Excitation of cyclotron resonances from random fluctuations of stellarator windings

We have investigated the effect of random fluctuation of stellarator windings in a modified betatron accelerator configuration on the dynamics of the beam centroid by solving numerically the equations of motion. Our results show that random displacements of the windings by a few millimeters produce field errors that excite the cyclotron resonance modes that efficiently direct most of the input energy from the axial to transverse direction. These random displacements become completely harmless when their maximum amplitude is reduced to ±0.5 mm. When even such small displacements cannot be attained, the errors that are produced from the mispositioning of the windings may become benign by using a crowbar on the current of the windings before the critical resonance is reached. At l=m (≅ 6 in our case), where l is the value of the cyclotron mode and m is the value of field periods in the device, i.e., when the frequency of the cyclotron mode is equal to the frequency of the strong focusing mode, the beam centroid encounters a potent resonance and locks in at it, even when the windings are located at their ideal positions. If crossing of the l=m=6 mode is desired, using a crowbar on the strong focusing field may be the only remedy. copyright 1996 The American Physical Society