An attempt is made to trace the physical origin of the complex roots of the dispersion relation for a Maxwellian, non-relativistic, homogeneous, magnetized Vlasov plasma. For simplicity, the identification process is performed for the case of propagation perpendicular to the magnetic field. For a given real ω, there are infinitely many complex roots, in addition to a finite number of propagating solutions. The propagating waves correspond (in addition to the cold-plasma waves) to either the extraordinary Gross— Bernstein mode propagating just above the harmonics, or the pair of Dnestrovskij— Kostomarov modes (one ordinary and the other extraordinary) propagating just below the harmonics. The hot-plasma solutions asymptotically approach the harmonic frequencies as k‖→∞, and analytically continue across the harmonics as complex waves. These complex waves, originating in groups of three from each cyclotron harmonic, apparently remain distinct, giving rise to an infinity of complex roots for a given frequency (since there are an infinite number of cyclotron harmonics). Detailed analysis reveals that, for the ordinary and the extraordinary Dnestrovskij-Kostomarov modes, electric displacement and magnetic induction, respectively, are the dominant field components.
Hot plasma waves surrounding the Schwarzschild event horizon in a Veselago medium