Shot-noise-induced lower temperature limit of the nonneutral plasma parallel temperature diagnostic

Abstract We develop a new algorithm to estimate the temperature of a nonneutral plasma in a Penning-Malmberg trap. The algorithm analyzes data obtained by slowly lowering a voltage that confines one end of the plasma and collecting escaping charges, and is a maximum likelihood estimator based on a physically-motivated model of the escape protocol presented in (Beck in Measurement of the magnetic and temperature dependence of the electron-electron anisotropic temperature relaxation rate. PhD thesis, 1990). Significantly, our algorithm may be used on single-count data, allowing for improved fits with low numbers of escaping electrons. This is important for low-temperature plasmas such as those used in antihydrogen trapping. We perform a Monte Carlo simulation of our algorithm, and assess its robustness to intrinsic shot noise and external noise. The assumptions in this paper allow for a lower bound for measurable plasma temperatures of approximately $3\,\mathrm{K}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>3</mml:mn> <mml:mspace/> <mml:mi>K</mml:mi> </mml:math> for plasmas of length $1\,\mathrm{cm}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>1</mml:mn> <mml:mspace/> <mml:mi>cm</mml:mi> </mml:math> , with approximately 100 particle counts needed for an accuracy of $\pm 10 \%$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>±</mml:mo> <mml:mn>10</mml:mn> <mml:mi>%</mml:mi> </mml:math> .