The dynamics of electrode heating, electron transport, and surface contaminant plasma evolution have been studied numerically in a series of publications.1-4 These dynamics can lead to the shunting of current before reaching the Z-pinch load, thus degrading load performance. The impact of metal electrode material in the inner Magnetically Insulated Transmission Line (MITL) near the load could also be significant particularly for next generation high current accelerators. The combined densities of contaminant and electrode plasma can easily exceed 10 19 cm-3 with >> Mega-Gauss magnetic fields.

Hybrid-implicit particle-in-cell (PIC) algorithms permit the simulation of complex problems involving both kinetic and fluid plasma regimes over large spatial and temporal scales. Fluid electrons can be computationally fast where and when fluid assumptions are valid. Additional flexibility is obtained if discrete PIC macroparticles, with velocities advanced by either fluid or kinetic equations, are permitted to dynamically migrate between the two descriptions based on phase space criteria. Ideally, these migrations result in energetic particles treated kinetically and dense thermal plasma particles as a fluid. With an energy-conserving particle advance, resolution of the plasma Debye length is not required for numerical accuracy or stability. For pulsed-power applications, the simulation time step is usually constrained by the electron cyclotron frequency, not the more restrictive plasma frequency. A new implicit technique permits accurate particle orbits even at highly underresolved cyclotron frequencies. Thus, greater temporal and spatial scales can be accurately modeled relative to conventional PIC techniques. In this paper, we describe the hybrid PIC technique and fully electromagnetic, hybrid simulations of plasma evolution and current shunting in an idealized accelerator designed for driving a $Z$-pinch load. The dynamics of electrode heating, electron transport, and surface contaminant evolution are studied in a series of relativistic hybrid-implicit PIC simulations. These dynamics can lead to the shunting of current before reaching the $Z$-pinch load, thus degrading load performance. Examining two previously published power flow problems, we compare results from fully kinetic, multifluid, and hybrid kinetic-fluid simulations and discuss the computational performance of these three options. The key thrust of the work is to identify possible computational acceleration, through hybrid methods, required for accelerator understanding and design.

The dynamics of electrode heating, sheath flow, and contaminant plasma evolution in Sandia National Laboratories' high-power Z accelerator is studied in a series of 2D relativistic particle-in-cell simulations. These dynamics can lead to the shunting of current before reaching the Z pinch load, thus degrading load performance. Previous work has focused on current diverted in the upstream magnetically insulated transmission lines ( MITLs) and post-hole convolute regions of Z. In these regions, losses were found to scale strongly with load impedance as well as the system vacuum and were calculated to be as high as 1-2 MA. Downstream from the convolute region in Z, current measurement is problematic, leading to a lack of understanding of the loss mechanisms in the small radius (< 3 cm) MITL feeding the load. In this paper, we present the first ever 2D fully electromagnetic, fully kinetic simulations of plasma evolution and current shunting in the inner MITL region of Z. This region is defined by a radially converging MITL, which is a feature common to MA-scale Z pinch accelerators. The electrodes in this region are rapidly heated via mainly Ohmic or skin depth heating. Plasmas quickly form, and surface contaminants are liberated as the temperatures exceed 700 K. Instabilities lead to a rapid plasma density fill of the inner MITL and subsequent current loss. The instability growth is likely due to the resistivity of the magnetized electrode plasma. The plasma, after exceeding 10(15) cm(-3) density, leads to an additional 1-2 MA current loss in the inner MITL region.

The dynamics of electrode heating, sheath flow, and contaminant plasma evolution in Sandia National Laboratories' high-power $Z$ accelerator is studied in a series of 2D relativistic particle-in-cell simulations. These dynamics can lead to the shunting of current before reaching the $Z$ pinch load, thus degrading load performance. Previous work has focused on current diverted in the upstream magnetically insulated transmission lines (MITLs) and post-hole convolute regions of $Z$. In these regions, losses were found to scale strongly with load impedance as well as the system vacuum and were calculated to be as high as 1--2 MA. Downstream from the convolute region in $Z$, current measurement is problematic, leading to a lack of understanding of the loss mechanisms in the small radius ($<3\text{ }\text{ }\mathrm{cm}$) MITL feeding the load. In this paper, we present the first ever 2D fully electromagnetic, fully kinetic simulations of plasma evolution and current shunting in the inner MITL region of $Z$. This region is defined by a radially converging MITL, which is a feature common to MA-scale $Z$ pinch accelerators. The electrodes in this region are rapidly heated via mainly Ohmic or skin depth heating. Plasmas quickly form, and surface contaminants are liberated as the temperatures exceed 700 K. Instabilities lead to a rapid plasma density fill of the inner MITL and subsequent current loss. The instability growth is likely due to the resistivity of the magnetized electrode plasma. The plasma, after exceeding ${10}^{15}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}3}$ density, leads to an additional 1--2 MA current loss in the inner MITL region.

The concept of a parametric antenna in ionospheric plasma is analyzed. Such antennas are capable of exciting electromagnetic radiation fields, specifically the creation of whistler waves generated at the very low frequency (VLF) range, which are also capable of propagating large distances away from the source region. The mechanism of whistler wave generation is considered a parametric interaction of quasi-electrostatic whistler waves (also known as low oblique resonance (LOR) oscillations) excited by a conventional loop antenna. The interaction of LOR waves with quasi-neutral density perturbations in the near field of an antenna gives rise to electromagnetic whistler waves on combination frequencies. It is shown in this work that the amplitude of these waves can considerably exceed the amplitude of whistler waves directly excited by a loop. Additionally, particle-in-cell simulations, which demonstrate the excitation and spatial structure of VLF waves excited by a loop antenna, are presented. Possible applications including the wave-particle interactions to mitigate performance anomalies of low Earth orbit satellites, active space experiments, communication via VLF waves, and modification experiments in the ionosphere will be discussed.

A novel algorithm for the simulation of cathode plasmas in particle-in-cell codes is described and applied to investigate cathode plasma evolution in magnetically insulated transmission lines (MITLs). The MITL electron sheath is modeled by a fully kinetic electron species. Electron and ion macroparticles, both modeled as fluid species, form a dense plasma which is initially localized at the cathode surface. Energetic plasma electron particles can be converted to kinetic electrons to resupply the electron flux at the plasma edge (the “effective” cathode). Using this model, we compare results for the time evolution of the cathode plasma and MITL electron flow with a simplified (isothermal) diffusion model. Simulations in 1D show a slow diffusive expansion of the plasma from the cathode surface. But in multiple dimensions, the plasma can expand much more rapidly due to anomalous diffusion caused by an instability due to the strong coupling of a transverse magnetic mode in the electron sheath with the expanding resistive plasma layer.

We have developed conceptual designs of two petawatt-class pulsed-power accelerators: Z 300 and Z 800. The designs are based on an accelerator architecture that is founded on two concepts: single-stage electrical-pulse compression and impedance matching [Phys. Rev. ST Accel. Beams 10, 030401 (2007)]. The prime power source of each machine consists of 90 linear-transformer-driver (LTD) modules. Each module comprises LTD cavities connected electrically in series, each of which is powered by 5-GW LTD bricks connected electrically in parallel. (A brick comprises a single switch and two capacitors in series.) Six water-insulated radial-transmission-line impedance transformers transport the power generated by the modules to a six-level vacuum-insulator stack. The stack serves as the accelerator's water-vacuum interface. The stack is connected to six conical outer magnetically insulated vacuum transmission lines (MITLs), which are joined in parallel at a 10-cm radius by a triple-post-hole vacuum convolute. The convolute sums the electrical currents at the outputs of the six outer MITLs, and delivers the combined current to a single short inner MITL. The inner MITL transmits the combined current to the accelerator's physics-package load. Z 300 is 35 m in diameter and stores 48 MJ of electrical energy in its LTD capacitors. The accelerator generates 320 TW of electrical power at the output of the LTD system, and delivers 48 MA in 154 ns to a magnetized-liner inertial-fusion (MagLIF) target [Phys. Plasmas 17, 056303 (2010)]. The peak electrical power at the MagLIF target is 870 TW, which is the highest power throughout the accelerator. Power amplification is accomplished by the centrally located vacuum section, which serves as an intermediate inductive-energy-storage device. The principal goal of Z 300 is to achieve thermonuclear ignition; i.e., a fusion yield that exceeds the energy transmitted by the accelerator to the liner. 2D magnetohydrodynamic (MHD) simulations suggest Z 300 will deliver 4.3 MJ to the liner, and achieve a yield on the order of 18 MJ. Z 800 is 52 m in diameter and stores 130 MJ. This accelerator generates 890 TW at the output of its LTD system, and delivers 65 MA in 113 ns to a MagLIF target. The peak electrical power at the MagLIF liner is 2500 TW. The principal goal of Z 800 is to achieve high-yield thermonuclear fusion; i.e., a yield that exceeds the energy initially stored by the accelerator's capacitors. 2D MHD simulations suggest Z 800 will deliver 8.0 MJ to the liner, and achieve a yield on the order of 440 MJ. Z 300 and Z 800, or variations of these accelerators, will allow the international high-energy-density-physics community to conduct advanced inertial-confinement-fusion, radiation-physics, material-physics, and laboratory-astrophysics experiments over heretofore-inaccessible parameter regimes.

The interaction of two lasers with a difference frequency near that of the ambient plasma frequency produces beat waves that can resonantly accelerate thermal electrons. These beat waves can be used to drive electron current and thereby embed magnetic fields into the plasma [Welch et al., Phys. Rev. Lett. 109, 225002 (2012)]. In this paper, we present two-dimensional particle-in-cell simulations of the beat-wave current-drive process over a wide range of angles between the injected lasers, laser intensities, and plasma densities. We discuss the application of this technique to the magnetization of dense plasmas, motivated in particular by the problem of forming high-β plasma targets in a standoff manner for magneto-inertial fusion. The feasibility of a near-term experiment embedding magnetic fields using lasers with micron-scale wavelengths into a ∼1018 cm−3-density plasma is assessed.

We describe a particle advance algorithm for particle-in-cell simulation of highly magnetized charged particles that relaxes the time step constraint due to cyclotron motion.The method preserves the correct cyclotron radius for large time steps and corrects for magnetic field gradients without requiring explicit calculation of the particle magnetic moment.Application of the algorithm is illustrated with electron and ion single particle orbit calculations in a field reversed configuration with rotating magnetic fields.This technique is efficient and applicable to massively parallel simulation.

Three-dimensional fully electromagnetic (EM) models are being used to optimize the design of a petawatt-class pulsepower accelerator.1,2 In this design, a cylindrical array of linear-transformer-driver (LTD) modules3 feed power into radial-transmission-line impedance transformers followed by a vacuum line and convolute section which delivers the combined current to the load.1 In the limit of small ratio of pulse width to one-way wave transit time, we have previously demonstrated that transport efficiency is maximized when the impedance profile is exponential but deviates for increasing ratio.4 We build on that result here with the construction of a virtual accelerator that includes a 3D EM model of a realistic next-generation design for the accelerator's impedance transformer, and circuit models for the LTD drive circuits, vacuum magnetically insulated transmission lines, and load. Variable timing for each LTD module will enable pulse shaping.

A frequency-dependent impedance model for laminated ferromagnetic cores is presented and analyzed. The model assumes a multiple-winding ferromagnetic induction core composed of multiple thin layers with linear material response. This model builds on the analysis presented by Rose et al. [Phys. Rev. ST Accel. Beams 13, 090401 (2010)], that determined an equivalent time-dependent resistance that was used to successfully model the loss currents in a linear transformer device cavity containing ferromagnetic cores. The new core impedance model is more general and has been implemented as a surface-impedance boundary condition [K. S. Oh and J. E. Schutt-Aine, IEEE Trans. Antennas Propag. 43, 660 (1995)] which is suitable for use in multidimensional finite-difference time-domain codes.