Ultra-relativistic electrostatic Bernstein waves

A new general form of the dispersion relation for electrostatic Bernstein waves in ultra-relativistic pair plasmas, characterized by a−1 = kBT/(mec) 1, is derived in this paper. The parameter Sp = a 0/ωp, where 0 is the rest cyclotron frequency for electrons or positrons and ωp is the electron (or positron) plasma frequency, plays a crucial role in characterizing these waves. In particular, Sp has a restricted range for permitted wave solutions; this range is effectively unlimited for classical plasmas, but is significant for the ultra-relativistic case. The characterization of these waves is applied in particular to the presence of such plasmas in pulsar atmospheres. (Some figures may appear in colour only in the online journal)