Small-signal gain of Cherenkov radiation generated by hot electrons in the collective regime

The growth characteristics of Cherenkov free-electron laser are studied in the collective regime. In order to take into account the effect of finite electron temperature, the linearized Boltzmann equation is used to describe the electron flow. A realistic model is used to describe the equilibrium electron distribution function. Effect of the electron relaxation is newly taken into account. We show that the electron relaxation and temperature play complementary roles to the growth rate of Cherenkov laser. We also show that our results fit with those of other well-known treatments in the cold beam limit.