Research undertaken with Prof E W Laing
Bernstein modes are electrostatic kinetic plasma waves. Classically, they occur at harmonics of the cyclotron frequency, and propagate at the plasma sound speed. Relativistically though the picture is different: we have examined the behaviour of weakly relativstic Bernstein modes in pair plasmas and found the dispersion relation, and character, of the waves to be significantly different from the classical case.
Laing, E. W., and Diver, D. A.: 2005, Damped Bernstein modes in a weakly relativistic pair plasma, Physical Review E, 72 036409
Below are shown numerically evaluated dispersion relations for the classical case (left) and the weakly relativistic cases a=10 and a=50. The parameter a=(rest mass energy)/(thermal energy) controls the degree of relativity: the smaller it is, the more relativistic.
