Consider a plasma in which the electrons have a Maxwellian velocity distribution with temperature T e ,

Question:

Consider a plasma in which the electrons have a Maxwellian velocity distribution with temperature T_e, the protons are Maxwellian with temperature T_p, and T_p ≪ T_e. Consider an ion acoustic mode in this plasma for which

(i.e., the wave’s phase velocity is between the left and right tick marks in Fig. 22.3). As was argued in the text, for such a mode it is reasonable to expect weak damping: |ω_i| ≪ ω_r. Making approximations based on these “≪” inequalities, show that the small-|ω_i| dispersion relation (22.40) reduces to Eqs. (22.44).

Equations.