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# hwk5 - 2 t ω ω-kv-Ω(2 where Ω = eB/m e c is the...

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Physics 762 Homework #5 Spring ‘11 Dr. Drake 1. Calculate the growth rate of the firehose instability using the fluid equations with a gyrotropic pressure tensor P = P k bb + P ( I - bb ) (1) where I is the unit tensor and b = B /B . Assume that the initial magnetic field B 0 is uniform and is in the z direction and that the wavevector k is also along in the z direction. Hint: you will find that you do not need to perturb the pressure. 2. Derive 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 and with an initial isotropic Maxwellian distribution, k 2 c 2 ω 2 pe = - Z dv πv t e
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Unformatted text preview: 2 t ω ω-kv-Ω , (2) where Ω = eB /m e c is the electron cyclotron frequency and k is the wavevector in the z direction. The calculation is simpliﬁed if you assume that the wave is right-hand circularly polarized so that the perturbed electric ﬁeld can be written as ˆ E = ˆ E ˆ x + i ˆ E ˆy . (3) From this polarization it follows that the perturbed distribution is proportional to e iθ , where θ is the polar angle of the velocity vector perpendicular to the magnetic ﬁeld. Also assume that ω pe ± Ω, which allows you to discard the displacement current in Ampere’s law....
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• Fall '08
• drake
• Work, Fundamental physics concepts, initial magnetic ﬁeld, propagating whistler/electron cyclotron, gyrotropic pressure tensor, perturbed electric ﬁeld, initial isotropic Maxwellian

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