November 2025 - A Paper About A Penning Trap Experiment
On my (largely unsuccessful) search for a paper that shows the construction of a Penning Trap as it was used, I found one focused directly about Electron Penning Traps. This may not be exactly what I'm looking for, but it's short and it includes actual measurements and a sketch. These are study notes, so I'm not including the sketch here, but I assure you, it's nice.
"Observation of Spherical Focus in an Electron Penning Trap" by Mitchell, Schauer and Barnes is mostly a study of the Penning Trap's function. It acknowledges the use of the Penning Trap in confining non-neutral plasma. The experiment uses anode rings of 6mm inner diameter, with 400 μm diameter holes, allowing for e- injection via the lower-end cathode, through which low-angular momentum e- are sent. The beam diameter is about 200 μm. The trap voltage ranges from 500 V to 10 kV with the corresponding magnetic fields ranging from 0.05 T to 0.22 T. I will likely use the upper ends of these operations. Above the trap is a microchannel plate/phosphor screen (MCP), so electrons can be transported through an opening in the upper end cathode and two drift tubes to the MCP. The MCP can either count particles or screen images using a CCD camera.
Measurements of currents to various electrodes can be made. Total current scattered from beam to anode is measured, and the scattered electrons is counted by the MCP. Higher voltage leads to a deeper potential well. At V0, a nearly spherically symmetric state of the trapped particles emerges. It requires the current be above the threshold current.
The way the experiment is constructed, electrons will keep filling the potential well, until a steady-state equilibrium is reached within it. Said steady-state equilibrium includes a dense central core of electrons. This is only possible for spherical states. This core density can vastly outpace the Brillouin density, a theoretical limit on particle concentration of static traps.