A deuterium plasma ( ) has

PHYSICS · Multi-part · Fermi University Physics · Plasma Physics · Waves in plasmas · Waves in plasmas

Plasma Physics, Ch Waves that need pressure or tension: Langmuir, ion-acoustic, Alfven and magnetosonic

Problem

A deuterium plasma (

m_i = 2m_p

) has

B = 1.0\,\mathrm{T}

n_e = n_i = 1.0\times10^{19}\,\mathrm{m^{-3}}

and

T_e = T_i = 500\,\mathrm{eV}

. Take

\gamma_{\rm ad} = 5/3

. ((a)) Find the Alfven speed

v_A = B/(\mu_0\rho)^{1/2}

(with

\rho = n_im_i

) and the sound speed

c_s = (\gamma_{\rm ad}p/\rho)^{1/2}

with

p = n_eT_e + n_iT_i

. ((b)) Using

\dfrac{\omega^2}{k^2} = \tfrac{1}{2}\left[v_A^2+c_s^2 \pm \left((v_A^2+c_s^2)^2 - 4v_A^2c_s^2\cos^2\theta\right)^{1/2}\right]

, find the fast and slow magnetosonic speeds at

\theta = 0^\circ

45^\circ

and

90^\circ

, where

\theta

is the angle between

\mathbf{k}

and

\mathbf{B}_0