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})$

The dispersion relation

$\epsilon =1-{\frac {{F}\omega ^{2}}{(\omega ^{2}-\omega _{0}^{2})}}$ omega is plasma frequency