CESRA 2018 Summer school (September 10-14,2018, Brussels, Belgium)

Lecture slides “Theory and modelling of radio emission” (September 11, 2018)

Further reading/slides on wave-particle and wave-wave interactions can be found here: http://www.astro.gla.ac.uk/users/eduard/lectures/index.html.

Tutorial questions for discussion:

1) What is meant by the coherent plasma radio emission?

2) Using the information in the Figure 1, state why is the burst to the right is said to be due to coherent plasma emission? (Estimate the brightness temperature)

Figure 1: Dynamic spectrum of type III burst (Fundamental and Harmonic components are visible)

Sketch solution:

From the dynamic spectrum, we have time, frequency and flux. From R-J relation, the brightness temperature for 30 MHz is

where the solid angle subtended by the source is

First method to estimate the source size is to take the rise time at a given frequency (say 30 MHz) multiplied by the speed of light, Area = (c*0.5 sec)^2 hence we have:

Second method is to use frequency rage of a stria to estimate the size as  

Then,  we have

Therefore, in case 1 we have:

>>> 3e8**2*1e-22/(2*30e6**2*1.38e-23)*1e3/1e-6

362318840579.71014=3.6e11

And in case 2 we have:

>>> 3e8**2*1e-22/(2*30e6**2*1.38e-23)*1e3/1e-9

362318840579710.1=3.6e14

So we find that the brightness temperature is 10¹² -10¹⁵  K, which corresponds to kinetic energy of particle 86 MeV – 86 GeV , which is too high for incoherent emission.

ð Therefore the emission observed has to be coherent.