Cyclotron Resonance: Method for Determining Collision Cross Sections for Low-Energy Electrons

The Boltzmann transfer equation is solved for the distribution function of electrons moving under the influence of a constant magnetic field and a high-frequency electric field. The power absorbed from the microwave is calculated for the two customary assumptions: (a) constant mean free time, and (b) constant mean free path.For the case of constant mean free time, the absorption spectrum exhibits a "Lorentzian" resonance peak. The half-width of this line gives a direct measure of the collision frequency. Experimental data in support of this result are presented. The constant mean free path assumption leads to integrals which can be evaluated closely by the saddle-point method, and the results are presented in graphical form. It is found that the line shape is not very sensitive to the dependence of the collision cross section upon electron velocity.