Measurement and simulation of plasma densification in the PFRC-2

Abstract

Understanding the startup behavior of the PFRC-2 by odd-parity rotating magnetic fields ($\textrm{RMF}_{o}$) is essential for consistently producing discharges at high magnetic fields with high density ($n_{e}>10^{13}$/cm$^{3}$), temperature ($T_{e},T_{i}>100$~eV), and absorbed power fraction ($>0.5$). Experiments on the PFRC-2 have indicated the existence of two distinct phases of density rise: a slow rise to a critical density of $n_{c}\sim 1-3\times 10^{11}$/cm$^{3}$ (with $\tau_{slow}\sim 150$~$\mu$s) followed by an abrupt transition to a rapid brief density rise to $n_{e,\textsc{max}} \sim 5\times 10^{12}$/cm$^{3}$ characterized by $\tau_{\textsc{RD}}\sim 5-7$~$\mu$s. At lower field, higher pressure, and higher power conditions, the rapid densification phase may occur at delay ($t_{\textsc{RD}}$) of less than 50~$\mu$s from application of RF power. The opposite conditions tend to result in a longer delay, exceeding 3~ms for certain gases. The variation in delay before the onset of rapid densification also increases with the delay time. To facilitate the analysis of many consecutive discharges with variable $t_{\textsc{RD}}$, an autoencoder neural net has been created and trained to pick out $t_{\textsc{RD}}$ from interferometer waveforms, allowing a form of averaging that preserves the short-time behavior of the rapid densification phase while greatly improving the signal-to-noise ratio. A zero-dimensional global balance model which captures relevant atomic, molecular, and plasma processes has been developed to compare against the experimental data, and guide investigations into which processes drive plasma behavior before and during rapid densification. This model has allowed the elimination of various hypotheses for what physics controls the startup process, and indicates that understanding power absorption in the plasma (and, more generally, power flows in the PFRC-2) is key to understanding the onset of rapid densification. Candidate processes that merit further investigation include skin depth effects and a rapid change in plasma radius; preliminary Langmuir probe experiments also hint at the latter process, but are not conclusive. A 3D PIC code has been used to examine fast ion slowing down physics at the end of the startup phase, yielding results comparable to unmagnetized slowing down theory and providing support for a method of rapid ash, energy, and tritium removal from a PFRC-derived reactor. While the goal was to study startup in the PFRC-2 as well, applying this PIC code to the startup phase itself proved to be out-of-scope for this work. Finally, empirical scaling laws for the PFRC-2 and future devices have been derived, primarily from the experimental data, with a few notable conclusions and implications. Firstly, a very long $t_{\textsc{RD}}$ is predicted for a reactor-scale PFRC-derived device, pointing to a need for reactor designs to incorporate auxiliary systems for heating and/or plasma production during startup. Secondly, full ionization is predicted for high-power PFRC-2 operation, indicating that the PFRC-2 should be able to transition to ion heating under conditions of high power, high magnetic field, and low pre-fill pressure. 3D PIC modeling of rapid densification as well as additional instrumentation on the PFRC-2 to enable a detailed accounting of the power balance during discharges are highlighted as fruitful paths for future investigation of startup in the PFRC-2 and next-step devices.