Draft:Cherenkov instability

Cherenkov instability  is instability in name of Pavel Cherenkov can be recognised in Fourier spectrum of Field probe, signal port and voltage probe. It represents the Cherenkov effect To mitigate the instability of Wave-particle interaction. The material particle Permittivity frequency dependence is $$\epsilon (\omega)= \epsilon_\infty(1- \epsilon_\infty)((1-r)\omega_R /{\omega_R - j\omega  + r\omega_0^2/(\omega_0^2 + j\omega \delta - \omega^2}))$$ The Attenuation is

$$\left\vert A_L/{A_0} \right\vert=$$$$\exp(-\epsilon_r\prime\prime(\omega)\omega L /{c})$$