Molecular Dynamics Simulations of Temperature Relaxation in Non-Neutral Plasmas Relevant to Antimatter Experiments

TL;DR

This work tests a recently proposed theory of temperature relaxation in strongly magnetized, two-component non-neutral plasmas using first-principles MD simulations. By combining non-equilibrium MD (MD-N) and Green-Kubo MD (MD-GK), the authors extract multiple relaxation and coupling rates that govern the evolution of four characteristic temperatures: $T_{i\parallel}$, $T_{i\perp}$, $T_{e\parallel}$, and $T_{e\perp}$. The results show that magnetization accelerates parallel energy exchange while suppressing perpendicular relaxation, with electron isotropization decaying exponentially as the magnetization grows; ion-electron equilibration is enhanced at moderate magnetization and plateaus at strong magnetization. The findings validate the multistage relaxation picture and have direct relevance for cooling schemes in antimatter experiments, such as those in Penning-Malmberg traps, where precise control of temperature anisotropy can impact antihydrogen production. The Green-Kubo framework also provides a route to access all relevant rates from equilibrium fluctuations, informing future experimental and theoretical work on magnetized, two-component plasmas.

Abstract

An important process for antimatter experiments is the cooling of particles in a Penning-Malmberg trap to experimentally useful temperatures. A non-neutral plasma of one species (e.g. antiprotons) can be collisionally cooled on another colder species (e.g. electrons). Modeling temperature relaxation in these devices is challenging from a plasma physics perspective because the particles are strongly magnetized (the gyrofrequency exceeds the plasma frequency). Recently, a theoretical model was proposed to describe the temperature evolution in these conditions, predicting a multistep relaxation process where temperatures parallel to the magnetic field relax much faster than perpendicular to it. Here, this model is tested using molecular dynamics simulations. Two analysis methods are applied: one based on an imposed temperature difference, and the other based on a Green-Kubo relation. The results of the simulations support the theoretical predictions. This work extends previous studies of temperature anisotropy relaxation in one-component non-neutral plasmas to the two-component systems relevant to trapped antimatter experiments.

Figures (6)

• Figure 1: Temperature evolution from MD simulations (blue, orange, green, and red) averaged over several runs, compared with the numerical evaluation of the model from Ref. josePRE2025 (violet, white, pink, and black). Shaded regions indicate the standard deviation from the run-to-run average.
• Figure 2: The ion-electron relaxation rate $(\eta^{ie})$ is displayed as a function of electron magnetization strength $(\beta_e)$. The blue curve represents the theory. The triangles are from MD-N. The circles are from MD-GK. The cyan arrow shows a previous unmagnetized stopping power MD-N simulation bernstein2022method. The black arrow shows a previous unmagnetized MD-N simulation Dimonte_PRL_2008.
• Figure 3: Three rates related to electron isotropization are shown: the electron isotropization rate $(\eta^e)$ (blue), the electron isotropization rate due to electron-electron collisions $(\eta^{e,e|e})$ (purple-pink), and the rate predicted by the reduced model in Eq. (\ref{['eq: DeltadTe_slow_full']}) ($\eta^{e}- \rho^{ie}_{e}$) (orange). Model predictions are shown as solid or dashed lines. Filled in markers display new ion-electron MD data, where MD-GK are circles and MD-N are triangles. Also shown with hollow markers are results of previously published work for a one-component plasma that used a similar MD-N method: Ref. Baalrud_PRE_2017 (triangles) for a magnetized plasma, and Ref. Baalrud_CPP_2017 (pink arrow) for an unmagnetized plasma, and results using an MD-GK method jose_submitted_2025 (circles).
• Figure 4: Ion isotropization rate as a function of electron magnetization strength $\beta_e$ (bottom axis) and ion magnetization strength $\beta_i$ (top axis). The MD–GK results (blue circles) are compared with the theoretical model predictions for ion isotropization $\eta^i$ (blue line). Also shown are the model prediction for ion isotropization due to ion-ion collisions (purple line) and a previous unmagnetized MD study (pink arrow) for ion isotropization in a pure ion plasma Baalrud_CPP_2017.
• Figure 5: Time correlation functions as a function of time in electron plasma periods at a magnetization strength of $\beta_e=8.7$. Autocorrelations are normalized to their initial value: ion-electron (dashed red), ion (dashed blue), and electron (dashed purple). The cross-correlation between the ion-electron temperature difference and the electron anisotropy is normalized to its maximum value (pink line).