sol5 - Astro 405/505, fall semester 2004 Homework, 5th set,...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Astro 405/505, fall semester 2004 Homework, 5th set, solutions. Problem 1: Electrostatic waves The momentum conservation equation (14.5 in the notes) now reads m e n e ~ V e ∂t + ( ~ V e · ∇ ) ~ V e + ~ P = - e n e ~ E Be careful, because c s will also be perturbed! Using ∂P ∂r = ∂P ∂ρ ∂ρ ∂r ∂P ∂ρ = c 2 s ∂P ∂r = c 2 s A Z m p ∂n e ∂r we derive the perturbation equation in Fourier representation. n e, 0 ı ω v 1 = e n e, 0 m e E 1 + c 2 s A Z m p m e ı k n e, 1 which must be solved together with the three unchanged equations. ı k E 1 = - 4 π e n e, 1 ı ω E 1 = - 4 π e v 1 n e, 0 ω n e, 1 = n e, 0 k v 1 The solution is ω 2 = ω 2 p + c 2 s A Z m p m e k 2 = ω 2 p + γ κT m e k 2 so the mean thermal velocity of the electrons enters the dispersion relation as a characteristic scale. The phase velocity is v φ = ω k = v u u t ω 2 p k 2 + γ κT m e ' ω p k small k q γ κT m e large k The group velocity is v gr
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/29/2012 for the course PHYS 227 taught by Professor Rabe during the Fall '08 term at Rutgers.

Page1 / 2

sol5 - Astro 405/505, fall semester 2004 Homework, 5th set,...

This preview shows document pages 1 - 2. Sign up to view the full document.

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