Collisional Damping of Transverse Plasma Oscillations

The effect of Coulomb collisions on the transverse electron oscillations in a fully ionized hot plasma is studied by means of the Fokker‐Planck equation. The damping coefficient for the electron‐ion collisions γ_i turns out to be much greater than the one for the electron‐electron collisions γ_e. To first order in electron‐collision frequency, these are given by, $$\begin{array}{c}{\gamma }_i{\mathrm{\hspace{0.17em}=\hspace{0.17em}[\nu }}_{\mathrm{c}}{\text{/3(2π)}}^{\frac{1}{2}}{\mathrm{][\omega }}_{\mathrm{p}}^2{\mathrm{/(c}}^2{k}^2{\mathrm{+\omega }}_{\mathrm{p}}^2\mathrm{)]}\\ {\text{·[1+(2.075k}}^2{\upsilon }_0^2{\mathrm{)/(c}}^2{k}^2{\mathrm{+\omega }}_{\mathrm{p}}^2{\mathrm{)-k}}^2{\upsilon }_0^2{\omega }_{\mathrm{p}}^2{\mathrm{/(c}}^2{k}^2{\mathrm{+\omega }}_{\mathrm{p}}^2{)}^2\mathrm{],}\\ {\gamma }_{\mathrm{e}}{\text{=(41/16)[ν}}_{\mathrm{c}}{\text{/3π}}^{\frac{1}{2}}{\mathrm{][\omega }}_{\mathrm{p}}^2{\mathrm{/(c}}^2{k}^2{\mathrm{+\omega }}_{\mathrm{p}}^2{\mathrm{)][k}}^2{\upsilon }_0^2{\mathrm{/(c}}^2{k}^2{\mathrm{+\omega }}_{\mathrm{p}}^2\mathrm{)],}\end{array}$$ where v₀ and ω_p are the electron thermal speed and the plasma frequency, respectively.