotropic electron distributions, which contrast strongly with the expectations from the standard model that invokes strong downward beaming, including a collisional thick-target model. |
BibTeX:
@article{KontarBrown2006,
author = {Kontar, Eduard P. and Brown, John C.},
title = {Stereoscopic Electron Spectroscopy of Solar Hard X-Ray Flares with a Single Spacecraft},
journal = {The Astrophysical Journal Letters},
year = {2006},
volume = {653},
pages = {L149-L152},
url = {http://adsabs.harvard.edu/abs/2006ApJ...653L.149K}
}
|
| Kontar EP and Brown JC (2006), "Solar flare hard X-ray spectra possibly inconsistent with the collisional thick target model", Advances in Space Research. Vol. 38, pp. 945-950. |
| Abstract: Recent progress in solar hard X-ray (HXR) observations with RHESSI data and methods for spectral inversion allow us to study model-independent mean electron flux spectra in solar flares. We report several hard X-ray events observed by RHESSI in which the photon spectra I(γ) are such that the inferred source mean electron spectra are not consistent with the standard model of collisional transport in solar flares. The observed photon spectra are so flat locally that the recovered mean electron flux spectra show a dip around 17 31 keV. While we note that alternative explanations, unrelated to electron transport, have not been ruled out, we focus on the physical implications of this tentative result for the collisional thick target model. |
BibTeX:
@article{KontarBrown2006a,
author = {Kontar, Eduard P. and Brown, John C.},
title = {Solar flare hard X-ray spectra possibly inconsistent with the collisional thick target model},
journal = {Advances in Space Research},
year = {2006},
volume = {38},
pages = {945--950},
url = {http://adsabs.harvard.edu/abs/2006AdSpR..38..945K}
}
|
| Kontar EP, MacKinnon AL, Schwartz RA and Brown JC (2006), "Compton backscattered and primary X-rays from solar flares: angle dependent Green's function correction for photospheric albedo", Astronomy and Astrophysics. Vol. 446, pp. 1157-1163. |
| Abstract: The observed hard X-ray (HXR) flux spectrum I(ɛ) from solar flares is a combination of primary bremsstrahlung photons I_P(ɛ) with a spectrally modified component from photospheric Compton backscatter of downward primary emission. The latter can be significant, distorting or hiding the true features of the primary spectrum which are key diagnostics for acceleration and propagation of high energy electrons and of their energy budget. For the first time in solar physics, we use a Green's function approach to the backscatter spectral deconvolution problem, constructing a Green's matrix including photoelectric absorption. This approach allows spectrum-independent extraction of the primary spectrum for several HXR flares observed by the Ramaty High Energy Solar Spectroscopic Imager (RHESSI). We show that the observed and primary spectra differ very substantially for flares with hard spectra close to the disk centre. We show in particular that the energy dependent photon spectral index γ (ɛ)=-d log I/d log ɛ is very different for I_P(ɛ) and for I(ɛ) and that inferred mean source electron spectra F(E) differ greatly. Even for a forward fitting of a parametric F(E) to the data, a clear low-energy cutoff required to fit I(ɛ) essentially disappears when the fit is to I_P(ɛ) - i.e. when albedo correction is included. The self-consistent correction for backscattered photons is thus shown to be crucial in determining the energy spectra of flare accelerated electrons, and hence their total number and energy. |
BibTeX:
@article{KontarMacKinnonSchwartzBrown2006,
author = {Kontar, E. P. and MacKinnon, A. L. and Schwartz, R. A. and Brown, J. C.},
title = {Compton backscattered and primary X-rays from solar flares: angle dependent Green's function correction for photospheric albedo},
journal = {Astronomy and Astrophysics},
year = {2006},
volume = {446},
pages = {1157--1163},
url = {http://adsabs.harvard.edu/abs/2006A%26A...446.1157K}
}
|
| Prato M, Piana M, Brown JC, Emslie AG, Kontar EP and Massone AM (2006), "Regularized Reconstruction of the Differential Emission Measure from Solar Flare Hard X-Ray Spectra", Solar Physics. Vol. 237, pp. 61-83. |
| Abstract: We address the problem of how to test whether an observed solar hard X-ray bremsstrahlung spectrum ( I(ɛ)) is consistent with a purely thermal (locally Maxwellian) distribution of source electrons, and, if so, how to reconstruct the corresponding differential emission measure (ξ( T)). Unlike previous analysis based on the Kramers and Bethe-Heitler approximations to the bremsstrahlung cross-section, here we use an exact (solid-angle-averaged) cross-section. We show that the problem of determining ξ( T) from measurements of I(ɛ) invOlves two successive inverse problems: the first, to recover the mean source-electron flux spectrum (overlineF( E)) from I(ɛ) and the second, to recover ξ( T) from overlineF( E). We discuss the highly pathological numerical properties of this second problem within the framework of the regularization theory for linear inverse problems. In particular, we show that an iterative scheme with a positivity constraint is effective in recovering δ-like forms of ξ( T) while first-order Tikhonov regularization with boundary conditions works well in the case of power-law-like forms. Therefore, we introduce a restoration approach whereby the low-energy part of overlineF ( E), dominated by the thermal component, is inverted by using the iterative algorithm with positivity, while the high-energy part, dominated by the power-law component, is inverted by using first-order regularization. This approach is first tested by using simulated overlineF( E) derived from a priori known forms of ξ( T) and then applied to hard X-ray spectral data from the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). |
BibTeX:
@article{PratoPianaBrownEmslieKontarMassone2006,
author = {Prato, M. and Piana, M. and Brown, J. C. and Emslie, A. G. and Kontar, E. P. and Massone, A. M.},
title = {Regularized Reconstruction of the Differential Emission Measure from Solar Flare Hard X-Ray Spectra},
journal = {Solar Physics},
year = {2006},
volume = {237},
pages = {61--83},
url = {http://adsabs.harvard.edu/abs/2006SoPh..237...61P}
}
|
| Brown JC and Kontar EP (2005), "Problems and progress in flare fast particle diagnostics", Advances in Space Research. Vol. 35, pp. 1675-1682. |
| Abstract: Recent progress in the diagnosis of flare fast particles is critically discussed with the main emphasis on high resolution hard X-ray (HXR) data from RHESSI and coordinated data from other instruments. Spectacular new photon data findings are highlighted as are advances in theoretical aspects of their use as fast particle diagnostics, and some important comparisons made with interplanetary particle data. More specifically the following topics are addressed:RHESSI data on HXR (electron) versus gamma-ray line (ion) source locations.RHESSI hard X-ray source spatial structure in relation to theoretical models and loop density structure.Energy budget of flare electrons and the Neupert effect.Spectral deconvolution methods including blind target testing and results for RHESSI HXR spectra, including the reality and implications of dips inferred in electron spectra.The relation between flare in situ and interplanetary particle data. |
BibTeX:
@article{BrownKontar2005,
author = {Brown, John C. and Kontar, Eduard P.},
title = {Problems and progress in flare fast particle diagnostics},
journal = {Advances in Space Research},
year = {2005},
volume = {35},
pages = {1675--1682},
url = {http://adsabs.harvard.edu/abs/2005AdSpR..35.1675B}
}
|
| Galloway RK, MacKinnon AL, Kontar EP and Helander P (2005), "Fast electron slowing-down and diffusion in a high temperature coronal X-ray source", Astronomy and Astrophysics. Vol. 438, pp. 1107-1114. |
| Abstract: Finite thermal velocity modifications to electron slowing-down rates may be important for the deduction of solar flare total electron energy. Here we treat both slowing-down and velocity diffusion of electrons in the corona at flare temperatures, for the case of a simple, spatially homogeneous source. Including velocity diffusion yields a consistent treatment of both “accelerated” and “thermal” electrons. It also emphasises that one may not invoke finite thermal velocity target effects on electron lifetimes without simultaneously treating the contribution to the observed X-ray spectrum from thermal electrons. We present model calculations of the X-ray spectra resulting from injection of a power-law energy distribution of electrons into a source with finite temperature. Reducing the power-law distribution low-energy cutoff to lower and lower energies only increases the relative magnitude of the |
BibTeX:
@article{GallowayMacKinnonKontarHelander2005,
author = {Galloway, R. K. and MacKinnon, A. L. and Kontar, E. P. and Helander, P.},
title = {Fast electron slowing-down and diffusion in a high temperature coronal X-ray source},
journal = {Astronomy and Astrophysics},
year = {2005},
volume = {438},
pages = {1107--1114},
url = {http://adsabs.harvard.edu/abs/2005A%26A...438.1107G}
}
|
| Kašparová J, Karlický M, Kontar EP, Schwartz RA and Dennis BR (2005), "Multi-Wavelength Analysis of High-Energy Electrons in Solar Flares: A Case Study of the August 20, 2002 Flare", Solar Physics. Vol. 232, pp. 63-86. |
| Abstract: A multi-wavelength spatial and temporal analysis of solar high-energy electrons is conducted using the August 20, 2002 flare of an unusually flat (γ1 = 1.8) hard X-ray spectrum. The flare is studied using RHESSI, Hα, radio, TRACE, and MDI observations with advanced methods and techniques never previously applied in the solar flare context. A new method to account for X-ray Compton backscattering in the photosphere (photospheric albedo) has been used to deduce the primary X-ray flare spectra. The mean electron flux distribution has been analysed using both forward fitting and model-independent inversion methods of spectral analysis. We show that the contribution of the photospheric albedo to the photon spectrum modifies the calculated mean electron flux distribution, mainly at energies below ˜100 keV. The positions of the Hα emission and hard X-ray sources with respect to the current-free extrapolation of the MDI photospheric magnetic field and the characteristics of the radio emission provide evidence of the closed geometry of the magnetic field structure and the flare process in low altitude magnetic loops. In agreement with the predictions of some solar flare models, the hard X-ray sources are located on the external edges of the Hα emission and show chromospheric plasma heated by the non-thermal electrons. The fast changes of Hα intensities are located not only inside the hard X-ray sources, as expected if they are the signatures of the chromospheric response to the electron bombardment, but also away from them. |
BibTeX:
@article{KasparovaKarlickyKontarSchwartzDennis2005,
author = {Kašparová, Jana and Karlický, Marian and Kontar, Eduard P. and Schwartz, Richard A. and Dennis, Brian R.},
title = {Multi-Wavelength Analysis of High-Energy Electrons in Solar Flares: A Case Study of the August 20, 2002 Flare},
journal = {Solar Physics},
year = {2005},
volume = {232},
pages = {63--86},
url = {http://adsabs.harvard.edu/abs/2005SoPh..232...63K}
}
|
| Kontar EP, Emslie AG, Piana M, Massone AM and Brown JC (2005), "Determination of Electron Flux Spectra in a Solar Flare with an Augmented Regularization Method: Application to Rhessi Data", Solar Physics. Vol. 226, pp. 317-325. |
| Abstract: Kontar et al. (2004) have shown how to recover mean source electron spectra bar F(E) in solar flares through a physical constraint regularization analysis of the bremsstrahlung photon spectra I(ɛ) that they produce. They emphasize the use of non-square inversion techniques, and preconditioning combined with physical properties of the spectra to achieve the most meaningful solution to the problem. Higher-order regularization techniques may be used to generate bar F(E) forms with certain desirable properties (e.g., higher-order derivatives). They further note that such analysis may be used to infer properties of the electron energy spectra at energies well above the maximum photon energy observed. In this paper we apply these techniques to data from a solar flare observed by RHESSI on 26 February, 2002. Results using different orders of regularization are presented and compared for various time intervals. Clear evidence is presented for a change in the value of the high-energy cutoff in the mean source electron spectrum with time. We also show how the construction of the injected electron spectrum F0(E0) (assuming that Coulomb collisions in a cold target dominate the electron transport) is facilitated by the use of higher-order regularization methods. |
BibTeX:
@article{KontarEmsliePianaMassoneBrown2005,
author = {Kontar, Eduard P. and Emslie, A. Gordon and Piana, Michele and Massone, Anna Maria and Brown, John C.},
title = {Determination of Electron Flux Spectra in a Solar Flare with an Augmented Regularization Method: Application to Rhessi Data},
journal = {Solar Physics},
year = {2005},
volume = {226},
pages = {317--325},
url = {http://adsabs.harvard.edu/abs/2005SoPh..226..317K}
}
|
| Kontar EP and MacKinnon AL (2005), "Regularized Energy-Dependent Solar Flare Hard X-Ray Spectral Index", Solar Physics. Vol. 227, pp. 299-310. |
| Abstract: The deduction from solar flare X-ray photon spectroscopic data of the energy-dependent model-independent spectral index is considered as an inverse problem. Using the well-developed regularization approach we analyze the energy dependency of spectral index for a high-resolution energy spectrum provided by Ramaty High Energy Solar Spectroscopic Imager (RHESSI). The regularization technique produces much smoother derivatives while avoiding additional errors typical of finite differences. It is shown that observations imply a spectral index varying significantly with energy, in a way that also varies with time as the flare progresses. The implications of these findings are discussed in the solar flare context. |
BibTeX:
@article{KontarMacKinnon2005,
author = {Kontar, Eduard P. and MacKinnon, Alexander L.},
title = {Regularized Energy-Dependent Solar Flare Hard X-Ray Spectral Index},
journal = {Solar Physics},
year = {2005},
volume = {227},
pages = {299--310},
url = {http://adsabs.harvard.edu/abs/2005SoPh..227..299K}
}
|
| Kontar EP and Pécseli HL (2005), "Nonlinear wave interactions as a model for naturally enhanced ion acoustic lines in the ionosphere", Geophysical Research Letters. Vol. 32, pp. 05110. |
| Abstract: Incoherent radar scatter from the ionosphere will, for equilibrium conditions, show two symmetric ion-acoustic lines, one for each direction of wave propagation. Many observations, from the EISCAT Svalbard Radar (ESR) for instance, demonstrate that the symmetry of this ion line can be broken. An enhanced, nonthermal, level of fluctuations, i.e., Naturally Enhanced Ion-Acoustic Lines (NEIALs) might be observed. Several models have been proposed for explaining these naturally enhanced lines. Here, we consider one of these, suggesting that decay of electron beam excited Langmuir waves gives rise to enhanced asymmetric ion lines in the ionosphere. We use a weak-turbulence approximation, and identify crucial parameters for Langmuir decay processes to be effective in generating the observed signals. |
BibTeX:
@article{KontarPecseli2005,
author = {Kontar, E. P. and Pécseli, H. L.},
title = {Nonlinear wave interactions as a model for naturally enhanced ion acoustic lines in the ionosphere},
journal = {Geophysical Research Letters},
year = {2005},
volume = {32},
pages = {05110},
url = {http://adsabs.harvard.edu/abs/2005GeoRL..3205110K}
}
|
| Kontar EP, Piana M, Massone AM, Emslie AG and Brown JC (2004), "Generalized Regularization Techniques with Constraints for the Analysis of Solar Bremsstrahlung X-ray Spectra", Solar Physics. Vol. 225, pp. 293-309. |
| Abstract: Hard X-ray spectra in solar flares provide knowledge of the electron spectrum that results from acceleration and propagation in the solar atmosphere. However, the inference of the electron spectra from solar X-ray spectra is an ill-posed inverse problem. Here, we develop and apply an enhanced regularization algorithm for this process making use of physical constraints on the form of the electron spectrum. The algorithm incorporates various features not heretofore employed in the solar flare context: Generalized Singular Value Decomposition (GSVD) to deal with different orders of constraints; rectangular form of the cross-section matrix to extend the solution energy range; regularization with various forms of the smoothing operator; and “preconditioning” of the problem. We show by simulations that this technique yields electron spectra with considerably more information and higher quality than previous algorithms. |
BibTeX:
@article{KontarPianaMassoneEmslieBrown2004,
author = {Kontar, Eduard P. and Piana, Michele and Massone, Anna Maria and Emslie, A. Gordon and Brown, John C.},
title = {Generalized Regularization Techniques with Constraints for the Analysis of Solar Bremsstrahlung X-ray Spectra},
journal = {Solar Physics},
year = {2004},
volume = {225},
pages = {293--309},
url = {http://adsabs.harvard.edu/abs/2004SoPh..225..293K}
}
|
| Massone AM, Emslie AG, Kontar EP, Piana M, Prato M and Brown JC (2004), "Anisotropic Bremsstrahlung Emission and the Form of Regularized Electron Flux Spectra in Solar Flares", The Astrophysical Journal. Vol. 613, pp. 1233-1240. |
| Abstract: The cross section for bremsstrahlung photon emission in solar flares is, in general, a function of the angle θ between the incoming electron and the outgoing photon directions. Thus the electron spectrum required to produce a given photon spectrum is a function of this angle, which is related to the position of the flare on the solar disk and the direction(s) of the precollision electrons relative to the local solar vertical. We compare mean electron flux spectra for the flare of 2002 August 21 using cross sections for parameterized ranges of the angle θ. Implications for the shape of the mean source electron spectrum and for the injected power in nonthermal electrons are discussed. |
BibTeX:
@article{MassoneEmslieKontarPianaPratoBrown2004,
author = {Massone, Anna Maria and Emslie, A. Gordon and Kontar, Eduard P. and Piana, Michele and Prato, Marco and Brown, John C.},
title = {Anisotropic Bremsstrahlung Emission and the Form of Regularized Electron Flux Spectra in Solar Flares},
journal = {The Astrophysical Journal},
year = {2004},
volume = {613},
pages = {1233--1240},
url = {http://adsabs.harvard.edu/abs/2004ApJ...613.1233M}
}
|
| Brown JC, Emslie AG and Kontar EP (2003), "The Determination and Use of Mean Electron Flux Spectra in Solar Flares", The Astrophysical Journal Letters. Vol. 595, pp. L115-L117. |
| Abstract: Hard X-ray spectra in solar flares provide information on electron acceleration and propagation processes. We here point out that the inference of these processes involves two distinct steps: (1) the model-independent deconvolution of the hard X-ray spectrum to obtain the effective mean electron spectrum F(E) in the source and (2) the model-dependent interpretation of this mean spectrum in terms of physical processes operating in that source. Thus, the mean electron spectrum is a natural ``middle ground'' on which to compare the predictions of models with observations, and we urge the presentation of results, both from analysis of photon spectra and from modeling of candidate physical processes, in the form of F(E) spectra. We consider the constraints that various source models impose on F(E), and we present explicit forms for an illustrative F(E) corresponding to the injection of a power-law spectrum of electrons into a thick target with a nonuniform ionization level. |
BibTeX:
@article{BrownEmslieKontar2003,
author = {Brown, John C. and Emslie, A. Gordon and Kontar, Eduard P.},
title = {The Determination and Use of Mean Electron Flux Spectra in Solar Flares},
journal = {The Astrophysical Journal Letters},
year = {2003},
volume = {595},
pages = {L115-L117},
url = {http://adsabs.harvard.edu/abs/2003ApJ...595L.115B}
}
|
| Conway AJ, Brown JC, Eves BAC and Kontar E (2003), "Implications of solar flare hard X-ray ``knee'' spectra observed by RHESSI", Astronomy and Astrophysics. Vol. 407, pp. 725-734. |
| Abstract: We analyse the RHESSI photon spectra of four flares that exhibit significant deviations from power laws - i.e. changes in the ``local'' Hard X-ray spectral index. These spectra are characterised by two regions of constant power law index connected by a region of changing spectral index - the ``knee''. We develop theoretical and numerical methods of describing such knees in terms of variable photon spectral indices and we study the results of their inversions for source mean thin target and collisional thick target injection electron spectra. We show that a particularly sharp knee can produce unphysical negative values in the electron spectra, and we derive inequalities that can be used to test for this without the need for an inversion to be performed. Such unphysical features would indicate that source model assumptions were being violated, particularly strongly for the collisional thick target model which assumes a specific form for electron energy loss. For all four flares considered here we find that the knees do not correspond to unphysical electron spectra. In the three flares that have downward knees we conclude that the knee can be explained in terms of transport effects through a region of non-uniform ionisation. In the other flare, which has an upward knee, we conclude that it is most likely a feature of the accelerated spectrum. |
BibTeX:
@article{ConwayBrownEvesKontar2003,
author = {Conway, A. J. and Brown, J. C. and Eves, B. A. C. and Kontar, E.},
title = {Implications of solar flare hard X-ray ``knee'' spectra observed by RHESSI},
journal = {Astronomy and Astrophysics},
year = {2003},
volume = {407},
pages = {725--734},
url = {http://adsabs.harvard.edu/abs/2003A%26A...407..725C}
}
|
| Emslie AG, Kontar EP, Krucker S and Lin RP (2003), "RHESSI Hard X-Ray Imaging Spectroscopy of the Large Gamma-Ray Flare of 2002 July 23", The Astrophysical Journal Letters. Vol. 595, pp. L107-L110. |
| Abstract: We present Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) hard X-ray images in different energy bands for the large X-class flare of 2002 July 23; these images are used to construct spatially resolved hard X-ray spectra for each of four prominent features: a bright, soft source high in the corona, two localized, hard footpoints in opposite polarity magnetic regions that show highly correlated flux and spectral variations in time, and a third footpoint bounded by the other three sources. The power-law spectral indices of the two correlated footpoints differ by ~0.3-0.4, which may be the result of differing column densities from the electron source. |
BibTeX:
@article{EmslieKontarKruckerLin2003,
author = {Emslie, A. Gordon and Kontar, Eduard P. and Krucker, Säm and Lin, Robert P.},
title = {RHESSI Hard X-Ray Imaging Spectroscopy of the Large Gamma-Ray Flare of 2002 July 23},
journal = {The Astrophysical Journal Letters},
year = {2003},
volume = {595},
pages = {L107-L110},
url = {http://adsabs.harvard.edu/abs/2003ApJ...595L.107E}
}
|
| Kontar EP, Brown JC, Emslie AG, Schwartz RA, Smith DM and Alexander RC (2003), "An Explanation for Non-Power-Law Behavior in the Hard X-Ray Spectrum of the 2002 July 23 Solar Flare", The Astrophysical Journal Letters. Vol. 595, pp. L123-L126. |
| Abstract: High-resolution Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) data reveal that solar flare hard X-ray spectra show systematic deviations from power-law behavior. Even for injection of a power-law electron spectrum, such deviations are expected because of a number of effects, including nonuniform target ionization and solar albedo backscattering of the primary hard X-ray flux. In this Letter, we examine 1 keV resolution hard X-ray spectra for the intense 2002 July 23 event, corrected for the effects of decimation, pulse pileup, and background. We find that the observed spectra indeed deviate from a power-law behavior in a manner consistent with the effects of nonuniform target ionization. Further, this interpretation of the observed deviations requires that the amount of coronal material increases during the initial phase of the flare. The implications of this discovery for models of atmospheric response to flare heating are discussed. |
BibTeX:
@article{KontarBrownEmslieSchwartzSmithAlexander2003,
author = {Kontar, Eduard P. and Brown, John C. and Emslie, A. Gordon and Schwartz, Richard A. and Smith, David M. and Alexander, R. Calum},
title = {An Explanation for Non-Power-Law Behavior in the Hard X-Ray Spectrum of the 2002 July 23 Solar Flare},
journal = {The Astrophysical Journal Letters},
year = {2003},
volume = {595},
pages = {L123-L126},
url = {http://adsabs.harvard.edu/abs/2003ApJ...595L.123K}
}
|
| Kontar EP and Mel'Nik VN (2003), "Weakly turbulent electron cloud transport in a plasma with an external electric field", Physics of Plasmas. Vol. 10, pp. 2732-2737. |
| Abstract: The propagation of a fast electron cloud in a relatively cold and dense plasma in an electric field is investigated in the framework of weak turbulence theory. The dynamics of an electron cloud in the external electric field is studied both analytically and numerically. It is shown that electrons propagate as a beam-plasma structure and that the structure becomes accelerated. For propagation along the field the structure loses particles and the velocity of the structure declines whereas propagation against the field leads to structure acceleration and a high level of plasma waves behind the structure. |
BibTeX:
@article{KontarMelNik2003,
author = {Kontar, E. P. and Mel'Nik, V. N.},
title = {Weakly turbulent electron cloud transport in a plasma with an external electric field},
journal = {Physics of Plasmas},
year = {2003},
volume = {10},
pages = {2732--2737},
url = {http://adsabs.harvard.edu/abs/2003PhPl...10.2732K}
}
|
| Mel'Nik VN and Kontar EP (2003), "Plasma Radio Emission of Beam-Plasma Structures in the Solar Corona", Solar Physics. Vol. 215, pp. 335-341. |
| Abstract: Recent progress in the description of electron beam propagation in a plasma allows us to obtain explicit expressions for Langmuir turbulence generated by the beam. Radio emission of an electron beam accompanied by Langmuir turbulence (beam-plasma structure - BPS), propagating in the solar corona is considered within the plasma emission mechanism. The maximum brightness temperatures of a BPS radio emission with velocity vBPS~0.35 c at fundamental and harmonic frequencies are found to be equal to TF=1013 K, TH=1016 K, respectively. It is shown that the temperature of radio emission sharply declines with the decrease of BPS velocity. The dominant drift velocity of Type III sources (~0.3 c) and broad range of observable brightness temperatures are naturally explained by the latter fact. |
BibTeX:
@article{MelNikKontar2003,
author = {Mel'Nik, V. N. and Kontar, E. P.},
title = {Plasma Radio Emission of Beam-Plasma Structures in the Solar Corona},
journal = {Solar Physics},
year = {2003},
volume = {215},
pages = {335--341},
url = {http://adsabs.harvard.edu/abs/2003SoPh..215..335M}
}
|
| Piana M, Massone AM, Kontar EP, Emslie AG, Brown JC and Schwartz RA (2003), "Regularized Electron Flux Spectra in the 2002 July 23 Solar Flare", The Astrophysical Journal Letters. Vol. 595, pp. L127-L130. |
| Abstract: By inverting the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) hard X-ray photon spectrum with the Tikhonov regularization algorithm, we infer the effective mean electron source spectrum for a time interval near the peak of the 2002 July 23 event. This inverse approach yields the smoothest electron flux spectrum consistent with the data while retaining real features, such as local minima, that cannot be found with forward model-fitting methods that involve only a few parameters. A significant dip in the recovered mean source electron spectrum near E=55 keV is noted, and its significance briefly discussed. |
BibTeX:
@article{PianaMassoneKontarEmslieBrownSchwartz2003,
author = {Piana, Michele and Massone, Anna Maria and Kontar, Eduard P. and Emslie, A. Gordon and Brown, John C. and Schwartz, Richard A.},
title = {Regularized Electron Flux Spectra in the 2002 July 23 Solar Flare},
journal = {The Astrophysical Journal Letters},
year = {2003},
volume = {595},
pages = {L127-L130},
url = {http://adsabs.harvard.edu/abs/2003ApJ...595L.127P}
}
|
| Aschwanden MJ, Brown JC and Kontar EP (2002), "Chromospheric Height and Density Measurements in a Solar Flare Observed with RHESSI II. Data Analysis", Solar Physics. Vol. 210, pp. 383-405. |
| Abstract: We present an analysis of hard X-ray imaging observations from one of the first solar flares observed with the Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI) spacecraft, launched on 5 February 2002. The data were obtained from the 22 February 2002, 11:06 UT flare, which occurred close to the northwest limb. Thanks to the high energy resolution of the germanium-cooled hard X-ray detectors on RHESSI we can measure the flare source positions with a high accuracy as a function of energy. Using a forward-fitting algorithm for image reconstruction, we find a systematic decrease in the altitudes of the source centroids z(ɛ) as a function of increasing hard X-ray energy ɛ, as expected in the thick-target bremsstrahlung model of Brown. The altitude of hard X-ray emission as a function of photon energy ɛ can be characterized by a power-law function in the ɛ=15 50 keV energy range, viz., z(ɛ)≈2.3(ɛ/20 keV)-1.3 Mm. Based on a purely collisional 1-D thick-target model, this height dependence can be inverted into a chromospheric density model n(z), as derived in Paper I, which follows the power-law function n e(z)=1.25×1013(z/1 Mm)-2.5 cm-3. This density is comparable with models based on optical/UV spectrometry in the chromospheric height range of h≲1000 km, suggesting that the collisional thick-target model is a reasonable first approximation to hard X-ray footpoint sources. At h≈1000 2500 km, the hard X-ray based density model, however, is more consistent with the `spicular extended-chromosphere model' inferred from radio sub-mm observations, than with standard models based on hydrostatic equilibrium. At coronal heights, h≈2.5 12.4 Mm, the average flare loop density inferred from RHESSI is comparable with values from hydrodynamic simulations of flare chromospheric evaporation, soft X-ray, and radio-based measurements, but below the upper limits set by filling-factor insensitive iron line pairs. |
BibTeX:
@article{AschwandenBrownKontar2002,
author = {Aschwanden, Markus J. and Brown, John C. and Kontar, Eduard P.},
title = {Chromospheric Height and Density Measurements in a Solar Flare Observed with RHESSI II. Data Analysis},
journal = {Solar Physics},
year = {2002},
volume = {210},
pages = {383--405},
url = {http://adsabs.harvard.edu/abs/2002SoPh..210..383A}
}
|
| Brown JC, Aschwanden MJ and Kontar EP (2002), "Chromospheric Height and Density Measurements in a Solar Flare Observed with RHESSI I. Theory", Solar Physics. Vol. 210, pp. 373-381. |
| Abstract: We obtain a theoretical description of the height (z) distribution of flare hard X-rays in the collisional thick-target model as a function of photon energy ɛ. This depends on the target atmosphere density structure n(z) and on the beam spectral index δ. We show that by representing the data in terms of the 1-D function z(ɛ) defining where the emission peaks as a function of ɛ it is possible to derive n(z) from data on z(ɛ). This is done first on the basis of a simple stopping depth argument then refined to allow for the dependence on spectral index δ. The latter is worked out in detail for the case of a parameterization n(z)=n 0 (z/z 0)-b which yields numerical results for z(ɛ) well fit by z(ɛ)˜ɛ-α, with α dependent on δ, which is also found to fit well to actual observations. This enables derivation of flare loop n(z) in terms of n 0,b from RHESSI data in an entirely novel way, independent of other density diagnostic methods, and also of how n(z) varies with time in flares such as by evaporation, as detailed in companion Paper II. |
BibTeX:
@article{BrownAschwandenKontar2002,
author = {Brown, John C. and Aschwanden, Markus J. and Kontar, Eduard P.},
title = {Chromospheric Height and Density Measurements in a Solar Flare Observed with RHESSI I. Theory},
journal = {Solar Physics},
year = {2002},
volume = {210},
pages = {373--381},
url = {http://adsabs.harvard.edu/abs/2002SoPh..210..373B}
}
|
| Kontar EP, Brown JC and McArthur GK (2002), "Nonuniform Target Ionization and Fitting Thick Target Electron Injection Spectra to RHESSI Data", Solar Physics. Vol. 210, pp. 419-429. |
| Abstract: Past analyses of flare hard X-ray (HXR) spectra have largely ignored the effect of nonuniform ionization along the electron paths in the thick-target model, though it is very significant for well-resolved spectra. The inverse problem (photon spectrum to electron injection spectrum F 0(E 0)) is disturbingly non-unique. However, we show that it is relatively simple to allow for the effect in forward fitting of parametric models of F 0(E 0)) and provide an expression to evaluate it for the usual single power-law form of F 0(E 0)).The expression involves the column depth N * of the transition region in the flare loop as one of the parameters so data fitting can enable derivation of N * (and its evaporative evolution) as part of the fitting procedure. The fit to RHESSI data on four flares for a single power law F 0(E 0)) is much improved when ionization structure is included compared to when the usual fully ionized approximation is used. This removes the need, in these events at least, to invoke broken power laws, or other forms, of the acceleration spectrum F 0(E 0)) to explain the observed photon spectrum |
BibTeX:
@article{KontarBrownMcArthur2002,
author = {Kontar, Eduard P. and Brown, John C. and McArthur, Guillian K.},
title = {Nonuniform Target Ionization and Fitting Thick Target Electron Injection Spectra to RHESSI Data},
journal = {Solar Physics},
year = {2002},
volume = {210},
pages = {419--429},
url = {http://adsabs.harvard.edu/abs/2002SoPh..210..419K}
}
|
| Kontar EP and Pécseli HL (2002), "Nonlinear development of electron-beam-driven weak turbulence in an inhomogeneous plasma", Physical Review E. Vol. 65, pp. 66408. |
| Abstract: The self-consistent description of Langmuir wave and ion-sound wave turbulence in the presence of an electron beam is presented for inhomogeneous nonisothermal plasmas. Full numerical solutions of the complete set of kinetic equations for electrons, Langmuir waves, and ion-sound waves are obtained for an inhomogeneous unmagnetized plasma. The results show that the presence of inhomogeneity significantly changes the overall evolution of the system. The inhomogeneity is effective in shifting the wave numbers of the Langmuir waves, and can thus switch between different processes governing the weakly turbulent state. The results can be applied to a variety of plasma conditions, where we choose solar coronal parameters as an illustration, when performing the numerical analysis. |
BibTeX:
@article{KontarPecseli2002,
author = {Kontar, E. P. and Pécseli, H. L.},
title = {Nonlinear development of electron-beam-driven weak turbulence in an inhomogeneous plasma},
journal = {Physical Review E},
year = {2002},
volume = {65},
pages = {66408},
url = {http://adsabs.harvard.edu/abs/2002PhRvE..65f6408K}
}
|
| Kontar EP (2001), "Dynamics of electron beams in the inhomogeneous solar corona plasma", Solar Physics. Vol. 202, pp. 131-149. |
| Abstract: Dynamics of a spatially-limited electron beam in the inhomogeneous solar corona plasma is considered in the framework of weak turbulence theory when the temperature of the beam significantly exceeds that of surrounding plasma. The numerical solution of kinetic equations manifests that generally the beam accompanied by Langmuir waves propagates as a beam-plasma structure with a decreasing velocity. Unlike the uniform plasma case the structure propagates with the energy losses in the form of Langmuir waves. The results obtained are compared with the results of observations of type III bursts. It is shown that the deceleration of type III sources can be explained by corona inhomogeneity. The frequency drift rates of the type III sources are found to be in good agreement with the numerical results of beam dynamics. |
BibTeX:
@article{Kontar2001,
author = {Kontar, Eduard P.},
title = {Dynamics of electron beams in the inhomogeneous solar corona plasma},
journal = {Solar Physics},
year = {2001},
volume = {202},
pages = {131--149},
url = {http://adsabs.harvard.edu/abs/2001SoPh..202..131K}
}
|
| Kontar EP (2001), "Numerical consideration of quasilinear electron cloud dynamics in plasma", Computer Physics Communications. Vol. 138, pp. 222-233. |
| Abstract: The dynamics of a hot electron cloud in the solar corona-like plasma based on the numerical solution of kinetic equations of weak turbulence theory is considered. Different finite difference schemes are examined to fit the exact analytical solutions of quasilinear equations in hydrodynamic limit (gas-dynamic solution). It is shown that the scheme suggested demonstrates correct asymptotic behavior and can be employed to solve initial value problems for an arbitrary initial electron distribution function. |
BibTeX:
@article{Kontar2001a,
author = {Kontar, E. P.},
title = {Numerical consideration of quasilinear electron cloud dynamics in plasma},
journal = {Computer Physics Communications},
year = {2001},
volume = {138},
pages = {222--233},
url = {http://adsabs.harvard.edu/abs/2001CoPhC.138..222K}
}
|
| Kontar EP (2001), "Dynamics of electron beams in the solar corona plasma with density fluctuations", Astronomy and Astrophysics. Vol. 375, pp. 629-637. |
| Abstract: The problem of beam propagation in a plasma with small scale and low intensity inhomogeneities is investigated. It is shown that the electron beam propagates in a plasma as a beam-plasma structure and is a source of Langmuir waves. The plasma inhomogeneity changes the spatial distribution of the waves. The spatial distribution of the waves is fully determined by the distribution of plasma inhomogeneities. The possible applications to the theory of radio emission associated with electron beams are discussed. |
BibTeX:
@article{Kontar2001b,
author = {Kontar, E. P.},
title = {Dynamics of electron beams in the solar corona plasma with density fluctuations},
journal = {Astronomy and Astrophysics},
year = {2001},
volume = {375},
pages = {629--637},
url = {http://adsabs.harvard.edu/abs/2001A%26A...375..629K}
}
|
| Kontar EP (2001), "Propagation of a fast electron cloud in a solar-like plasma of decreasing density", Plasma Physics and Controlled Fusion. Vol. 43, pp. 589-601. |
| Abstract: The influence of plasma inhomogeneity on the quasilinear dynamics of a spatially limited electron beam is investigated. It is shown that the electron beam propagates in a plasma of decreasing density as a beam-plasma structure with a decreasing velocity. Plasma inhomogeneity leads to the beam-plasma structure having energy losses. |
BibTeX:
@article{Kontar2001c,
author = {Kontar, Eduard P.},
title = {Propagation of a fast electron cloud in a solar-like plasma of decreasing density},
journal = {Plasma Physics and Controlled Fusion},
year = {2001},
volume = {43},
pages = {589--601},
url = {http://adsabs.harvard.edu/abs/2001PPCF...43..589K}
}
|
| Kontar EP, Mel'nik VN and Lapshin VI (2001), "Dynamics of a fast Maxwellian electron cloud in coronal plasma", Radio Science. Vol. 36, pp. 1757-1764. |
| Abstract: Dynamics of a hot electron cloud with an initially Maxwellian electron distribution is considered both numerically and analytically. It is shown that only a small group of the electrons propagates into the plasma but the main group of the electrons is concentrated near the initial location of the cloud. The distribution of the electrons left presents a plateau with the maximum velocity growing linearly with distance. |
BibTeX:
@article{KontarMelnikLapshin2001,
author = {Kontar, E. P. and Mel'nik, V. N. and Lapshin, V. I.},
title = {Dynamics of a fast Maxwellian electron cloud in coronal plasma},
journal = {Radio Science},
year = {2001},
volume = {36},
pages = {1757--1764},
url = {http://adsabs.harvard.edu/abs/2001RaSc...36.1757K}
}
|
| Mel'Nik VN and Kontar EP (2000), "To gasdynamic description of a hot electron cloud in a cold plasma", New Astronomy. Vol. 5, pp. 35-42. |
| Abstract: The quasi-gasdynamic equations are reassessed and the nonconsistency of these equations is shown. The correct gasdynamic system of equations is found. The solution of these equations are obtained in special cases. The solution presents a new nonlinear object, beam-plasma structure, that consists of electrons and Langmuir waves, and moves with a constant speed. Numerical simulations corroborate the gasdynamic theory very well. |
BibTeX:
@article{MelNikKontar2000,
author = {Mel'Nik, V. N. and Kontar, E. P.},
title = {To gasdynamic description of a hot electron cloud in a cold plasma},
journal = {New Astronomy},
year = {2000},
volume = {5},
pages = {35--42},
url = {http://adsabs.harvard.edu/abs/2000NewA....5...35M}
}
|
| Mel'nik VN, Kontar EP and Lapshin VI (2000), "Propagation of a Maxwellian Electron Cloud in a Plasma", Solar Physics. Vol. 196, pp. 199-212. |
| Abstract: We consider the dynamics of an electron cloud with an initially Maxwellian electron distribution and a temperature significantly exceeding that of the surrounding plasma. It is demonstrated that only the fastest electrons propagate into the plasma as a beam-plasma structure, whereas the main part of the cloud of electrons is locked by the Langmuir turbulence generated by the electrons remaining. |
BibTeX:
@article{MelnikKontarLapshin2000,
author = {Mel'nik, V. N. and Kontar, E. P. and Lapshin, V. I.},
title = {Propagation of a Maxwellian Electron Cloud in a Plasma},
journal = {Solar Physics},
year = {2000},
volume = {196},
pages = {199--212},
url = {http://adsabs.harvard.edu/abs/2000SoPh..196..199M}
}
|
| Mel'nik VN and Kontar EP (1999), "The spread of the hot electron cloud in the solar corona", New Astronomy. Vol. 4, pp. 41-44. |
| Abstract: The spread of the electron cloud generating solar type III bursts is discussed. It is shown that the maximum velocity of the electron distribution function, plateau, cannot exceed the velocity of free propagation u=x/t. It appeared that despite the plateau formation at the electron distribution function the asymptotic self-similar solution u(x,t)=2x/t never occurred. |
BibTeX:
@article{MelnikKontar1999,
author = {Mel'nik, V. N. and Kontar, E. P.},
title = {The spread of the hot electron cloud in the solar corona},
journal = {New Astronomy},
year = {1999},
volume = {4},
pages = {41--44},
url = {http://adsabs.harvard.edu/abs/1999NewA....4...41M}
}
|
| Mel'Nik VN, Lapshin V and Kontar E (1999), "Propagation of a Monoenergetic Electron Beam in the Solar Corona", Solar Physics. Vol. 184, pp. 353-362. |
| Abstract: The dynamics of an electron beam is considered when the initial electron distribution is localized in a space region. Analysis is conducted for the parameters of the beam and plasma that give radio emission. We demonstrate both numerically and analytically that beam electrons propagate as a beam-plasma structure at large distances. The speed of the beam-plasma structure is equal to half of the maximum velocity of the electrons involved in this structure. The structure conserves the shape of the initial spatial distribution of electrons. A plateau with a constant maximum velocity is formed at the electron distribution function in each spatial point. |
BibTeX:
@article{MelNikLapshinKontar1999,
author = {Mel'Nik, V. N. and Lapshin, V. and Kontar, E.},
title = {Propagation of a Monoenergetic Electron Beam in the Solar Corona},
journal = {Solar Physics},
year = {1999},
volume = {184},
pages = {353--362},
url = {http://adsabs.harvard.edu/abs/1999SoPh..184..353M}
}
|
| Kontar' EP, Lapshin VI and Mel'Nik VN (1998), "Numerical and analytical study of the propagation of a monoenergetic electron beam in a plasma", Plasma Physics Reports. Vol. 24, pp. 772-776. |
| Abstract: Not Available |
BibTeX:
@article{KontarLapshinMelNik1998,
author = {Kontar', E. P. and Lapshin, V. I. and Mel'Nik, V. N.},
title = {Numerical and analytical study of the propagation of a monoenergetic electron beam in a plasma},
journal = {Plasma Physics Reports},
year = {1998},
volume = {24},
pages = {772--776},
url = {http://adsabs.harvard.edu/abs/1998PlPhR..24..772K}
}
|
| Mel'nik VN and Kontar EP (1998), "Beam-Plasma Structures at Propagation of Electron Beams in Plasma", Physica Scripta. Vol. 58, pp. 510-517. |
| Abstract: In the frame of the theory of weak turbulence the propagation of electron beams is considered. Using the smallness of quasilinear time transition from kinetic equations to gas-dynamic ones has been done. The obtained gas-dynamic equations are solved for one, two and N monoenergetic beams. It is shown that each beam generally propagates as a beam-plasma structure consisting of electrons and Langmuir waves. Interaction of the structures at their propagation leads to electron exchange and spatial shape changing. Different situations are discussed in dependence on initial beam velocities and densities. |
BibTeX:
@article{MelnikKontar1998,
author = {Mel'nik, V. N. and Kontar, E. P.},
title = {Beam-Plasma Structures at Propagation of Electron Beams in Plasma},
journal = {Physica Scripta},
year = {1998},
volume = {58},
pages = {510--517},
url = {http://adsabs.harvard.edu/abs/1998PhyS...58..510M}
}
|
| Mel'Nik VN and Kontar EP (1998), "Gasdynamic description of electron-beam flying-off in a plasma", Journal of Plasma Physics. Vol. 60, pp. 49-64. |
| Abstract: Available from http://journals.cambridge.org/bin/bladerunner?REQUNIQ=1105385180&REQSESS=958582&118000REQEVENT=&REQINT1=18323&REQAUTH=0 |
BibTeX:
@article{MelNikKontar1998,
author = {Mel'Nik, V. N. and Kontar, E. P.},
title = {Gasdynamic description of electron-beam flying-off in a plasma},
journal = {Journal of Plasma Physics},
year = {1998},
volume = {60},
pages = {49--64},
url = {http://adsabs.harvard.edu/abs/1998JPlPh..60...49M}
}
|