Two-stream instability

Abstract

For an introduction to the instability, see Chapter 6.6 of the plasma physics textbook by Chen. We imagine a plasma with cold electrons moving relative to cold ions. The dispersion relation is 1 F k ω  ()  0  where F k ω  () ω pe 2 ω k v   () 2 ω pi 2 ω 2   The little black boxes indicate that evaluation has been disabled. Let's give the variables some values: ω pe 10  ω pi 10  k 1  v 20  F k ω  () ω pe 2 ω k v   () 2 ω pi 2 ω 2   Now we plot this function using  values that miss the singularities. We make two plots, one with k = 1 and one with k = 2. Also we plot a line one unit above zero.