  A gyromonotron is based on energy transformation of the transverse motion of
beam particles into electromagnetic wave radiation. This property is proposed
to be used for electron beam cooling in the accelerator. The energy of the
transverse beam motion is converted into stimulated oscillations of the H111
fundamental mode in the gyromonotron resonator. The H111 mode excitation is the
result of simultaneous excitation of H111 and E010 modes in the resonator of
the given length L, where L is determined by by the start-oscillation condition
for certain values of transit angle {\theta}0 in a monotron. The H111 mode
actually determines the amplitude of the pump mode, which exists at whatever
value of transverse velocities of the beam. We have determined basic
gyromonotron parameters such as the radius R and length L of the resonator, and
the amplitude of the guiding magnetic field Hz for intended radio frequency f1.
