A cold electron beam of density and speed streams into a background plasma

PHYSICS · Multi-part · Fermi University Physics · Plasma Physics · Kinetic theory, collisions and transport · Kinetic theory, collisions and transport

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

Problem

A cold electron beam of density nb=2.0×1013 m−3n_b = 2.0\times10^{13}\,\mathrm{m^{-3}} and speed vb=3.0×107 m s−1v_b = 3.0\times10^{7}\,\mathrm{m\,s^{-1}} streams into a background plasma. Quasilinear relaxation flattens it into a plateau extending from near zero velocity up to vbv_b, with the number of beam electrons conserved. ((a)) Find the beam's initial kinetic energy density. ((b)) Find the plateau's final kinetic energy density. ((c)) Find the energy density transferred to Langmuir waves.

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