Magnetized Target Plasma Research Articles

An interface tracking, finite volume code for modeling axisymmetric implosion of a rotating liquid metal liner with free surface

We present Integrated System Model-hydrodynamics (ISM-hydro)—an interface tracking, finite volume code for modeling a shaped implosion of a rotating, initially cylindrical, fluid shell (liner) with a free surface. The code is a novel implementation of the mixed Lagrangian–Eulerian approach, applied to a compressible fluid in an axisymmetric geometry described by cylindrical coordinates (r, ϕ, z). In ISM-hydro, a structured quadrilateral mesh follows fluid elements in the r-direction (radially Lagrangian) and is fixed in the z-direction (axially Eulerian). This approach accurately captures the motion of the liner's free surface, making it an interface tracking method. Using this mesh, we derive a finite volume discretization of the axisymmetric Euler equations for a rotating compressible fluid that has an exact balance of kinetic energy. An extensive comparison between ISM-hydro and the open-source software OpenFOAM is presented; results for different test cases show very good agreement in simulated implosion trajectories and flow fields. ISM-hydro is the purely hydrodynamic component of the Integrated System Model (ISM), a framework developed at General Fusion (GF) for comprehensive predictive modeling of GF's magnetized target fusion (MTF) scheme, where an imploding rotating liquid metal liner compresses a magnetized plasma target to fusion conditions. Among advantages of the code is its speed: a full implosion simulation with a coarse mesh takes on the order of one minute on a single core while preserving high accuracy. This makes ISM-hydro a valuable tool for the design optimization of GF's MTF machines.

Observations of Brillouin scattering process in Particle-In-Cell simulations for laser pulse interacting with magnetized overdense plasma

Parametric processes play an important role in applications related to laser plasma interaction [P K Kaw, Review of Modern Plasma Physics, 1.1 (2017)]. Occurrence of these processes has primarily been reported in the context of laser interacting with an un-magnetized plasma. The regime of magnetized plasma, on the other hand, has remained largely unexplored from this perspective. Recent technological advancements in the production of high magnetic fields [Nakamura, Daisuke, et al, Review of Scientific Instruments, 89.9, 095106 (2018)] bring the area of laser interaction with magnetized plasma targets to the forefront of investigation. In this study, the parametric process of Brillouin scattering for a magnetised plasma target has been demonstrated with the help of one dimensional Particle-in-cell simulations using the platform of OSIRIS-4.0. The external magnetic field has been chosen to be directed along the laser propagation direction. This geometry supports the propagation of right (R) and left (L) circularly polarized electromagnetic waves in the plasma when the laser frequency falls in the appropriate pass band of the respective dispersion curves. A detailed study identifying the scattering process with differing strengths of the applied external magnetic field, and for various polarizations of the incident electromagnetic pulse has been carried out. The conditions favouring the excitation of parametric Brillouin scattering process has been outlined. The nonlinear regime of the scattering process has also been investigated.

Study of the effect of magnetic field characteristics on Rayleigh-Taylor instability with density gradient layers

Inertial confinement fusion (ICF) is a possible path of fusion technology for fusion ignition, but during the implosion of a magnetized plasma target by compression, the magnetic Rayleigh-Taylor (R-T) instability similar to that at the interface of the denser and less dense phases can arise when the plasma is subjected to gravitational and magnetic forces, which in turn affect the confinement characteristic and the process of fusion burn. In this study, the R-T instability of two phases in the presence/ absence of a magnetic field in a two-dimensional rectangular duct is simulated based on the MHD model adopted in ANSYS FLUENT. The simulation results show that the R-T instability is substantially weakened for the case with an Atwood number of 0.29 where a constant (DC) magnetic field is imposed in the opposite direction to the gravitational acceleration, meanwhile, a strong countercurrent flow, which occurs near the side walls, enhances the heat and mass transport process, which is related to the M-shape velocity profile formed in the flow channel. Besides, when a DC magnetic field perpendicular to the direction of the gravitational acceleration is introduced, the R-T instability vanishes from the initial moment to the end. When a sinusoidal wave form of varying (AC) magnetic field is introduced, the R-T instability is substantially facilitated. The evolutions of the interface and pressure field distribution are significantly correlated with the change in intensity and direction of the AC magnetic field. After about one cycle of the magnetic field's variation, the density gradient layers in the vertical direction are entirely converted to a density stratification in the horizontal direction with the denser phase occupying the region near the sidewalls of the duct, and ever since then, the R-T instability disappears completely. These findings can provide supports for the design of nuclear fusion devices and magnetic fields.

Magnetohydrodynamics Solver for a Two-Phase Free Surface Flow Developed in OpenFOAM

A magnetohydrodynamics solver (“mhdCompressibleInterFoam”) has been developed for a compressible two-phase flow with a free surface by extending “compressibleInterFoam” solver within OpenFOAM suite. The primary goal is to develop a tool to simulate compression of magnetic fields in vacuum and simplified magnetized plasma targets by imploding rotating liquid metal liners in the context of a Magnetized Target Fusion (MTF) concept in pursuit by General Fusion Inc. At present, the solver is limited to axisymmetric problems and the magnetic field evolution is solved in terms of toroidal field component and poloidal flux functions. The solver has been validated and verified using a number of test cases for which analytical or other numerical solutions are provided. Those tests cases include: (i) compression of toroidal and poloidal magnetic fields in vacuum and cylindrical geometry, (ii) axisymmetric annular Hartmann flow, and (iii) compression of magnetized target initialized with a Grad–Shafranov equilibrium state in a cylindrical geometry. A methodology to incorporate conductive solid regions into simulation has also been developed. Capability of the code is demonstrated by simulating a complex case of compressing a magnetized target, which is injected during implosion of a rotating liquid metal liner with an initially soaked poloidal magnetic field. An application of the solver to simulate compression of a magnetized target in a geometry and parameters relevant to the Fusion Demonstration Plant (FDP) being developed by General Fusion Inc. is also demonstrated.

Formation of transient high-β plasmas in a magnetized, weakly collisional regime

We present experimental data providing evidence for the formation of transient ( ${\sim }20\ \mathrm {\mu }\textrm {s}$ ) plasmas that are simultaneously weakly magnetized (i.e. Hall magnetization parameter $\omega \tau > 1$ ) and dominated by thermal pressure (i.e. ratio of thermal-to-magnetic pressure $\beta > 1$ ). Particle collisional mean free paths are an appreciable fraction of the overall system size. These plasmas are formed via the head-on merging of two plasmas launched by magnetized coaxial guns. The ratio $\lambda _{\textrm {gun}}=\mu _0 I_{\textrm {gun}}/\psi _{\textrm {gun}}$ of gun current $I_{\textrm {gun}}$ to applied magnetic flux $\psi _{\textrm {gun}}$ is an experimental knob for exploring the parameter space of $\beta$ and $\omega \tau$ . These experiments were conducted on the Big Red Ball at the Wisconsin Plasma Physics Laboratory. The transient formation of such plasmas can potentially open up new regimes for the laboratory study of weakly collisional, magnetized, high- $\beta$ plasma physics; processes relevant to astrophysical objects and phenomena; and novel magnetized plasma targets for magneto-inertial fusion.

Laser-driven magneto-inertial fusion with magnetized cylindrical target

Laser-driven magneto-inertial fusion assumed plasma and magnetic flux compression by quasisymmetric laser-driven implosion of magnetized target. We develop a 1D radiation magnetohydrodynamic code and a formulation for the one-fluid two-temperature equations for simulating compressible non-equilibrium magnetized target plasma. Laser system with pulse radiation with 10 ns duration is considered for numerical experiments. A numerical study of a scheme of magnetized laser-driven implosion in the external magnetic field is carried out.

Experiment to Form and Characterize a Section of a Spherically Imploding Plasma Liner

We describe an experiment to form and characterize a section of a spherically imploding plasma liner by merging six supersonic plasma jets that are launched by newly designed contoured-gap coaxial plasma guns. This experiment is a prelude to forming a fully spherical imploding plasma liner using many dozens of plasma guns, as a standoff driver for plasma-jet-driven magneto-inertial fusion. The objectives of the six-jet experiments are to assess the evolution and scalings of liner Mach number and uniformity, which are important metrics for spherically imploding plasma liners to compress magnetized target plasmas to fusion conditions. This paper describes the design of the coaxial plasma guns, experimental characterization of the plasma jets, six-jet experimental setup and diagnostics, initial diagnostic data from three- and six-jet experiments, and the high-level objectives of associated numerical modeling.

Interaction of laser beams with magnetized substance in a strong magnetic field

Laser-driven magneto-inertial fusion assumed plasma and magnetic flux compression by quasisymmetric laser-driven implosion of magnetized target. We develop a 2D radiation magnetohydrodynamic code and a formulation for the one-fluid two-temperature equations for simulating compressible non-equilibrium magnetized target plasma. Laser system with pulse radiation with 10 ns duration is considered for numerical experiments. A numerical study of a scheme of magnetized laser-driven implosion in the external magnetic field is carried out.

Physics Criteria for a Subscale Plasma Liner Experiment

Spherically imploding plasma liners, formed by merging hypersonic plasma jets, are a proposed standoff driver to compress magnetized target plasmas to fusion conditions [S. C. Hsu et al., IEEE Trans. Plasma Sci. 40, 1287 (2012)]. In this paper, the parameter space and physics criteria are identified for a subscale, plasma-liner-formation experiment to provide data, e.g., on liner ram-pressure scaling and uniformity, that are relevant for addressing scientific issues of full-scale plasma liners required to achieve fusion conditions. Based on these criteria, we quantitatively estimate the minimum liner kinetic energy and mass needed, which informed the design of a subscale plasma liner experiment now under development.

Three-wave scattering in magnetized plasmas: From cold fluid to quantized Lagrangian.

Large amplitude waves in magnetized plasmas, generated either by external pumps or internal instabilities, can scatter via three-wave interactions. While three-wave scattering is well known in collimated geometry, what happens when waves propagate at angles with one another in magnetized plasmas remains largely unknown, mainly due to the analytical difficulty of this problem. In this paper, we overcome this analytical difficulty and find a convenient formula for three-wave coupling coefficient in cold, uniform, magnetized, and collisionless plasmas in the most general geometry. This is achieved by systematically solving the fluid-Maxwell model to second order using a multiscale perturbative expansion. The general formula for the coupling coefficient becomes transparent when we reformulate it as the scattering matrix element of a quantized Lagrangian. Using the quantized Lagrangian, it is possible to bypass the perturbative solution and directly obtain the nonlinear coupling coefficient from the linear response of the plasma. To illustrate how to evaluate the cold coupling coefficient, we give a set of examples where the participating waves are either quasitransverse or quasilongitudinal. In these examples, we determine the angular dependence of three-wave scattering, and demonstrate that backscattering is not necessarily the strongest scattering channel in magnetized plasmas, in contrast to what happens in unmagnetized plasmas. Our approach gives a more complete picture, beyond the simple collimated geometry, of how injected waves can decay in magnetic confinement devices, as well as how lasers can be scattered in magnetized plasma targets.

Semi-analytic model of plasma-jet-driven magneto-inertial fusion

A semi-analytic model for plasma-jet-driven magneto-inertial fusion is presented. Compressions of a magnetized plasma target by a spherically imploding plasma liner are calculated in one dimension (1D), accounting for compressible hydrodynamics and ionization of the liner material, energy losses due to conduction and radiation, fusion burn and alpha deposition, separate ion and electron temperatures in the target, magnetic pressure, and fuel burn-up. Results show 1D gains of 3–30 at spherical convergence ratio <15 and 20–40 MJ of liner energy, for cases in which the liner thickness is 1 cm and the initial radius of a preheated magnetized target is 4 cm. Some exploration of parameter space and physics settings is presented. The yields observed suggest that there is a possibility of igniting additional dense fuel layers to reach high gain.

Parallel Triggering and Conduction of Rail-Gap Switches in a High-Current Low-Inductance Crowbar Switch

The field-reversed configuration heating experiment (FRCHX) was designed to form closed-field-line magnetized target plasmas for magnetoinertial fusion and other high energy density plasma research. These plasmas are in a field-reversed configuration and are formed via a reversed-field theta pinch on an already magnetized background plasma. To extend the duration and temporal uniformity of the pinch, the capacitor bank driving the reversed-field discharge is crowbarred near the current peak. Four parallel rail-gap switches are used on the FRCHX for this application to ensure a low-inductance crowbar discharge path and to accommodate the large magnitude of the discharge current (often greater than 1 MA). Historically, parallel operation of spark gap switches in a crowbarring arrangement has often proved to be difficult due to the very low voltage present on the bank and across the switches at the time of peak current. In a low-inductance design, triggering can be further complicated by the rapid collapse of what little voltage there is across the switches as soon as the first spark gap begins conduction. This paper reports on the efforts that were made to develop a low-inductance crowbar switch for the FRCHX and to ultimately enable successful triggering and operation of the four parallel rail-gap switches used in the crowbar. The design of the low-inductance parallel switch assembly is presented first, followed by a description of the triggering scheme employed to ensure conduction of all four switches.

Analysis of the Compression and Heating of Magnetized Plasma Targets for Magneto-Inertial Fusion

This paper deals with the analysis of the possible use of magneto-inertial fusion (MIF) to create a neutron source. We consider the configuration of the target in the form of an axially symmetric magnetic trap with magnetic “plugs” or so-called “probkotron”. Heating and compression of a plasma target in the magnetic field is studied numerically. Parameters of the neutron source based on plasma-jet driven magneto-inertial fusion with a cylindrical target are given.

Analysis of the Compression and Heating of Magnetized Plasma Targets for Magneto-Inertial Fusion

Analysis of the Compression and Heating of Magnetized Plasma Targets for Magneto-Inertial Fusion

Review of Some Plasma Gun Techniques for Fusion at Megagauss Energy Densities

Plasma guns offer opportunities to generate and direct plasma flows at high energy density. Typically, such guns comprise coaxial electrodes that are connected to high-current sources (e.g., capacitor banks, pulse lines, inductive stores, or magnetic-flux-compression generators). The basic interactions include ionization of materials such as injected gas or preinstalled wires/foils, acceleration of these materials by the Lorentz force, and expulsion of the resulting plasma flows. We review the use of a particular arrangement in the form of a plasma flow switch that acts as a multimegampere commutator, but it can also provide a magnetized-plasma target for compression by an imploding liner. In a quite separate concept, a plurality of quasi-steady plasma guns in a spherical array provides converging, collimated jets to compress plasma with stand-off from the plasma generators and chamber walls. Such stand-off in a repetitively pulsed system can be crucial for the development of fusion power reactors at megagauss energy densities.

Low velocity ion slowing down in a strongly magnetized plasma target

AbstractIon projectile stopping at velocity smaller than target electron thermal velocity in a strong magnetic field is investigated within a novel diffusion formulation, based on Green-Kubo integrands evaluated in magnetized one component plasma models, respectively, framed on target ions and electron. Analytic expressions are reported for slowing down orthogonal and parallel to an arbitrary large magnetic field, which are free from the usual uncertainties plaguing the standard perturbative derivations.

Estimates of confinement time and energy gain for plasma liner driven magnetoinertial fusion using an analytic self-similar converging shock model

Plasma liner driven magnetoinertial fusion (PLMIF) is a fusion energy concept that utilizes an imploding plasma liner to shock heat and compress a magnetized target plasma to fusion conditions. The fusion burn fraction is linearly proportional to the confinement (or “dwell”) time of the liner-target system at peak compression, and therefore it is important to estimate the dwell time accurately in order to assess the fusion energy yield and gain. In this work, the dwell time has been estimated using the exact solution to a self-similar converging shock model. The dwell time was found to be determined by the sum of the outgoing shock and rarefaction times through the plasma liner at peak compression, and for chosen PLMIF conditions the dwell time was on the order of 1 μs. In addition, we show that the engineering gain, i.e., the total energy extracted as electricity (from fusion plus expanded liner energy) divided by the electrical energy required to implode the liner, exceeds unity for a wide range of liner thicknesses and specific heat ratios.

Low ion velocity slowing down in a strongly magnetized plasma target

Ion projectile stopping at velocity less than the target electron thermal velocity in a strong magnetic field is investigated within a novel diffusion formulation based on Green–Kubo integrands (GKI) evaluated in magnetized one-component plasma (OCP) models framed on target ions and electron. Analytical expressions are reported for slowing down orthogonal and parallel to an arbitrary large magnetic field, and these expressions are free from usual uncertainties plaguing the standard perturbative derivations.

Low ion-velocity slowing down in a strongly magnetized plasma target

An ion projectile stopping at a velocity smaller than the target electron thermal velocity in a strong magnetic field is investigated within a different diffusion formulation, based on Green-Kubo integrands evaluated in magnetized one component plasma models, respectively framed on target ions and electrons. Analytic expressions are reported for slowing down orthogonal and parallel to an arbitrary large magnetic field, which are free from the usual uncertainties plaguing the standard perturbative derivations. Magnetic and target temperature dependences of the low velocity slowing down are thoroughly detailed for dense plasmas of fast ignition concern and ultracold plasmas envisioned for ion beam cooling, as well.

C60-Fullerene Hyper-Velocity High-Density Plasma Jets for MIF and Disruption Mitigation

We present an innovative idea to use hyper-velocity (>30 km/s) high-density (>1017 cm−3) plasma jets of D-T/H and C60-fullerene for magneto-inertial fusion (MIF), high energy density laboratory plasma (HEDLP), and disruption mitigation in magnetic fusion plasma devices. The mass (~1–2 g) of sublimated C60 and hydrogen (or D-T fuel) produced in a pulsed power source is ionized and accelerated as a plasma slug in a coaxial plasma accelerator. For MIF/HEDLP we propose to create a magnetized plasma target by injecting two high-Mach number high-density jets with fuel (D-T) and liner (C60/C) structure along the axis of a pulsed magnetic mirror. The magnetized target fusion (MTF) plasma created by head-on collision and stagnation of jets is compressed radially by a metallic liner (Z-pinch) and axially by the C60/C liner. For disruption mitigation, the C60 plasma jets were shown to be able to provide the required impurity mass (J Fusion Energy 27:6, 2008).