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hwk2 - Physics 762 Homework#2 Spring 11 Dr Drake 1 Show...

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Physics 762 Homework #2 Spring ‘11 Dr. Drake 1. Show that the Z function satisfies the following differential equation: dZ ( ξ ) = - 2(1 + ξZ ( ξ )) . (1) 2. Calculate the kinetic dispersion relation for ion acoustic waves in a plasma with a Maxwellian distribution of ions. The electrons are also Maxwellian but with a mean velocity U e = U ˆ z . Take the wavevector parallel to U e . Show that the general dispersion relation is given by ( k, ω ) = 1 - k 2 Di 2 k 2 Z 0 ( ω kv ti ) - k 2 De 2 k 2 Z 0 ( ω - kU kv te ) . (2) 3. Show that the real frequency
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