  The self-consistent problem of the wave and particle spectrum is formulated
and solved for acceleration of particles in a homogeneous magnetic field that
varies periodically with time. It follows from the obtained solutions that when
account is taken of the synchrotron radiation, the diffusion coefficient Do of
ultrarelativistic electrons does not differ from the Fermi value. An expression
is obtained for the minimum concentration of the accelerated particles, at
which the cyclotron instability ensures the scattering necessary for effective
acceleration.
