Electron cyclotron modes of Bernstein waves in different plasma environments

Electron Bernstein waves are studied in plasma environment (relativistic, weakly relativistic and non- relativistic). The dispersion relation for electron Bernstein is derived by using the Maxwell-Juttner distribution function. As the integration in the relativistic dispersion relation cannot be solved analytically so the integration is approximated with the trapezoidal rule. It is observed that more than one mode exists for the Bernstein waves for a single harmonic number n due to relativistic effects defined by the value of η = mc 2 k B T e (ratio of rest mass energy to thermal energy).