Consider a plasma with a distribution function F(v) that has precisely two peaks, at v = v
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Consider a plasma with a distribution function F(v) that has precisely two peaks, at v = v1 and v = v2 [with F(v2) ≥ F(v1)], and a minimum between them at v = vmin, and assume that the minimum is deep enough to satisfy the Penrose criterion for instability [Eq. (22.52)]. Show that there will be at least one unstable mode for every wave number k in the range kmin max, where
Show, further, that the marginally unstable mode at k = kmax has phase velocity ω/k = vmin, and the marginally unstable mode at k = kmin has ω/k = v1.
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Related Book For
Modern Classical Physics Optics Fluids Plasmas Elasticity Relativity And Statistical Physics
ISBN: 9780691159027
1st Edition
Authors: Kip S. Thorne, Roger D. Blandford
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