Beam Dynamics for Induction Accelerators
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70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
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Load dynamics of double planar foil liners and double planar wire arrays on the UM MAIZE LTD generator
In previous studies using the University of Nevada, Reno's (UNR's) high-impedance Zebra Marx generator (1.9 Ω, 1.7 MA, 100 ns), Double Planar Wire Arrays (DPWAs) proved to be excellent radiators, and Double Planar Foil Liners (DPFLs) proved useful for future inertial confinement fusion applications. This article presents the results of joint UNR/UM (University of Michigan) experiments with aluminum (Al) DPWAs, Al DPFLs, and tungsten (W) DPWAs using UM's Michigan Accelerator for Inductive Z-Pinch Experiments (MAIZE) generator, a low-impedance Linear Transformer Driver (LTD) (0.1 Ω, 0.5–1 MA, and 100–250 ns). The main goals of this study were twofold: the first was a pioneering effort to test whether a relatively heavy Al DPFL could successfully be imploded on a low-impedance university-scale LTD like the MAIZE generator, and, if so, to analyze the results and make comparisons to the optimized, lighter DPWA configurations that have been previously studied. The DPWAs consisted of two planes of micrometer-scale diameter Al or W wires, while the DPFLs consisted of two planes of micrometer-scale thickness Al foils. Diagnostics include filtered Si-diodes, an absolutely calibrated filtered PCD, x-ray pinhole cameras, spectrometers, and gated optical self-emission imaging. The implosion dynamics and radiative properties of Al DPWAs and DPFLs and W DPWAs on the MAIZE LTD are discussed and compared. Time-dependent load inductance calculations derived from measurements of the load current and a MAIZE circuit model provide a relative measurement of pinch strength. In experiments on MAIZE, W planar wire arrays exhibited a higher peak load inductance throughout the pinch than Al DPWAs and DPFLs, while x-ray pulses from Al DPFLs had the longest emission duration.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Study of the interrelation between the electrotechnical parameters of the plasma focus discharge circuit and the plasma compression dynamics on the PF-3 and PF-1000 facilities
The main stages of the plasma current sheath (PCS) dynamics on two plasma focus (PF) facilities with different geometries of the electrode system, PF-3 (Filippov type) and PF-1000 (Mather type), were studied by analyzing the results of the current and voltage measurements. Some dynamic characteristics, such as the PCS velocity in the acceleration phase in the Mather-type facility (PF-1000), the moment at which the PCS reaches the anode end, and the plasma velocity in the radial stage of plasma compression in the PF-3 Filippov-type facility, were determined from the time dependence of the inductance of the discharge circuit with a dynamic plasma load. The energy characteristics of the discharge circuit of the compressing PCS were studied for different working gases (deuterium, argon, and neon) at initial pressures of 1.5–3 Torr in discharges with energies of 0.3–0.6 MJ. In experiments with deuterium, correlation between the neutron yield and the electromagnetic energy deposited directly in the compressed PCS was investigated.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Toward fusion plasma scenario planning for NSTX-U using machine-learning-accelerated models
One of the most promising devices for realizing power production through nuclear fusion is the tokamak. To maximize performance, it is preferable that tokamak reactors achieve advanced operating scenarios characterized by good plasma confinement, improved magnetohydrodynamic (MHD) stability, and a largely non-inductively driven plasma current. Such scenarios could enable steady-state reactor operation with high \emph{fusion gain} --- the ratio of produced fusion power to the external power provided through the plasma boundary. Precise and robust control of the evolution of the plasma boundary shape as well as the spatial distribution of the plasma current, density, temperature, and rotation will be essential to achieving and maintaining such scenarios. The complexity of the evolution of tokamak plasmas, arising due to nonlinearities and coupling between various parameters, motivates the use of model-based control algorithms that can account for the system dynamics. In this work, a learning-based accelerated model trained on data from the National Spherical Torus Experiment Upgrade (NSTX-U) is employed to develop planning and control strategies for regulating the density and temperature profile evolution around desired trajectories. The proposed model combines empirical scaling laws developed across multiple devices with neural networks trained on empirical data from NSTX-U and a database of first-principles-based computationally intensive simulations. The reduced execution time of the accelerated model will enable practical application of optimization algorithms and reinforcement learning approaches for scenario planning and control development. An initial demonstration of applying optimization approaches to the learning-based model is presented, including a strategy for mitigating the effect of leaving the finite validity range of the accelerated model. The approach shows promise for actuator planning between experiments and in real-time.
machine learning↗
Transportation of high-current ion and electron beams in the accelerator drift gap in the presence of an additional electron background
The dynamics of a high-current ion beam propagating in the drift gap of a linear induction accelerator with collective focusing is studied using 3D numerical simulations in the framework of the full system of the Vlasov–Maxwell equations (code KARAT). The ion beam is neutralized by a comoving electron beam in the current density and, partially, in space charge, since the velocities of electrons and ions differ substantially. The dynamics of the high-current ion beam is investigated for different versions of additional neutralization of its space charge. It is established that, for a given configuration of the magnetic field and in the presence of a specially programmed injection of additional electrons from the boundary opposite to the ion injection boundary, the angular divergence of the ion beam almost vanishes, whereas the current of the ion beam at the exit from the accelerator drift gap changes insignificantly and the beam remains almost monoenergetic.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Review of pulsed power-driven high energy density physics research on Z at Sandia
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.
Sinars, D. B. (ORCID:0000000155473532)↗
Electron cloud considerations for HIF drivers
Here, we review some previous results on electron-cloud dynamics and accumulation and the impact of electron clouds on ion beam dynamics, and assess these in the context of a magnetic-quadrupole-based heavy-ion fusion driver. We present a new analysis which exploits analytic solution of linearized envelope equations between accelerating gaps to derive a set of mapping equations which we use to extrapolate from previously obtained particle-simulation results for a beam transport system to an HIF driver.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
The electro-thermal stability of tantalum relative to aluminum and titanium in cylindrical liner ablation experiments at 550 kA
Presented are the results from the liner ablation experiments conducted at 550 kA on the Michigan Accelerator for Inductive Z-Pinch Experiments. These experiments were performed to evaluate a hypothesis that the electrothermal instability (ETI) is responsible for the seeding of magnetohydrodynamic instabilities and that the cumulative growth of ETI is primarily dependent on the material-specific ratio of critical temperature to melting temperature. This ratio is lower in refractory metals (e.g., tantalum) than in non-refractory metals (e.g., aluminum or titanium). The experimental observations presented herein reveal that the plasma-vacuum interface is remarkably stable in tantalum liner ablations. This stability is particularly evident when contrasted with the observations from aluminum and titanium experiments. These results are important to various programs in pulsed-power-driven plasma physics that depend on liner implosion stability. Furthermore, examples include the magnetized liner inertial fusion (MagLIF) program and the cylindrical dynamic material properties program at Sandia National Laboratories, where liner experiments are conducted on the 27-MA Z facility.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Short intense ion pulses for materials and warm dense matter research
We have commenced experiments with intense short pulses of ion beams on the Neutralized Drift Compression Experiment-II at Lawrence Berkeley National Laboratory, by generating beam spots size with radius r<1 mm within 2 ns FWHM and approximately 10 10 ions/pulse. To enable the short pulse durations and mm-scale focal spot radii, the 1.2 MeV Li + ion beam is neutralized in a 1.6-meter drift compression section located after the last accelerator magnet. An 8-Tesla short focal length solenoid compresses the beam in the presence of the large volume plasma near the end of this section before the target. The scientific topics to be explored are warm dense matter, the dynamics of radiation damage in materials, and intense beam and beam-plasma physics including selected topics of relevance to the development of heavy-ion drivers for inertial fusion energy. Finally, we describe the accelerator commissioning and time-resolved ionoluminescence measurements of yttrium aluminum perovskite using the fully integrated accelerator and neutralized drift compression components.
43 PARTICLE ACCELERATORS↗
Characterization of self-magnetic pinch (SMP) radiographic diode performance on RITS-6 at Sandia National Laboratories. I. Diode dynamics, DC heating to extend radiation pulse
Radiographic diodes focus on an intense electron beam to a small spot size to minimize the source area of energetic photons for radiographic interrogation. The self-magnetic pinch (SMP) diode has been developed as such a source and operated as a load for the six-cavity radiographic integrated test stand (RITS-6) inductive voltage adder driver. While experiments support the generally accepted conclusion that a 1:1 aspect diode (cathode diameter equals anode–cathode gap) delivers optimum SMP performance, such experiments also show that reducing the cathode diameter, while reducing spot size, also results in reduced radiation dose, by as much as 50%, and degraded shot reproducibility. Analysis of the effective electron impingement angle on the anode converter with time made possible by a newly developed dose-rate array diagnostic indicates that fast-developing oscillations of the angle are correlated with early termination of the radiation pulse on many of the smaller-diameter SMP shots. This behavior as a function of relative cathode size persists through experiments with output voltages and currents up to 11.5 MV and 225 kA, respectively, and with spot sizes below approximately few millimeters. Since simulations to date have not predicted such oscillatory behavior, considerable discussion of the angle behavior of SMP shots is made to lend credence to the inference. We report there is clear anecdotal evidence that DC heating of the SMP diode region leads to stabilization of this oscillatory behavior. This is the first of two papers on the performance of the SMP diode on the RITS-6 accelerator.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Inductively Driven, 3D Liner Compression of a Magnetized Plasma to Megabar Energy Densities
To take advantage of the smaller scale, higher density regime of fusion an efficient method for achieving the compressional heating required to reach fusion gain conditions must be found. What is proposed is a more flexible metallic liner compression scheme that minimizes the kinetic energy required to reach fusion. It is believed that it is possible to accomplish this at sub-megajoule energies. This however will require operation at very small scale. To have a realistic hope of inexpensive, repetitive operation, it is essential to have the liner kinetic energy under a megajoule which allows for the survivability of the vacuum and power systems. At small scale the implosion speed must be reasonably fast to maintain the magnetized plasma (FRC) equilibrium during compression. For limited liner kinetic energy, it becomes clear that the thinnest liner imploded to the smallest radius consistent with the requirements for FRC equilibrium lifetime is desired. The proposed work is directed toward accomplishing this goal. Typically an axial (Z) current is employed for liner compression. There are however several advantages to using a θ-pinch coil. With the θ-pinch the liner currents are inductively driven which greatly simplifies the apparatus and vacuum system, and avoids difficulties with the post implosion vacuum integrity. With fractional flux leakage, the foil liner automatically provides for the seed axial compression field. To achieve it with optimal switching techniques, and at an accelerated pace however will require additional funding. This extra expense is well justified as the compression technique that will be enabled by this funding is unique in the ability to implode individual segments of the liner at different times. This is highly advantageous as the liner can be imploded in a manner that maximizes the energy transfer to the FRC. Production of shaped liner implosions for additional axial compression can thus be readily accomplished with the modified power modules. The additional energy and switching capability proposed will thus provide for optimal utilization of the liner energy. The following tasks were outlined for the three year effort: (1) Design and assemble the foil liner compression test structure and chamber including the compression bank and test foils [Year 1]. (2) Perform foil liner compression experiments and obtain performance data over a range on liner dimensions and bank parameters [Year 2]. (3) Carry out compression experiments of the FRC plasma to Megagauss fields and measure key fusion parameters [Year 3]. (4) Develop numerical codes and analyze experimental results, and determine the physics and scaling for future work [Year 1-3]. The principle task of the project was to design and assemble the foil liner FRC formation chamber, the full compression test structure and chamber including the compression bank. This task was completed successfully. The second task was to test foils in the test facility constructed in year one and characterize the performance obtained from liner compression. These experimental measurements were then compared with analytical predictions, and numerical code results. The liner testing was completed and compared with both the analytical results as well as the code work performed with the 3D structural dynamics package of ANSYS Metaphysics®. This code is capable of modeling the dynamic behavior of materials well into the non-linear regime (e.g. a bullet hit plate glass). The liner dynamic behavior was found to be remarkably close to that predicted by the 3D structural dynamics results. Incorporating a code that can also include the magnetics and plasma physics has also made significant progress at the UW. The remaining test bed construction and assembly task is was completed, and the FRC formation and merging experiments were carried out as planned. The liner compression of the FRC to Megagauss fields was not performed due to not obtaining a sufficiently long lived FRC during the final year of the grant. Modifications planned to correct this deficiency included a larger FRC source as well as a much larger liner driver energy storage system. Due to discontinuation of the grant neither of these improvements were carried out.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Algebraic motion of vertically displacing plasmas
In this paper, the vertical motion of a tokamak plasma is analytically modelled during its non-linear phase by a free-moving current-carrying rod inductively coupled to a set of fixed conducting wires or a cylindrical conducting shell. The solutions capture the leading term in a Taylor expansion of the Green's function for the interaction between the plasma column and the surrounding vacuum vessel. The plasma shape and profiles are assumed not to vary during the vertical drifting phase such that the plasma column behaves as a rigid body. In the limit of perfectly conducting structures, the plasma is prevented to come in contact with the wall due to steep effective potential barriers created by the induced Eddy currents. Resistivity in the wall allows the equilibrium point to drift towards the vessel on the slow timescale of flux penetration. The initial exponential motion of the plasma, understood as a resistive vertical instability, is succeeded by a non-linear “sinking” behaviour shown to be algebraic and decelerating. Finally, the acceleration of the plasma column often observed in experiments is thus concluded to originate from an early sharing of toroidal current between the core, the halo plasma, and the wall or from the thermal quench dynamics precipitating loss of plasma current.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Two-fluid description of wave-particle interactions in strong Buneman turbulence
To understand the nature of anomalous resistivity in magnetic reconnection, we investigate turbulence-induced momentum transport and energy dissipation while a plasma is unstable to the Buneman instability in force-free current sheets. Using 3D particle-in-cell simulations, we find that the macroscopic effects generated by wave-particle interactions in Buneman instability can be approximately described by a set of electron fluid equations. We show that both energy dissipation and momentum transport along electric current in the current layer are locally quasi-static, but globally dynamic and irreversible. Turbulent drag dissipates both the streaming energy of the current sheet and the associated magnetic energy. The net loss of streaming energy is converted into the electron component heat conduction parallel to the magnetic field and increases the electron Boltzmann entropy. The growth of self-sustained Buneman waves satisfies a Bernoulli-like equation that relates the turbulence-induced convective momentum transport and thermal momentum transport. Electron trapping and de-trapping drive local momentum transports, while phase mixing converts convective momentum into thermal momentum. The drag acts like a micro-macro link in the anomalous heating processes. The decrease of magnetic field maintains an inductive electric field that re-accelerates electrons, but most of the magnetic energy is dissipated and converted into the component heat of electrons perpendicular to the magnetic field. This heating process is decoupled from the heating of Buneman instability in the current sheets. Ion heating is weak but ions play an important role in assisting energy exchanges between waves and electrons. Cold ion fluid equations together with our electron fluid equations form a complete set of equations that describes the occurrence, growth, saturation and decay of the Buneman instability.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
ELECTRON HEATING IN A RELATIVISTIC, WEIBEL-UNSTABLE PLASMA
The dynamics of two initially unmagnetized relativistic counter-streaming homogeneous ion–electron plasma beams are simulated in two dimensions (2D) using the particle-in-cell (PIC) method. It is shown that current filaments, which form due to the Weibel instability, develop a large-scale longitudinal electric field in the direction opposite to the current carried by the filaments as predicted by theory. This field, which is partially inductive and partially electrostatic, is identified as the main source of net electron acceleration, greatly exceeding that due to magnetic field decay at later stages. The transverse electric field, although larger than the longitudinal field, is shown to play a smaller role in heating electrons, contrary to previous claims. It is found that in one dimension, the electrons become strongly magnetized and are not accelerated beyond their initial kinetic energy. Rather, the heating of the electrons is enhanced by the bending and break up of the filaments, which releases electrons that would otherwise be trapped within a single filament and slow the development of the Weibel instability (i.e., the magnetic field growth) via induction as per Lenz’s law. In 2D simulations, electrons are heated to about one quarter of the initial kinetic energy of ions. The magnetic energy at maximum is about 4%, decaying to less than 1% by the end of the simulation. The ions are found to gradually decelerate until the end of the simulation, by which time they retain a residual anisotropy of less than 10%.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Characterization of Self-Magnetic Pinch (SMP) radiographic diode performance on RITS-6 at Sandia National Laboratories: 1) Diode Dynamics, DC Heating to extend Radiation Pulse
Radiographic diodes focus an intense electron beam to a small spot size to minimize the source area of energetic photons for radiographic interrogation. The self-magnetic pinch (SMP) diode has been developed as such a source and operated as a load for the RITS-6 Inductive Voltage Adder (IVA) driver. While experiments support the generally accepted conclusion that a 1:1 aspect diode (cathode diameter equals anode-cathode gap) delivers optimum SMP performance, such experiments also show that reducing the cathode diameter, while reducing spot size, also results in reduced radiation dose, by as much as 50%, and degraded shot reproducibility. Analyzation of the effective electron impingement angle on the anode converter with time made possible by a newly developed dose-rate array diagnostic indicates that fast-developing oscillations of the angle are correlated with early termination of the radiation pulse on many of the smaller-diameter SMP shots. This behavior as a function of relative cathode size persists through experiments with output voltages and currents up to 11.5 MV and 225 kA, respectively, and with spot sizes below ~ few mm. Since simulations to date have not predicted such oscillatory behavior, considerable discussion of the angle-behavior of SMP shots is made to lend credence to the inference. There is clear anecdotal evidence that DC heating of the SMP diode region leads to stabilization of this oscillatory behavior. This is the first of two papers on the performance of the SMP diode on the RITS-6 accelerator.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Analysis of ELM stability with extended MHD models in JET, JT-60U and future JT-60SA tokamak plasmas
The stability with respect to a peeling–ballooning mode (PBM) was investigated numerically with extended MHD simulation codes in JET, JT-60U and future JT-60SA plasmas. The MINERVA-DI code was used to analyze the linear stability, including the effects of rotation and ion diamagnetic drift (${\omega }_{* {\rm{i}}}$), in JET-ILW and JT-60SA plasmas, and the JOREK code was used to simulate nonlinear dynamics with rotation, viscosity and resistivity in JT-60U plasmas. It was validated quantitatively that the ELM trigger condition in JET-ILW plasmas can be reasonably explained by taking into account both the rotation and ${\omega }_{* {\rm{i}}}$ effects in the numerical analysis. When deuterium poloidal rotation is evaluated based on neoclassical theory, an increase in the effective charge of plasma destabilizes the PBM because of an acceleration of rotation and a decrease in ${\omega }_{* {\rm{i}}}$. The difference in the amount of ELM energy loss in JT-60U plasmas rotating in opposite directions was reproduced qualitatively with JOREK. By comparing the ELM affected areas with linear eigenfunctions, it was confirmed that the difference in the linear stability property, due not to the rotation direction but to the plasma density profile, is thought to be responsible for changing the ELM energy loss just after the ELM crash. A predictive study to determine the pedestal profiles in JT-60SA was performed by updating the EPED1 model to include the rotation and ${\omega }_{* {\rm{i}}}$ effects in the PBM stability analysis. It was shown that the plasma rotation predicted with the neoclassical toroidal viscosity degrades the pedestal performance by about 10% by destabilizing the PBM, but the pressure pedestal height will be high enough to achieve the target parameters required for the ITER-like shape inductive scenario in JT-60SA.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Development of an x-ray Talbot-Lau moiré deflectometer for fast density profile measurements of dense plasmas generated by beam-target interactions
We report that for the first time an x-ray Talbot-Lau moiré deflectometer is being developed that will use a flash tube source and fast detector for dynamic density gradient measurements. In Talbot-Lau moiré deflectometry, an x-ray grating makes an image of itself on a second grating (the Talbot effect) to produce a moiré pattern on a detector. The test object is placed between these gratings, with variations in index of refraction changing the pattern. A third grating in front of an incoherent x-ray source produces an array of coherent sources. With a 150 kV x-ray flash tube as the source, the gratings are placed in a glancing angle setup for performance at ~60 keV. The detector is a gated CCD with a fast scintillator for x-ray conversion. This diagnostic, designed for the Dual-Axis Radiographic Hydrodynamic Test facility (DARHT) at Los Alamos National Laboratory, measures the density profile of dense plasma plumes ejected from beam-target interactions. DARHT has two high-current, pulsed, inductive linear electron accelerators with bremsstrahlung targets at the end of each beam line to create 2-D radiographic images of hydrodynamic tests. One multi-pulse accelerator has up to four beam pulses striking the same target within 2 μs. Computer simulations that model target evolution and ejected material between pulses are used to design these targets for optimal radiographic performance; the x-ray deflectometer will directly measure density gradients in the ejected plumes and provide the first experimental constraints to these models. During the first year, currently underway, the diagnostic systems are being designed. In year two, the flash tube and fast detector will be deployed at DARHT for radiographic imaging while the deflectometer is built and tested on the bench with a continuous source. In year three, the fast deflectometer will be installed on DARHT and density measurements will be performed.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Runaway electron beam dynamics at low plasma density in DIII-D: energy distribution, current profile, and internal instability
Parameters of the post-disruption runaway electron (RE) beam in the collisionless background plasma achieved after deuterium injection are investigated in DIII-D. The spatially resolved RE energy distribution function is measured for the first time during the RE plateau stage by inverting hard X-ray bremsstrahlung spectra. It has maximum energy up to 20 MeV and a non-monotonous feature at 5{6 MeV observed only in the core of the beam supporting the possibility of kinetic instabilities. The RE current profile is reconstructed for the first time using the spatially resolved RE energy distribution. It is found to be more peaked than the pre-disruption plasma current, with higher internal inductance, suggesting preferential formation of REs in the core plasma or potentially a radially inward motion of the REs. The accessed relatively low-current (180 kA) RE beam is found stable, likely due to its elevated q profile. From this base stable equilibrium, instability is accessed by ramping the solenoid current. Under a large applied accelerating loop voltage an internal kink mode is observed. The kink mode leads to sawtooth-like relaxation of the RE current profile, but drives no RE loss. Under conditions of a large decelerating voltage, chirping Alfvénic instabilities driven by REs during the RE plateau stage are observed for the first time. The low-frequency (0.1{7 MHz) Alfvénic instabilities, supposedly compressional Alfvén eigenmodes, are found to be correlated with a RE loss signal. Finally, this provides novel plasma conditions to study these instabilities and investigate opportunities to utilize them for RE control. Bifurcated electron cyclotron emission (ECE) spectrum is measured during the collisionless RE plateau, with a break point at ≈100 GHz suggesting resonant absorption of the ECE at low frequencies.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗