Ideal Gas Approximation for an Ion Cloud in a Penning Trap

Penning t raps are very useful experimental devices wherever high precision measurements require spatial confinement of charged particles over prolonged periods of time. (For general reviews see [1] and [2].) Some experiments are done with single (or very few) particles, but usually one has to deal with a low density cloud of charged particles containing on the order of 10 to 10 particles. The analysis of a specific experiment requires unders tanding not only of the individual particle orbi ts [3], but also of the collective properties of the particle cloud. O n e expects that over a period of t ime a state of equi l ibr ium is at tained, which can be studied using s t anda rd methods of statistical physics [4]. F o r a low density cloud it seems reasonable to assume that the particles move mainly independently of each other, except for occasional close encounters and the mutua l C o u l o m b repulsion of the particles. O n the one hand , by causing an exchange of energy, m o m e n t u m and angular m o m e n t u m between the particles, these interact ions are ins t rumental in establishing a thermal equil ibr ium in the particle cloud, on the other hand, they may be considered as only a negligible per tu rba t ion to the average particle mot ion, provided the t ime average of the interaction potentials is small compared to the average energy of a single charged particle. F o r particle densities which are low enough for these assumpt ions to hold, one may a t tempt a description of the particle cloud as an ideal gas of non-interact ing particles in thermal equilibrium. F o r reasons of simplicity we assume an ideal Penning t r ap (no anha rmon ic per turbat ions) and the absence of a background of neutral particles.