A new approximate electrostatic relativistic dispersion relation for electron Bernstein waves (EBWs) in a Maxwellian plasma has been derived. The relation is reasonably simple for analytical analysis and accurate enough for numerical applications. Comparisons with corresponding exact formulae are presented. Formulae for absorption of the EBWs based on this dispersion relation have been implemented into a ray-tracing code routinely used for the EBW heating and current drive simulations on MAST at Culham Science Centre, UK. Typical simulation run time of the EBW package takes a couple of minutes on a moderate workstation with a single processor.
Numerical solution of the linear dispersion relation in a relativistic pair plasma