A coronal loop is modelled as a uniform hydrogen plasma with ( )

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 coronal loop is modelled as a uniform hydrogen plasma with

B = 1.0\times10^{-3}\,\mathrm{T}

(

10\,\mathrm{G}

n_e = n_i = 1.0\times10^{15}\,\mathrm{m^{-3}}

and

T_e = T_i = 100\,\mathrm{eV}

. Take

\gamma_{\rm ad} = 5/3

and

m_i = m_p

. ((a)) Find the Alfven speed

v_A

and the sound speed

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

, with

p = n_eT_e+n_iT_i

and

\rho = n_im_i

. ((b)) Find the fast magnetosonic speed for propagation along the loop (

\theta=0^\circ

) and across the loop (

\theta=90^\circ

), and the slow speed at these same two angles.