Particle trapping with an rf cavity

It is in principle possible to trap charged particles in an rf cavity. In this note the authors calculate the trapping mechanism of the field pattern given by (1). The trapping occurs for either sign of the charge of the particles. The mode pattern (1) traps particles around the node point (0,0,0). Such a trapping mechanism is of course considered favorable for a particle trap. On the other hand, it may also happen that undesirable stray particles are trapped at nodes of an rf device, which then perturbs the normal operation of an accelerator. Such trappings are then undesirable and are to be avoided