Two-stream instability:
Two-stream instability:¶
Version 1 (cf. [CGLSonnendrucker08]):
\[
f_0 = (1+\varepsilon \cos(k_xx))0.5 /\sqrt{2\pi} (\exp(-0.5 (v-v_0)^2)+ \exp(-0.5(v+v_0)^2))
\]
Version 2 (cf. [FSonnendrucker03]):
\[
f_0 = \frac{2}{7\sqrt{2\pi}}\left( 1+ 5v^2 \right)
\left( 1+ \alpha \left( (\cos(2kx)+\cos(3kx)
\right)/1.2 + \cos(kx) \right) \mathrm{e}^{-v^2/2}
\]