A Deterministic Ionization Algorithm for the OSIRIS Particle-in-Cell Framework

Abstract

Ionization is critical in the formation and evolution of plasma dynamics; collisional ionization, in particular, is an often overlooked source of electrons when dealing with laser-plasma interactions. Ionization plays a crucial role in understanding the complex plasma kinetics, ranging from cold and sparse astrophysical settings to hot and dense fusion systems. In this paper, we describe the underlying theory for and development, validation, and verification of an extension to the standard particle-in-cell method to include a deterministic algorithm for collisional ionization physics. This algorithm offers improved accuracy, achieving up to two orders of magnitude decrease in the error of the ionization rate calculations, scales linearly in execution time with the number of macro-particles per cell, has been tested for physical correctness and benchmarked against several codes.

Figures (24)

• Figure 1: Plasma properties as a function of temperature and density.
• Figure 2: An example of the cross sections calculated as a function of incident electron kinetic energy. This highlights the individual cross sections of each subshell of neutral argon and the total cross section obtained by summing each subshell. The region magnified by the inset is highlighted with the red box.
• Figure 3: The total cross sections for electron-impact ionization for different charge states of argon, ranging from neutral to +8. Also shown are the average energy lost by electrons and energy transferred to newly ionized electrons for those same charge states. These curves are an example calculation. Only the first eight charge states of argon are shown.
• Figure 4: We calculate the different field ionization rates as a function of electric field strength for various ionization states of argon. \ref{['chap:implementation:eq:bruh_rate', 'chap:implementation:eq:bm_rate', 'chap:implementation:eq:bsi_rate']} were used to calculate the lines labeled Bruhwiler, BM, and BSI, respectively. Overlayed on these individual rate curves is the ionization rate used within Osiris when a user uses field ionization with and without BSI calculations. The vertical lines indicate the transitionary electric fields, $E_{1}$ and $E_{2}$, when using the BSI ionization rate.
• Figure 5: Flow chart of the ionization and collision routines in the PIC loop. During ionization, the ionization rates are calculated and the rates used to advance the ion densities, inject new macro-particles, and, if desired, perform Coulomb collisions. This is done every timestep before returning to the usual set of operations.