Experimental Design of a Magnetic Flux Compression Experiment

Generation of ultrahigh magnetic fields is an interesting topic of high-energy-density physics, and an essential aspect of Magnetized Target Fusion (MTF). To examine plasma formation from conductors impinged upon by ultrahigh magnetic fields, in a geometry similar to that of the MAGO experiments, an experiment is under design to compress magnetic flux in a toroidal cavity, using the Shiva Star or Atlas generator. An initial toroidal bias magnetic field is provided by a current on a central conductor. The central current is generated by diverting a fraction of the liner current using an innovative inductive current divider, thus avoiding the need for an auxiliary power supply. A 50-mm-radius cylindrical aluminum liner implodes along glide planes with velocity of about 5 km/s. Inward liner motion causes electrical closure of the toroidal chamber, after which flux in the chamber is conserved and compressed, yielding magnetic fields of 2–3 MG. Plasma is generated on the liner and central rod surfaces by Ohmic heating. Diagnostics include B-dot probes, Faraday rotation, radiography, filtered photodiodes, and VUV spectroscopy. Optical access to the chamber is provided through small holes in the walls.     

The Challenge of Wall–Plasma Interaction with Pulsed Megagauss Magnetic Fields

A method is described for choosing experimental parameters in studies of high-energy-density (HED) physics relevant to fusion energy, as well as other applications. An important HED issue for magneto-inertial fusion (MIF) is the interaction of metal pusher materials with megagauss (MG) magnetic fields during liner compression of magnetic flux and fusion fuel. The experimental approach described here is to study a stationary conductor when a pulsed current generates MG fields at the surface, instead of studying the inner surface of a moving liner. This places less demand upon the pulsed power system, and significantly improves diagnostic access. Thus the deceptively simple geometry chosen for this work is that of a z pinch composed of a metal cylinder carrying large current. Consideration of well known stability issues for the z pinch shows that for given peak current and rise time from a particular power supply, there is a minimum radius and thus maximum B field that can be created without disruption of the conductor before peak current. The reasons are reviewed why MG levels of magnetic field, as required for MIF, result in high temperatures and plasma formation at the surface of the metal in response to Ohmic heating. The distinction is noted between the liner regime obtained with cylindrical rods, which have a skin depth small compared to the conductor radius, and the exploding thin-wire regime, which has skin depth larger than the wire radius. A means of diagnostic development is described using a small facility (DPM15) built at the University of Nevada, Reno. It is argued that surface plasma temperature measurements in the 10-eV range are feasible based on the intensity of visible light emission.     

Compression, Heating and Fusion of Colliding Plasmoids by a Z-theta Driven Plasma Liner

A potentially promising approach to fusion employs a plasma shell to radially compress two colliding plasmoids. The presence of the magnetic field in the target plasma suppresses the thermal transport to the confining shell, thus lowering the imploding power needed to compress the target to fusion conditions. With the momentum flux being delivered by an imploding plasma shell, many of the difficulties encountered in imploding a solid metal liner are eliminated or minimized. The best plasma for the target in this approach is the FRC. It has demonstrated both high β, and robustness in translation and compression that is demanded for the target plasma. A high density compressed plasmoid is formed by a staged axial and radial compression of two colliding/merging FRCs where the energy that is required for the implosion compression and heating of the magnetized target plasmoid is stored in the kinetic energy of the plasmas used to compress it. An experimental apparatus is being constructed for the demonstration of both the target plasmoid formation as well as the compression of the plasmoid by a plasma liner. It is believed that with the confinement properties and the high β nature of the FRC, combined with the unique approach to be taken, that an nτ_E T _i triple product ∼5 × 10¹⁷ m⁻³ s keV can be achieved.     

The Plasma Liner Compression Experiment

Magnetic fusion at high energy density requires compression of a magnetized target in a manner that can be repetitively performed. One approach being investigated in these experiments is the radial compression of a FRC target by a cylindrical plasma liner. A circular array consisting of 16 small coaxial plasma sources were placed at each end of a quartz chamber radially near the wall to form the plasma liner. Liner masses of 3 mg have been formed in Xenon and have been accelerated to a velocity of 50 km/s. An FRC was produced in an adjacent chamber and translated inside the plasma liner where theta-pinch coils were employed to drive the plasma liner radially inward compressing the FRC. Close agreement is found between experimental results and 2D MHD numerical calculations. Efficient coupling (~50%) between the compression bank and the plasma liner has been observed.     

An Eulerian MHD model for the analysis of magnetic flux compression by expanding diamagnetic fusion plasma sphere

The process of magnetic flux compression (MFC) inside a solenoid by expanding diamagnetic plasma sphere produced by an inertial fusion micro-explosions and its application as a direct energy conversion scheme to convert a part of plasma kinetic energy into pulsed electrical energy has been recently reported [1]. For a detailed analysis of this concept, an Eulerian multi-material MHD model is developed using magnetic vector potential formulation for electro-magnetic field calculations and classical volume-of-fluid method for material interface tracking. The diffusion term in the magnetic induction equation is solved implicitly while the advection terms are computed using a second-order MUSCL scheme. An iteration procedure using ADI scheme is used for the free space field calculation. In this paper, we describe the details of the new MHD model, its validation against the semi-analytical solutions (for magnetic Reynolds number ?1) of magnetic convective-diffusion equations and application to explore the concept of MFC by expanding plasma sphere. The simulation results show that the algorithm is capable of handling complex plasma dynamics inside the MFC system. Also, the results indicate the development and the evolution of MRT like instability near the stagnation point. The magnetic field diffusion into the plasma during the expansion phase is found to be negligible.     

Observations and Simulations of Magnetic Fluctuations in MCX

Recently magnetic fluctuations in the Maryland centrifugal experiment (MCX) have been measured by an azimuthal array of 16 probes in the edge region of the plasma. A detailed analysis indicates that there is primarily a convection of m = 2 fluctuations by the azimuthally rotating plasma. However, the frequency spectrum of this mode is broad and is almost of the same order as the frequency. Furthermore, bicoherence analysis indicates dominant nonlinear interaction between m = 2 and a low frequency m = 0 mode. We utilize a 2D MHD code to investigate the dynamics of the primary interchange instability. For very low sheared rotation there is a broad spectrum (in m) of unstable modes. However, as the sheared rotation is increased the high mode numbers become stabilized. We will present detailed comparisons of spatio-temporal dynamics of our simulations with the data from the magnetic probes.     

Conversion of plasma energy into electrical pulse by magnetic flux compression

A conceptual study of magnetic flux compression inside a cylindrical coil by an expanding inertial fusion plasma sphere across the magnetic field produced by the coil itself have been performed numerically using a two-dimensional magnetohydrodynamic (MHD) simulations. The concept may find application in inertial fusion energy (IFE) system as a direct energy conversion scheme to convert a part of fusion plasma kinetic energy into pulsed electrical energy. Important theoretical and technical issues that has to be addressed are discussed. Preliminary theoretical analysis are given for the analysis of MHD interchange instabilities of expanding plasma across magnetic field. Overall efficiency of the system is determined numerically for a typical set of initial plasma and system parameters. Ultrahigh coil inter-turn voltages are predicted. Therefore, the application of magnetic self-insulation to avoid coil inter-turn break-down is considered. Also, we have analysed the system performance with different load conditions.     

Perspectives on Magnetized Target Fusion Power Plants

One approach to Magnetized Target Fusion (MTF) builds upon the ongoing experimental effort (FRX-L) to generate a Field Reversed Configuration (FRC) target plasma suitable for translation and cylindrical-liner (i.e., converging flux conserver) implosion. Numerical modeling is underway to elucidate key performance drivers for possible future power-plant extrapolations. The fusion gain, Q (ratio of DT fusion yield to the sum of initial liner kinetic energy plus plasma formation energy), sets the power-plant duty cycle for a nominal design electric power [e.g. 1,000 MWe(net)]. A pulsed MTF power plant of this type derives from the historic Fast Liner Reactor (FLR) concept and shares attributes with the recent Inertial Fusion Energy (IFE) Z-pinch and laser-driven pellet HYLIFE-II conceptual designs. Work supported by the Office of Science, OFES, through Los Alamos National Laboratory, under DOE contract W-7405-ENG-36.     

Linear and Nonlinear Development of the <Emphasis Type="Italic">m</Emphasis> = 0 Instability in Z-Pinch Equilibria with Axial Sheared Flows

The effect of sheared flows on the m = 0 instability development in a z-pinch is numerically investigated using a 2D magnetohydrodynamic (MHD) code. The behavior of both internal and free-boundary modes is studied by using two types of initial configurations: a diffuse Bennett equilibrium and a free-boundary parabolic equilibrium. It was found that sheared flows change the m = 0 development by reducing the linear growth rates, decreasing the saturation amplitude, and modifying the instability spectrum. Full stability can be obtained for supersonic plasma flows, but a larger shear is needed to obtain stabilization of free-boundary modes.     

Magnetic Field and Inductance Calculations in Theta-Pinch and Z-Pinch Geometries

Two codes have been developed to model solid metal or wire-wound conductors. The calculations are based on the decomposition of the conductors into arrays of thin wires. The first code, EDDY, models cylindrically symmetric conductors with currents in the theta direction. This code accurately models eddy current induction and magnetic diffusion. It was created in order to aid the design of magnetic-field shields in the FRX-L experiment for Magnetized Target Fusion (MTF). EDDY uses fast, accurate elliptic integral subroutines from MATLAB to solve for the time-dependent current flowing through each wire loop and the resultant magnetic field configuration. The second code, INDIV, models arbitrarily shaped conductors with current flow in the z direction. It was designed to model current division in an inductive divider that would inject current into a liner cavity, for magnetic flux and magnetized-plasma compression experiments. An experiment has been performed to test the INDIV code and the inductive division concept. The numerical results compare well with those of the experiment.     

Macron Formed Liner as a Practical Method for Enabling Magneto-Inertial Fusion

To take advantage of the smaller scale, higher density regime of MIF an efficient and repeatable method for achieving the compressional heating required to reach fusion gain conditions is needed. The macro-particle (macron) formed liner compression of the field reversed configuration (FRC) provides such a method. The approach to be described employs an assemblage of small, gram scale, macrons to form a more massive liner that both radially and axially compresses and heats the FRC plasmoid to fusion conditions. The large liner energy (several MJ) required to compress the FRC is carried in the kinetic energy of the full array of macrons. The much smaller energy required for each individual macron is obtained by accelerating the macron to ~3 km/s which can be accomplished remotely using conventional inductive techniques. 3D numerical calculations demonstrate that macron convergence can form a coherent liner provided minimum velocity and timing accuracy is met. Experimental results have demonstrated that a cylindrical or spherical macron can be accelerated to velocity within 2 m/s and timing less than 1 microsecond. Initial testing of a 6-stage launcher yielded 280 m/s at a final coupling efficiency of greater than 40%.     

The Experiment of Modulated Toroidal Current on HT-7 and HT-6M Tokamak

The Experiments of Modulated Toroidal Current were done on the HT-6M tokamak and HT-7 superconducting tokamak. The toroidal current was modulated by programming the Ohmic heating field. Modulation of the plasma current has been used successfully to suppress MHD activity in discharges near the density limit where large MHD m = 2 tearing modes were suppressed by sufficiently large plasma current oscillations. The improved Ohmic confinement phase was observed during modulating toroidal current (MTC) on the Hefei Tokamak-6M (HT-6M) and Hefei superconducting Tokamak-7 (HT-7). A toroidal frequency-modulated current, induced by a modulated loop voltage, was added on the plasma equilibrium current. The ratio of A.C. amplitude of plasma current to the main plasma current △Ip/Ip is about 12% ～ 30%. The different formats of the frequency-modulated toroidal current were compared.     

A Physics Exploratory Experiment on Plasma Liner Formation

Momentum flux for imploding a target plasma in magnetized target fusion (MTF) may be delivered by an array of plasma guns launching plasma jets that would merge to form an imploding plasma shell (liner). In this paper, we examine what would be a worthwhile experiment to explore the dynamics of merging plasma jets to form a plasma liner as a first step in establishing an experimental database for plasma-jets-driven magnetized target fusion (PJETS-MTF). Using past experience in fusion energy research as a model, we envisage a four-phase program to advance the art of PJETS-MTF to fusion breakeven (Q 1). The experiment (PLX) described in this paper serves as Phase 1 of this four-phase program. The logic underlying the selection of the experimental parameters is presented. The experiment consists of using 12 plasma guns arranged in a circle, launching plasma jets toward the center of a vacuum chamber. The velocity of the plasma jets chosen is 200 km/s, and each jet is to carry a mass of 0.2 mg to 0.4 mg. A candidate plasma accelerator for launching these jets consists of a coaxial plasma gun of the Marshall type.     

C<Subscript>60</Subscript>-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).     

Reversed-field pinch studies in the Madison Symmetric Torus

Studies of large-size (R=1.5 m,a=0.5 m), moderate current (I <750 kA) reversed-field pinch (RFP) plasmas are carried out in the Madison Symmetric Torus in order to evaluate and improve RFP confinement, study general toroidal plasma MHD issues, determine the mechanism of the RFP dynamo, and measure fluctuation-induced transport and anomalous ion heating. MST confinement scaling falls short of the RFP scaling trends observed in smaller RFPs, although the plasma resistance is classical. MHD tearing modes with poloidal mode numberm=1 and toroidal mode numbersn=5–7 are prevalent and nonlinearly couple to produce sudden relaxations akin to tokamak sawteeth. Edge fluctuation-induced transport has been measured with a variety of insertable probes. Ions exhibit anomalous heating, with increases of ion temperature occurring during strong MHD relaxation. The anomalous heating fraction decreases with increasing density, such that ion temperatures approach the lower limit given by electron-ion friction. The RFP dynamo has been studied with attention to various possible mechanisms, including motion-EMF drive, the Hall effect, and superthermal electrons. The toroidal field capacity of MST will be upgraded during Summer 1993 to allow low-current tokamak operation as well as improved RFP operation.     

Measurements of Plasma Jets and Collimated Flux Tubes that are the Precursors of Spheromak Self-organization

A magnetized planar coaxial plasma gun is used to study the physics of spheromak formation. Eight magnetic flux tubes spanning from the cathode to the anode electrode are first filled with plasma by a rapid MHD pumping mechanism which ingests plasma from nozzles at the wall. The ingested plasma convects toroidal flux and the pile-up of this flux in the flux tube causes the flux tube to become collimated. The eight collimated flux tubes first have the shape of spider legs, but then merge to form a central column jet. This jet lengthens, continuing to ingest plasma from the wall sources, and becomes kink unstable. At a later stage the root of the jet can break off from the electrode and this detachment has been identified as being associated with a sausage instability. The sausage instability takes place during the nonlinear stage of the kinking. The above statements are based on experimental observations and have been reconciled with MHD models.     

A Compact Torus Fusion Reactor Utilizing a Continuously Generated String of CT’s. The CT String Reactor, CTSR

A fusion reactor is described in which a moving string of mutually repelling compact toruses (alternating helicity, unidirectional Btheta) is generated by repetitive injection using a magnetized coaxial gun driven by continuous gun current with alternating poloidal field. An injected CT relaxes to a minimum magnetic energy equilibrium, moves into a compression cone, and enters a conducting cylinder where the plasma is heated to fusion-producing temperature. The CT then passes into a blanketed region where fusion energy is produced and, on emergence from the fusion region, the CT undergoes controlled expansion in an exit cone where an alternating poloidal field opens the flux surfaces to directly recover the CT magnetic energy as current which is returned to the formation gun. The CT String Reactor (CTSTR) reactor satisfies all the necessary MHD stability requirements and is based on extrapolation of experimentally achieved formation, stability, and plasma confinement. It is supported by extensive 2D, MHD calculations. CTSTR employs minimal external fields supplied by normal conductors, and can produce high fusion power density with uniform wall loading. The geometric simplicity of CTSTR acts to minimize initial and maintenance costs, including periodic replacement of the reactor first wall. Charles W. Hartman—LLNL retired; John Thomas—Privately employed.     

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 (Hsu et al. in 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.     

Extended MHD Simulations of the Compression and Stability of Spheromaks for Current Drive

We examine the compression and stability of spheromaks for magnetic field generation and heating by use of the 3D extended MHD code, NIMROD [C.R. Sovinec, et al., J. Comp. Phys. 195, 355 (2004)]. The formation of compact tori (CT) plasmas with strong magnetic fields by use of repetitive CT injection is being investigated experimentally and serves as impetus for this computational study. To reach high fields, the injected CT will require compression before injection. Stability of the spheromak to tilt and shift modes is examined during compression, as is the amplification of flux during co-helicity spheromak merging.     

Quasi-static magnetic compression of field-reversed configuration plasma: amended scalings and limits from two-dimensional MHD equilibrium

In this work, several key scaling laws of the quasi-static magnetic compression of field reversed configuration(FRC) plasma(Spencer et al 1983 Phys. Fluids 26 1564) are amended from a series of two-dimensional FRC MHD equilibriums numerically obtained using the Grad–Shafranov equation solver NIMEQ. Based on the new scaling for the elongation and the magnetic fields at the separatrix and the wall, the empirically stable limits for the compression ratio, the fusion gain, and the neutron yield are ...