Ion-acoustic waves can propagate in an unmagnetized plasma when the electron temperature T e greatly exceeds the
Question:
Ion-acoustic waves can propagate in an unmagnetized plasma when the electron temperature Te greatly exceeds the ion temperature Tp. In this limit, the electron density ne can be approximated by ne = n0 exp[eΦ/(kBTe)], where n0 is the mean electron density, and Φ is the electrostatic potential.
(a) Show that for ion-acoustic waves that propagate in the z direction, the nonlinear equations of continuity, the motion for the ion (proton) fluid, and Poisson’s equation for the potential take the form
Here n is the proton density, and u is the proton fluid velocity (which points in the z direction).
(b) Linearize Eqs. (21.35), and show that the dispersion relation for small-amplitude ion-acoustic modes is
where λD is the Debye length.
Step by Step Answer:
Modern Classical Physics Optics Fluids Plasmas Elasticity Relativity And Statistical Physics
ISBN: 9780691159027
1st Edition
Authors: Kip S. Thorne, Roger D. Blandford