Analysis and modeling of densification during startup of PFRC-2

Understanding the startup behavior of the PFRC-2 by odd-parity rotating magnetic fields is critical to producing discharges at high magnetic fields with high density ($n_{e}>10^{13}$/cm$^{3}$), temperature ($T_{e},T_{i}>100$~eV), absorbed power fraction ($>0.5$), and reproducibility. Experiments on the PFRC-2 have shown the existence of two distinct phases of density rise: a slow rise to $1-3\times 10^{11}$/cm$^{3}$ ($\tau\sim 150$~$\mu$s) followed by an abrupt transition to a rapid brief density rise to $5\times 10^{12}$/cm$^{3}$ characterized by $\tau\sim 5-7$~$\mu$s. At lower field, higher pressure, and higher power conditions, rapid densification phase may occur in less than 50~$\mu$s; the opposite conditions result in a longer delay, exceeding 3~ms for certain gases. The variation in delay before the onset of rapid densification increases with the delay time. 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. Empirical scaling laws and implications for high-power PFRC-2 operation and future PFRC-based reactor design will be discussed.