Longitudinal cooling of non-neutral plasma by energy exchange

The optimal values of Q and Δω (Δω≡ω-Ω) for cooling a pure electron plasma with a microwave bath have been calculated. An electron plasma, which has no internal degree of freedom, cannot be cooled below the temperature of a heat bath. However, longitudinal cooling can be achieved by energy transfer from the poorly cooled longitudinal degree of freedom to the well-cooled (by synchrotron radiation) transverse degree of freedom. To do this, a microwave bath is introduced to the electron plasma. A microwave tuned to a frequency below the gyrofrequency forces electrons moving towards the microwave to absorb a microwave photon. The electrons move up one in Landau state and then lose their longitudinal momenta. In this process, the longitudinal temperature of the electron plasma decreases. On the basis that the perpendicular temperature is below the Landau temperature of the plasma, we set up two level transition equations and then derive a Fokker-Planck equation from them. With the aid of a finite element method (FEM) code for the equation, the cooling times for several values of the magnetic field, the microwave cavity (Q), and the relative detuning frequency from the gyrofrequency (Δω) are calculated. Thus optimal values of the microwave cavity and the detuning frequency for longitudinal cooling of a strongly magnetized electron plasma with a microwave bath have been found. By applying these optimal values with an appropriate microwave intensity, the best cooling can be obtained. For an electron plasma magnetized to 10 T, the cooling time to the solid state is approximately two hours