STABLE TRAJECTORY OF CHARGED-PARTICLE IN PAUL TRAP - APPLICATION OF BAND THEORY

The purpose of this study is to develop a theory for the motion of a c harged particle in a trap with general rf trapping field. We first sho w that the equations of motion for a charged particle in the trap are equivalent to Scbrodinger equation for a one-dimensional system with p eriodic potential. Applying the band theory to the equation, we analyz e the region in a so-called (a, q) parameter-space with stable traject ory. It is shown that the stable region is roughly divided into two re gimes, namely the nearly free regime and the tight-binding regime. The a-q relations for the boundaries of each regime are obtained in expli cit formula. Using these results, we discuss the effects of the wavefo rm of the rf trapping field on the motion of a charged particle, aimin g to obtain a wider stable region in the parameter space for experimen tal studies.