The space cyclotron autoresonance interaction of an electron beam with microwaves of TE102 rectangular mode is simulated. It is shown that in these conditions the beam electrons can achieve energies which are sufficient to generate hard x-rays. The physical model consists of a rectangular cavity fed by a magnetron oscillator through a waveguide with a ferrite isolator, an iris window and a system of dc current coils which generates an axially symmetric magnetic field. The 3D magnetic field profile is that which maintains the electron beam in the space autoresonance regime. To simulate the beam dynamics, a full self-consistent electromagnetic particle-in-cell code is developed. It is shown that the injected 12keV electron beam of 0.5A current is accelerated to energy of 225keV at a distance of an order of 17cm by 2.45GHz standing microwave field with amplitude of 14kV/cm.