Modelling of electron heating in a Penning-Malmberg trap by means of a chaotic map

We have previously observed the production of an electron plasma in a Penning-Malmberg trap under ultra-high vacuum conditions by means of an original method, namely a radio-frequency excitation of a few Volt amplitude applied on one of the trap electrodes. We have explained the origin of such plasma formation as a consequence of a Fermi-like heating of free electrons in the residual gas, which in turn can cause gas ionization. The heating of a single electron has been modelled in terms of a two-dimensional, area-preserving map, where the particle bounces within a square potential well and an intermediate, oscillating square barrier represents the RF drive. Similar mappings have been used to describe a variety of physical situations. Even in its simplicity, this model shows a significant predictive power. The low-energy part of the Poincaré plot includes both stable and chaotic regions, where heating up to ionization energies is achievable. We perform an analysis of the map in order to define the conditions for an efficient heating. Chaotic properties and scaling laws are studied as a function of the control parameters, e.g. width of the potential well, barrier amplitude, frequency and position. These define a series of different cases that are evaluated and compared: RF drive with zero and non-zero static potential barrier; Different oscillation functions; Creation of one, two and three trapping regions. The effects on the ionization of a background gas, introducing a weak dissipation in the map, are also investigated using a Monte Carlo scheme.