(a) Show that, starting from the Vlasov equation and the laws of electrostatics, we obtain the following dispersion relation for the quasistatic wave propagating at an arbitrary direction with respect to an externally applied magnetostatic field B₀ in a hot plasma,

where

The function I_n(v̂) is the Bessel function of the second kind and θ is the angle between k and B₀, as indicated in Fig. 7.

(b) Rewrite this dispersion relation in the form

(c) Simplify this expression for the case of a very weak magnetostatic field to obtain the following approximate expression for the frequency of oscillation

Compare this result with the cold and warm plasma model results for both the cases of k parallel to Bo and k perpendicular to B₀.

Figure 7.

Transcribed Image Text:

Ne w² sin²0 pe = KBTe me (*)²- == +∞o exp (-v) Σ (1 + v Hn) In(v) 8118