A solar flare accelerates a cold electron beam of density and speed (treated…

PHYSICS · Multi-part · Fermi University Physics · Plasma Physics · Kinetic theory, collisions and transport · Laboratory, industrial and space plasmas

Plasma Physics, Ch Hot plasmas and free energy: beam instabilities, cyclotron damping and Bernstein waves

Problem

A solar flare accelerates a cold electron beam of density

n_b = 1.0\times10^{7}\,\mathrm{m^{-3}}

and speed

v_b = 8.0\times10^{7}\,\mathrm{m\,s^{-1}}

(treated non-relativistically, as the quasilinear plateau model requires) along a coronal flux tube of cross-sectional area

A = 1.0\times10^{13}\,\mathrm{m^2}

and length

\ell = 5.0\times10^{7}\,\mathrm{m}

. The beam relaxes quasilinearly to a plateau from near zero velocity up to

v_b

, with the number of beam electrons conserved. ((a)) Find the energy density released to Langmuir waves. ((b)) Find the total energy released along the whole flux tube.

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