NE528_HW4_Fall_2009_with_solutions

NE528_HW4_Fall_2009_with_solutions - NE528 Fall 2009...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
NE528 Fall 2009 HW#4 ( Total 60 points ) Due Wednesday, October 21st by class time 1. (30 points) In obtaining the dispersion relation for electron and ion plasma waves, perturbations were assumed for velocity, density and E-field. Solution requires linearization of the equation of motion, continuity equation, and Poisson’s equation for the electrons but not for the ions. Now, we will allow temperatures to also include perturbation such that 1 o TTT = + and () 11 jk x t x TT e ω = . This means that the p n p n γ ∇∇ but p n KT KT n KT n p nKT KT n γγ + == ⎝⎠ + , which is applicable for both electrons and ions. Obtain the new dispersion relation for electron and ion plasma waves for this case, i.e. with addition of temperatures perturbations. Discuss the implication of temperature perturbations on the dispersion relations. Worked Solutions Solution for electron plasma waves Poisson’s equation o e . o oo e jkE n n E E x ρ εε ε ∇= = =− Continuity equation 1 10 1 . 0 o nn nu n tt jn n nk k u j n u ∂∂ +∇ = = 1 u x −= Equation of motion 2 3 33 3 3 n pN ee e pn N n n e nKT KT n n KT n KT p e e e e K T n K T n K T e e n KT e pK T n n K T K T n e e e e 3 x x ∇+ = + = + ∇ + ∇ +
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
33 un KT ee mn enE KT n e x e e tx ∂∂ =− x 1 Linearizing 11 1 j m n u en E KT jkn n jkKT eo o e o ω −= Substituting 22 2 1 j 2 ) 1 () 2 3 ( 3 3 3 1 ( ) 1 3 1 1 e RMS e e e p o mnu en n jkKT o o kKT KT k mm u k o nk KT KT kv mu e jk u ωω =+ = + ++ e o u jk o n e m oe εω ε 2 3 3 1 1 e n kKT KT e o k m e e + u
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/08/2010 for the course PY 528 taught by Professor Bourham during the Fall '09 term at N.C. State.

Page1 / 6

NE528_HW4_Fall_2009_with_solutions - NE528 Fall 2009...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online