We report on the improvement of conditions for the rapid start of oscillations in magnetrons by increasing the amplitude of the operating wave that is responsible for the capture of electrons into spokes. This amplitude increase is achieved by using a hollow cathode with longitudinal strips removed, thereby making the cathode transparent to the wave electric field with azimuthal polarization. In addition, an optimal choice of the number and position of cathode strips provide favorable prebunching of the electron flow over the cathode for fast excitation of the operating mode. Particle-in-cell simulations of the A6 magnetron demonstrate these advantages of this novel cathode.