Quasiclassical distribution function of electrons in a homogeneous magnetic field

Vlasov's equation is used to find the classical nonrelativistic and relativistic distribution functions that describe an electron beam of bounded radius in a homogeneous magnetic field. In the quasiclassical approximation, by means of the exact wave functions of an electron in a homogeneous magnetic field, the quantum relativistic distribution function with allowance for the electron spin is found. The mean physical quantities that characterize the radially bounded electron beam are found as functions of the temperature and electron spin.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 50–56, July, 1976.It is a pleasant duty to thank Professor V. G. Bagrov for discussing the results.