# hwk6 - damping due to resonant particles assuming that |...

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Physics 762 Homework #6 Fall ‘11 Dr. Drake 1. Using the kinetic dispersion relation for parallel propagating whistler/electron cy- clotron waves in a plasma with an initially uniform magnetic ﬁeld B 0 in the z direction that you derived in the previous assignment, k 2 c 2 ω 2 pe = - Z dv πv t e - v 2 /v 2 t ω ω - kv - Ω , (1) where Ω = eB 0 /m e c is the electron cyclotron frequency and k is the wavevector in the z direction, take the cold plasma limit and calculate the dispersion relation for whister/electron cyclotron waves, ω k = Ω k 2 d 2 1 + k 2 d 2 , (2) where d = c/ω pe is the electron skin depth. Now include the correction due to the
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Unformatted text preview: damping due to resonant particles assuming that | ω-Ω | /kv t ± 1 so that the thermal corrections are weak. The result is the cyclotron damping rate, γ =-√ π ω k 1 + k 2 d 2 | v r | v t e-v 2 r /v 2 t , (3) where v r = ( ω k-Ω) /k is the resonant velocity. Note that the resonance now re-sults when the Doppler shifted frequency equals the cyclotron frequency and that the particle acceleration is associated with a perpendicular rather than parallel electric ﬁeld....
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