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Magnetically insulated transmission lines (MITLs) are used to deliver tens of MA to a Z-pinch load. The MITLs suffer current losses due to contaminant plasma located in the anode–cathode gap which is swept toward the load along the power flow. The swept up contaminant plasma can deposit mass and energy onto the load resulting in deformations or the seeding of macroscopic instabilities. This paper discusses 2D fully kinetic simulations of the contaminant plasma evolution which predict the current losses and the flux of mass and energy onto the load. The effects of a dynamic, i.e., imploding, load are shown to increase both the current loss and the mass and energy flux. The MITL used is a conical, radially converging design which is a feature common to MA-scale Z-pinch accelerators.

Kinetic simulations of Sandia National Laboratories’ Z machine are conducted to understand particle transport in the highly magnetized environment of a multi-MA accelerator. Joule heating leads to the rapid formation of electrode surface plasmas. These plasmas are implicated in reducing accelerator efficiency by diverting current away from the load [M.R. Gomez et al., Phys. Rev. Accel. Beams 20, 010401 (2017)PRABCJ2469-988810.1103/PhysRevAccelBeams.20.010401, N. Bennett et al., Phys. Rev. Accel. Beams 22, 120401 (2019)PRABCJ2469-988810.1103/PhysRevAccelBeams.22.120401]. The fully-relativistic, electromagnetic simulations presented in this paper show that particles emitted in a space-charge-limited manner, in the absence of plasma, are magnetically insulated. However, in the presence of plasma, particles are transported across the magnetic field in spite of being only weakly collisional. The simulated cross-gap currents are well-approximated by the Hall current in the generalized Ohm’s law. The Hall conductivities are calculated using the simulated particle densities and energies, and the parameters that increase the Hall current are related to transmission line inductance. Analogous to the generalized Ohm’s law, we extend the derivation of the magnetized diffusion coefficients to include the coupling of perpendicular components. These yield a Hall diffusion rate, which is equivalent to the empirical Bohm diffusion.

The objectives of this tutorial are as follows: 1) to help students and researchers develop a basic understanding of how pulsed-power systems are used to create high-energy-density (HED) matter; 2) to develop a basic understanding of a new, compact, and efficient pulsed-power technology called linear transformer drivers (LTDs); 3) to understand why LTDs are an attractive technology for driving HED physics (HEDP) experiments; 4) to contrast LTDs with the more traditional Marx-generator/pulse-forming-line approach to driving HEDP experiments; and 5) to briefly review the history of LTD technology as well as some of the LTD-driven HEDP research presently underway at universities and research laboratories across the globe. This invited tutorial is part of the Mini-Course on Charged Particle Beams and High-Powered Pulsed Sources, held in conjunction with the 44th International Conference on Plasma Science in May of 2017.

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.

Two-dimensional electromagnetic (EM) particle-in-cell (PIC) simulations of a radial magnetically-insulated-transmission-line are presented and compared to the model of E. M. Waisman, M. P. Desjarlais, and M. E. Cuneo [Phys. Rev. Accel. Beams 22, 030402 (2019)PRABCJ2469-988810.1103/PhysRevAccelBeams.22.030402 in the “high-enhancement” (WDC-HE) limit. The simulations use quasi-equilibrium current and voltage values based on the Sandia National Laboratories Z accelerator, with prescribed injection of an electron sheath that gives electron density profiles qualitatively similar to those used in the WDC-HE model. We find that the WDC-HE model accurately predicts the quasiequilibrium ion current losses in the EM PIC simulations for a wide range of current and voltage values. For the case of two ion species where one is magnetically insulated by the ambient magnetic field and the other is not, the charge of the lighter insulated species in the anode-cathode gap can modify the electric field profile, reducing the ion current density enhancement for the heavier ion species. On the other hand, for multiple ion species, when the lighter ions are not magnetically insulated and are a significant fraction of the anode plasma, they dominate the current loss, producing loss currents which are a significant fraction of the lighter ion WDC values. The observation of this effect in the present work is new to the field and may significantly impact the analysis of ion current losses in the Z machine inner MITL and convolute.

A challenge for the TW-class accelerators driving $Z$-pinch experiments, such as Sandia National Laboratories' $Z$ machine, is to efficiently couple power from multiple storage banks into a single multi-MA transmission line. The physical processes that lead to current loss are identified in new large-scale, multidimensional simulations of the $Z$ machine. Kinetic models follow the range of physics occurring during a pulse, from vacuum pulse propagation to charged-particle emission and magnetically-insulated current flow to electrode plasma expansion. Simulations demonstrate that current is diverted from the load through a combination of standard transport (uninsulated charged-particle flows) and anomalous transport. Standard transport occurs in regions where the electrode current density is a few $1{0}^{4}\ensuremath{-}{10}^{5}\text{ }\text{ }\mathrm{A}/{\mathrm{cm}}^{2}$ and current is diverted from the load via transport without magnetic insulation. In regions with electrode current density $g{10}^{6}\text{ }\text{ }\mathrm{A}/{\mathrm{cm}}^{2}$, electrode surface plasmas develop velocity-shear instabilities and a Hall-field-related transport which scales with electron density and may, therefore, lead to increased current loss.

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 ($l3\text{ }\text{ }\mathrm{cm}$) 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.

Pulsed power accelerators compress electrical energy in space and time to provide versatile experimental platforms for high energy density and inertial confinement fusion science. The 80-TW “Z” pulsed power facility at Sandia National Laboratories is the largest pulsed power device in the world today. Z discharges up to 22 MJ of energy stored in its capacitor banks into a current pulse that rises in 100 ns and peaks at a current as high as 30 MA in low-inductance cylindrical targets. Considerable progress has been made over the past 15 years in the use of pulsed power as a precision scientific tool. This paper reviews developments at Sandia in inertial confinement fusion, dynamic materials science, x-ray radiation science, and pulsed power engineering, with an emphasis on progress since a previous review of research on Z in Physics of Plasmas in 2005.

We have developed a conceptual design of a next-generation pulsed-power accelerator that is optimized for advanced high-energy-density-physics experiments. The prime power source of the machine consists of 210 impedance-matched Marx generators (IMGs). Each IMG drives a 150-ns-long coaxial-transmission-line impedance transformer. The coaxial lines provide a minimum of 300 ns of transit-time isolation between each pair of IMGs. The lines in turn drive six radial-transmission-line impedance transformers, which transport the power generated by the IMGs to a six-level vacuum-insulator stack. The stack is connected to six conical outer magnetically insulated vacuum transmission lines (MITLs); these are joined in parallel at a 12-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 load. Since the accelerator would be the largest and most-powerful pulsed-power machine developed to date, we refer to it as Jupiter. The conceptual design of Jupiter is 72 m in diameter, stores 140 MJ of electrical energy, and generates 960 TW of peak electrical power at the output of the IMG system. The design delivers 2700 TW, 67 MA, and 9.2 MJ in a 110-ns pulse to a 0D magnetized-liner inertial-fusion (MagLIF) target. The principal goal of the design is to achieve high-yield thermonuclear fusion; i.e., a fusion yield that exceeds the energy initially stored by the accelerator's capacitors.

The Z pulsed-power generator at Sandia National Laboratories drives high energy density physics experiments with load currents of up to 26 MA. Z utilizes a double post-hole convolute to combine the current from four parallel magnetically insulated transmission lines into a single transmission line just upstream of the load. Current loss is observed in most experiments and is traditionally attributed to inefficient convolute performance. The apparent loss current varies substantially for z-pinch loads with different inductance histories; however, a similar convolute impedance history is observed for all load types. This paper details direct spectroscopic measurements of plasma density, temperature, and apparent and actual plasma closure velocities within the convolute. Spectral measurements indicate a correlation between impedance collapse and plasma formation in the convolute. Absorption features in the spectra show the convolute plasma consists primarily of hydrogen, which likely forms from desorbed electrode contaminant species such as H_{2}O, H_{2}, and hydrocarbons. Plasma densities increase from 1×10^{16} cm^{−3} (level of detectability) just before peak current to over 1×10^{17} cm^{−3} at stagnation (tens of ns later). The density seems to be highest near the cathode surface, with an apparent cathode to anode plasma velocity in the range of 35–50 cm/μs. Similar plasma conditions and convolute impedance histories are observed in experiments with high and low losses, suggesting that losses are driven largely by load dynamics, which determine the voltage on the convolute.

Fusion yields from dense, $Z$-pinch plasmas are known to scale with the drive current, which is favorable for many potential applications. Decades of experimental studies, however, show an unexplained drop in yield for currents above a few mega-ampere (MA). In this work, simulations of DD $Z$-Pinch plasmas have been performed in 1D and 2D for a constant pinch time and initial radius using the code Lsp, and observations of a shift in scaling are presented. The results show that yields below 3 MA are enhanced relative to pure thermonuclear scaling by beamlike particles accelerated in the Rayleigh-Taylor induced electric fields, while yields above 3 MA are reduced because of energy lost by the instability and the inability of the beamlike ions to enter the pinch region.

Here, 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 acceleratormore » 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.« less

We have studied the parametric interaction between a fast magnetosonic (FM) mode and a lower oblique resonance (LOR) mode in a cold, magnetized plasma using a kinetic, three dimensional Particle-in-Cell simulation code called the Large Scale Plasma. The FM mode is excited with a loop antenna driven at a frequency below the lower hybrid frequency (ωLH), while the LOR is excited at a frequency above ωLH. For historical purposes explained in the Introduction, we call the antennas which drive the FM mode and LOR mode Extremely Low Frequency (ELF) and Very Low Frequency (VLF) antennas, respectively. The antennas are modeled as magnetic dipoles (ρant = 0) and are assigned a time varying current density within a finite sized current loop. The VLF and ELF antennas are driven at 10 A and 3 A, respectively. The parametric interaction is excited with a combined ELF/VLF antenna (which we call a parametric antenna) and includes both antennas driven simultaneously in the same simulation domain. We show that the parametric antenna non-linearly excites electromagnetic (EM) whistler waves to a greater extent than the VLF antenna alone. We also show that the parametric excitation of EM whistler waves leads to greater emitted EM power (measured in Watts) compared with a VLF antenna alone.We have studied the parametric interaction between a fast magnetosonic (FM) mode and a lower oblique resonance (LOR) mode in a cold, magnetized plasma using a kinetic, three dimensional Particle-in-Cell simulation code called the Large Scale Plasma. The FM mode is excited with a loop antenna driven at a frequency below the lower hybrid frequency (ωLH), while the LOR is excited at a frequency above ωLH. For historical purposes explained in the Introduction, we call the antennas which drive the FM mode and LOR mode Extremely Low Frequency (ELF) and Very Low Frequency (VLF) antennas, respectively. The antennas are modeled as magnetic dipoles (ρant = 0) and are assigned a time varying current density within a finite sized current loop. The VLF and ELF antennas are driven at 10 A and 3 A, respectively. The parametric interaction is excited with a combined ELF/VLF antenna (which we call a parametric antenna) and includes both antennas driven simultaneously in the same simulation domain. We show that the paramet...

Numerical simulations of a vacuum post-hole convolute driven by magnetically insulated vacuum transmission lines (MITLs) are used to study current losses due to charged particle emission from the MITL-convolute-system electrodes. This work builds on the results of a previous study [E. A. Madrid et al. Phys. Rev. ST Accel. Beams 16, 120401 (2013)PRABFM1098-440210.1103/PhysRevSTAB.16.120401] and adds realistic power pulses, Ohmic heating of anode surfaces, and a model for the formation and evolution of cathode plasmas. The simulations suggest that modestly larger anode-cathode gaps in the MITLs upstream of the convolute result in significantly less current loss. In addition, longer pulse durations lead to somewhat greater current loss due to cathode-plasma expansion. These results can be applied to the design of future MITL-convolute systems for high-current pulsed-power systems.