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We have conducted 0D, 1D, 2D, and 3D simulations of an idealized coaxial impedance-matched Marx generator (IMG) [Phys. Rev. Accel. Beams 20, 040402 (2017)PRABCJ2469-988810.1103/PhysRevAccelBeams.20.040402]. The 0D calculations were conducted with a four-element circuit model; the 1D, 2D, and 3D calculations were conducted with highly resolved, fully electromagnetic representations. The IMG consists of 30 stages distributed axially and connected electrically in series. Each stage is powered by two bricks separated by 180° and connected electrically in parallel. Each brick comprises two opposite-polarity capacitors in series with a single switch. The bricks drive an internal impedance-matched coaxial transmission line terminated by a resistive load. The simulations neglect effects due to the switch-triggering circuit, the capacitor-charging circuit, external conducting boundaries, and reactive components of the load. We find dimensionality does not significantly affect the electrical power delivered by the IMG to its load: peak load powers estimated by the 0D, 1D, 2D, and 3D simulations agree to within 1%. The 3D calculations demonstrate that electromagnetic power radiated by the bricks, and axial gaps between stages, reduces the peak load power by less than ∼1%. Each simulation assumes the load impedance is 34% above that at which the load power is maximized. Operating an IMG with such an overmatched load offers several advantages while decreasing the peak load power by only 2%. The 0D, 1D, 2D, and 3D models outlined herein could be adapted to assess computationally competing IMG designs, and conduct a variety of numerical IMG experiments, before an IMG is constructed.

Recent studies of power flow and particle transport in multi-MA pulsed-power accelerators demonstrate that electrode plasmas may reduce accelerator efficiency by shunting current upstream from the load [Bennett et al., Phys. Rev. Accel. Beams 24, 060401 (2021)PRABCJ2469-988810.1103/PhysRevAccelBeams.24.060401]. The detailed generation and evolution of these electrode plasmas are examined here using fully relativistic, Monte Carlo particle-in-cell (PIC) and magnetohydrodynamic (MHD) simulations over a range of peak currents (8–48 MA). The PIC calculations, informed by vacuum science, describe the electrode surface breakdown and particle transport prior to electrode melt. The MHD calculations show the bulk electrode evolution during melt. The physical description provided by this combined study begins with the rising local magnetic field that increases the local electrode surface temperature. This initiates the thermal desorption of contaminants from the electrode surface, with contributions from atoms outgassing from the bulk metal. The contaminants rapidly ionize forming a 10^{15}–10^{18} cm^{-3} plasma that is effectively resistive while weakly collisional because it is created within, and rapidly penetrated by, a strong magnetic field (>30 T). Prior to melting, the density of this surface plasma is limited by the concentration of absorbed contaminants in the bulk (∼10^{19} cm^{-3} for hydrogen), its diffusion, and ionization. Eventually, the melting electrodes form a conducting plasma (10^{21}–10^{23} cm^{-3}) that experiences j×B compression and a typical decaying magnetic diffusion profile. This physical sequence ignores the transport of collisional plasmas of 10^{19} cm^{-3} which may arise from electrode defects and associated instabilities. Nonetheless, this picture of plasma formation and melt may be extrapolated to higher-energy pulsed-power systems.

In linear induction accelerators, high-brightness electron beams are accelerated by voltages applied at gaps at discrete locations along the accelerator. At high currents, the beam itself induces wakefields in the accelerating gaps which can then feedback and distort the beam. The coupling of the gap-cavity modes and the beam can be characterized by frequency-dependent quantities known as the parallel and perpendicular gap impedances. Assessing the effects of instabilities resulting from these interactions requires accurate knowledge of these quantities. In this paper, we describe how a 3D finite-difference time-domain particle-in-cell code can be used to calculate both parallel and perpendicular gap impedances. We also demonstrate good agreement between full particle-in-cell simulations and results from a beam transport code making use of gap impedances to model beam centroid deflections. In practice, ferrite materials are often used in accelerating gaps to dampen cavity modes and reduce the severity of the resulting instabilities. We describe an implicit recursive convolution algorithm used to model the linear response of dispersive ferrite materials.

The characterization of a high current, relativistic electron beam, designated the Super Pinch electron beam, has been performed using compact pulsed-power accelerators of various architectures with a novel diode geometry. The Thunderbird accelerator has an initial 1.5-μs rise time and 150-kA peak current. The drive voltage is compressed to produce a 12-ns 500-kV voltage pulse generating a ∼40-kA electron beam, which apparently exceeds the Alvén current limit although the useful current at small radius is an order of magnitude less. Using an insulated hollow cathode with a 0.5-cm anode-cathode gap, the large current is enabled by the evolution of plasma from the dielectric sleeve enveloping the cathode and a 0.5-mm wire anode. Post-shot recovery of the anode target and measurements of its deformation and damage allow an evaluation of the enhanced electron-beam focusing whereby significant beam energy is delivered to the record small, microscopic volume inside the anode target. The electron beam is seen to have conditions favorable to those needed to ignite compressed fuel in inertial confinement fusion. These results motivated a deeper insight using theoretical modeling with hybrid particle-in-cell codes. The modeling presented in this paper shows an electron beam radius of 500 MA/cm^{2} current density. Scaling up the accelerator, such preferred focusing, target penetration, and affordability of the pulsed power generated electron beams open a new opportunity for the application of the mainstream pulsed power devices in the research and development of fusion energy.

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.

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 10^{4}-10^{5} A/cm^{2} and current is diverted from the load via transport without magnetic insulation. In regions with electrode current density >10^{6} A/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 (

We have developed a physics-based transmission-line-circuit model of the Z pulsed-power accelerator. The 33-m-diameter Z machine generates a peak electrical power as high as 85 TW, and delivers as much as 25 MA to a physics load. The circuit model is used to design and analyze experiments conducted on Z. The model consists of 36 networks of transmission-line-circuit elements and resistors that represent each of Zs 36 modules. The model of each module includes a Marx generator, intermediate-energy-storage capacitor, laser-triggered gas switch, pulse-forming line, self-break water switches, and tri-plate transmission lines. The circuit model also includes elements that represent Zs water convolute, vacuum insulator stack, four parallel outer magnetically insulated vacuum transmission lines (MITLs), double-post-hole vacuum convolute, inner vacuum MITL, and physics load. Within the vacuum-transmission-line system the model conducts analytic calculations of current loss. To calculate the loss, the model simulates the following processes: (i) electron emission from MITL cathode surfaces wherever an electric-field threshold has been exceeded; (ii) electron loss in the MITLs before magnetic insulation has been established; (iii) flow of electrons emitted by the outer-MITL cathodes after insulation has been established; (iv) closure of MITL anode-cathode (AK) gaps due to expansion of cathode plasma; (v) energy loss to MITL conductors operated at high lineal current densities; (vi) heating of MITL-anode surfaces due to conduction current and deposition of electron kinetic energy; (vii) negative-space-charge-enhanced ion emission from MITL anode surfaces wherever an anode-surface-temperature threshold has been exceeded; and (viii) closure of MITL AK gaps due to expansion of anode plasma. The circuit model is expected to be most accurate when the fractional current loss is small. We have performed circuit simulations of 52 Z experiments conducted with a variety of accelerator configurations and load-impedance time histories. For these experiments, the apparent fractional current loss varies from 0% to 20%. Results of the circuit simulations agree with data acquired on 52 shots to within 2%.

Balance control must be rapidly modified to provide stability in the face of environmental challenges. Although changes in reactive balance over repeated perturbations have been observed previously, only anticipatory postural adjustments preceding voluntary movements have been studied in the framework of motor adaptation and learning theory. Here, we hypothesized that adaptation occurs in task-level balance control during responses to perturbations due to central changes in the control of both anticipatory and reactive components of balance. Our adaptation paradigm consisted of a Training set of forward support-surface perturbations, a Reversal set of novel countermanding perturbations that reversed direction, and a Washout set identical to the Training set. Adaptation was characterized by a change in a motor variable from the beginning to the end of each set, the presence of aftereffects at the beginning of the Washout set when the novel perturbations were removed, and a return of the variable at the end of the Washout to a level comparable to the end of the Training set. Task-level balance performance was characterized by peak center of mass (CoM) excursion and velocity, which showed adaptive changes with repetitive trials. Only small changes in anticipatory postural control, characterized by body lean and background muscle activity were observed. Adaptation was found in the evoked long-latency muscular response, and also in the sensorimotor transformation mediating that response. Finally, in each set, temporal patterns of muscle activity converged towards an optimum predicted by a trade-off between maximizing motor performance and minimizing muscle activity. Our results suggest that adaptation in balance, as well as other motor tasks, is mediated by altering central sensitivity to perturbations and may be driven by energetic considerations.

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.

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.

Quasiequilibrium power flow in two radial magnetically insulated transmission lines (MITLs) coupled to a vacuum post-hole convolute is studied at 50 TW–200 TW using three-dimensional particle-in-cell simulations. The key physical dimensions in the model are based on the ZR accelerator [D. H. McDaniel, et al., Proceedings of 5th International Conference on Dense Z-Pinches, edited by J. Davis (AIP, New York, 2002), p. 23]. The voltages assumed for this study result in electron emission from all cathode surfaces. Electrons emitted from the MITL cathodes upstream of the convolute cause a portion of the MITL current to be carried by an electron sheath. Under the simplifying assumptions made by the simulations, it is found that the transition from the two MITLs to the convolute results in the loss of most of the sheath current to anode structures. The loss is quantified as a function of radius and correlated with Poynting vector stream lines which would be followed by individual electrons. For a fixed MITL-convolute geometry, the current loss, defined to be the difference between the total (i.e. anode) current in the system upstream of the convolute and the current delivered to the load, increases with both operating voltage and load impedance. It is also found that in the absence of ion emission, the convolute is efficient when the load impedance is much less than the impedance of the two parallel MITLs. The effects of space-charge-limited (SCL) ion emission from anode surfaces are considered for several specific cases. Ion emission from anode surfaces in the convolute is found to increase the current loss by a factor of 2–3. When SCL ion emission is allowed from anode surfaces in the MITLs upstream of the convolute, substantially higher current losses are obtained. Note that the results reported here are valid given the spatial resolution used for the simulations.

Longitudinal phase space and temperature measurements were conducted on a 2–3 μs long, singly charged K^{+} ion bunch with an ion energy of ∼0.3 MeV and current of 30 mA. The principal objective of these experiments was to measure the longitudinal beam dynamics and study the limits of axial compression. The differences between the measured beam energy, longitudinal beam dynamics, and the amplitude and time history of the Marx voltage waveform were all quantified. Longitudinal phase space measurements indicate a slight chromaticity (

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)PRABFM1098-440210.1103/PhysRevSTAB.13.090401], 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)IETPAK0018-926X10.1109/8.391136] which is suitable for use in multidimensional finite-difference time-domain codes.

A 3D fully electromagnetic (EM) model of the principal pulsed-power components of a high-current linear transformer driver (LTD) has been developed. LTD systems are a relatively new modular and compact pulsed-power technology based on high-energy density capacitors and low-inductance switches located within a linear-induction cavity. We model 1-MA, 100-kV, 100-ns rise-time LTD cavities [A. A. Kim et al., Phys. Rev. ST Accel. Beams 12, 050402 (2009)PRABFM1098-440210.1103/PhysRevSTAB.12.050402] which can be used to drive z-pinch and material dynamics experiments. The model simulates the generation and propagation of electromagnetic power from individual capacitors and triggered gas switches to a radially symmetric output line. Multiple cavities, combined to provide voltage addition, drive a water-filled coaxial transmission line. A 3D fully EM model of a single 1-MA 100-kV LTD cavity driving a simple resistive load is presented and compared to electrical measurements. A new model of the current loss through the ferromagnetic cores is developed for use both in circuit representations of an LTD cavity and in the 3D EM simulations. Good agreement between the measured core current, a simple circuit model, and the 3D simulation model is obtained. A 3D EM model of an idealized ten-cavity LTD accelerator is also developed. The model results demonstrate efficient voltage addition when driving a matched impedance load, in good agreement with an idealized circuit model.

A B-dot monitor that measures the current 6 cm from the axis of dynamic loads fielded on 10^{7}-A multiterawatt pulsed-power accelerators has been developed. The monitor improves upon the multimegampere load-current gauge described in Phys. Rev. ST Accel. Beams 11, 100401 (2008)PRABFM1098-440210.1103/PhysRevSTAB.11.100401. The design of the improved monitor was developed using three-dimensional particle-in-cell simulations that model vacuum electron flow in the transmission line near the monitor. The simulations include important geometric features of the B-dot probe and model the deposition of electron energy within the probe. The simulations show that the improved design reduces by as much as a factor of 5 the electron energy deposition to the interior of the monitor. Data taken on accelerator shots demonstrate that the improved monitor works as well as the original monitor on shots with low-impedance loads, and delivers superior performance on higher-impedance-load shots.

A three-dimensional, fully electromagnetic model of the principal pulsed-power components of the 26-MA ZR accelerator [D. H. McDaniel et al., in Proceedings of the 5th International Conference on Dense Z-Pinches (AIP, New York, 2002), p. 23] has been developed. This large-scale simulation model tracks the evolution of electromagnetic waves through the accelerator’s intermediate-storage capacitors, laser-triggered gas switches, pulse-forming lines, water switches, triplate transmission lines, and water convolute to the vacuum insulator stack. The insulator-stack electrodes are coupled to a transmission-line circuit model of the four-level magnetically insulated vacuum-transmission-line section and double-post-hole convolute. The vacuum-section circuit model is terminated by a one-dimensional self-consistent dynamic model of an imploding z-pinch load. The simulation results are compared with electrical measurements made throughout the ZR accelerator, and are in good agreement with the data, especially for times until peak load power. This modeling effort demonstrates that 3D electromagnetic models of large-scale, multiple-module, pulsed-power accelerators are now computationally tractable. This, in turn, presents new opportunities for simulating the operation of existing pulsed-power systems used in a variety of high-energy-density-physics and radiographic applications, as well as even higher-power next-generation accelerators before they are constructed.

Vacuum-post-hole convolutes are used in pulsed high-power generators to join several magnetically insulated transmission lines (MITL) in parallel. Such convolutes add the output currents of the MITLs, and deliver the combined current to a single MITL that, in turn, delivers the current to a load. Magnetic insulation of electron flow, established upstream of the convolute region, is lost at the convolute due to symmetry breaking and the formation of magnetic nulls, resulting in some current losses. At very high-power operating levels and long pulse durations, the expansion of electrode plasmas into the MITL of such devices is considered likely. This work examines the evolution and dynamics of cathode plasmas in the double-post-hole convolutes used on the Z accelerator [R. B. Spielman et al., Phys. Plasmas 5, 2105 (1998)PHPAEN1070-664X10.1063/1.872881]. Three-dimensional particle-in-cell (PIC) simulations that model the entire radial extent of the Z accelerator convolute—from the parallel-plate transmission-line power feeds to the z-pinch load region—are used to determine electron losses in the convolute. The results of the simulations demonstrate that significant current losses (1.5 MA out of a total system current of 18.5 MA), which are comparable to the losses observed experimentally, could be caused by the expansion of cathode plasmas in the convolute regions.

Longitudinal bunching factors in excess of 70 of a 300-keV, 27-mA K^{+} ion beam have been demonstrated in the neutralized drift compression experiment [P. K. Roy et al., Phys. Rev. Lett. 95, 234801 (2005)PRLTAO0031-900710.1103/PhysRevLett.95.234801] in rough agreement with particle-in-cell source-to-target simulations. A key aspect of these experiments is that a preformed plasma provides charge neutralization of the ion beam in the last one meter drift region where the beam perveance becomes large. The simulations utilize the measured ion source temperature, diode voltage, and induction-bunching-module voltage waveforms in order to determine the initial beam longitudinal phase space which is critical to accurate modeling of the longitudinal compression. To enable simultaneous longitudinal and transverse compression, numerical simulations were used in the design of the solenoidal focusing system that compensated for the impact of the applied velocity tilt on the transverse phase space of the beam. Complete source-to-target simulations, that include detailed modeling of the diode, magnetic transport, induction bunching module, and plasma neutralized transport, were critical to understanding the interplay between the various accelerator components in the experiment. Here, we compare simulation results with the experiment and discuss the contributions to longitudinal and transverse emittance that limit the final compression.

We have developed 1D analytic and 2D fully electromagnetic models of radial transmission-line impedance transformers. The models have been used to quantify the power-transport efficiency and pulse sharpening of such transformers as a function of voltage pulse width and impedance profile. For the cases considered, we find that in the limit as Γ→0 (where Γ is the ratio of the pulse width to the one-way transit time of the transformer), the transport efficiency is maximized when the impedance profile is exponential. As Γ increases from zero, the optimum profile gradually deviates from an exponential. A numerical procedure is presented that determines the optimum profile for a given pulse shape and width. The procedure can be applied to optimize the design of impedance transformers used in petawatt-class pulsed-power accelerators.

The linear growth of the two-stream instability for a charged-particle beam that is longitudinally compressing as it propagates through a background plasma (due to an applied velocity tilt) is examined. Detailed, 1D particle-in-cell (PIC) simulations are carried out to examine the growth of the wave packet produced by a small amplitude density perturbation in the background plasma. Recent analytic and numerical work by Startsev and Davidson [Phys. Plasmas 13, 062108 (2006)PHPAEN1070-664X10.1063/1.2212807] predicted reduced linear growth rates, which are indeed observed in the PIC simulations. Here, small-signal asymptotic gain factors are determined in a semianalytic analysis and compared with the simulation results in the appropriate limits. Nonlinear effects in the PIC simulations, including wave breaking and particle trapping, are found to limit the linear growth phase of the instability for both compressing and noncompressing beams.

Heavy ion drivers for heavy ion fusion and high energy density physics applications use space-charge-dominated ion beams which must undergo longitudinal bunch compression in order to meet the requisite beam intensities desired at the target. The Neutralized Drift Compression Experiment-1A (NDCX-1A) at Lawrence Berkeley National Laboratory is used to determine the effective limits of neutralized drift compression, which occurs due to an imposed longitudinal velocity tilt on the drifting beam and subsequent neutralization of the beam’s space charge with background plasma. The accurate and temporally resolved measurement of the ion beam’s current and pulse length, which has been longitudinally compressed to a few nanoseconds duration at its focal plane, is a critical diagnostic. This paper describes the design and experimental results for a fast and accurate ion beam probe, which reliably measures the absolute beam current in the presence of high density plasma at the focal plane as a function of time. A particle-in-cell code has been used to model the propagation of the intense ion beam and to design the diagnostic probe.

The growth of the resistive hose instability for intense proton beams is examined using three-dimensional particle-in-cell simulations. The simulation results are compared with a time-dependent model of resistive hose growth that uses a spread-mass formulation and a time-dependent conductivity model. Radius tailoring of the beam head is shown to suppress high-frequency instability growth. In addition, the effects of a reduced-density plasma channel on the growth of the resistive hose instability is calculated.