Relativistic Cyclotron Motion in a Polarized Electric Field

The study of the relativistic dynamics of charged particles moving in electric and magnetic fields is of prime importance in accelerator and plasma physics, where such devices as the cyclotron, tokamak, and free-electron laser are frequently encountered [1,2]. The recent surge of interest in this study stems partly from theoretical and experimental findings that such particles are capable of exhibiting chaotic behavior. Systems that have recently been found to exhibit chaos include electrons undergoing relativistic cyclotron motion [3–8], electrons moving at relativistic velocities through a wiggler in a free-electron laser device [9–15], and particles oscillating at relativistic velocities under the influence of a harmonic or nonharmonic potential [16,17]. These studies are not just of academic interest; identifying the cause of and finding a way of suppressing or controlling such “relativistic chaos” is directly linked to the practical problem of improving the performance of the device being considered, whether it be the cyclotron, the tokamak or the free-electron laser. Relativistic cyclotron motion is a subject of interest also in atomic physics, as it occurs, for example, in the Penning trap. Despite the fact that one usually deals with only weakly relativistic electrons in the Penning trap, some interesting relativistic effects, such as bistable hysteresis, were observed to occur in the cyclotron motion there [18,19].