hwk4 - energy in acoustic waves W a and plasma waves W...

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Physics 762 Homework #4 Spring ‘11 Dr. Drake 1. Calculate the momentum carried by an electrostatic plasma wave from the general relation P = k ω k W, (1) where W is the wave energy. Take the cold plasma limit. Now calculate the momentum directly from the quasilinear equation for non-resonant electrons derived in class for plasma waves. For the nonresonant electrons show that there is an invariant that allows you to solve for the final state of the distribution function for nonresonant particles. From this distribution function calculate the momentum gained by electrons as the wave energy increases from zero to its final value. Show that the resulting momentum is the same as calculated from the general expression above. Therefore, explain how an electrostatic wave can carry momentum since it has no Poynting flux. 2. Use the fluctuation dissipation theorem derived in class to calculate the wave
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Unformatted text preview: energy in acoustic waves W a and plasma waves W plasma in the limit k/k De 1 with T e T i , e.g. , W = < L 3 X | E kw | 2 8 > (2) where the sum over is around the acoustic resonance and similarly for the plasma waves. Which of the two waves produces the dominant contribution to the total energy W tot = T e / 2? Hint: expand the dielectric function kw around the resonance frequency for each of the waves. Dont forget that the resonant frequencies have positive and negative values for a given value of k . 3. Consider a cylindrical system with a uniform magnetic eld B = B z and a radial electric eld E = E r . Transform to a rotating frame to eliminate the electric eld (assume E/B 1) and calculate the resultant centrifugal drift. Is this drift largest for ions or electrons?...
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