Compact Torus Plasma Research Articles

Compact toroid dynamics in the Compact Toroid Injection Experiment

Work on the acceleration of a compact toroid plasma configuration between coaxial electrodes is reported. In the experiment the maximum poloidal field component and the full width at half maximum of the poloidal field are shown to increase and decrease with the accelerator voltage, respectively. The velocity of the compact toroid is shown to increase with accelerator voltage and then saturate as the accelerator voltage is increased above approximately 11 kV. The saturation in the velocity and field components of the compact toroid is due to crowbarring of the accelerator insulator. The crowbarring of the insulator is consistent with the onset of the `blowby' effect, which is the most likely triggering source.

Behaviour of compact toroid injected into an external magnetic field

The interactions of a compact toroid (CT) plasma with an external magnetic field and a tokamak plasma have been studied experimentally on the FACT and JFT-2M devices. Fast framing camera and soft X ray emission profile measurements indicate shift and/or reflection motions ofthe CT plasma. New electrostatic probe measurements indicate that the CT plasma reaches at least up to the separatrix for discharges with toroidal field strengths of 1.0-1.4 T and that there exists a trailing plasma behind the CT. A large amplitude fluctuation on the ion saturation current and magnetic coil signals is observed. Power spectrum analysis suggests that this fluctuation is related to magnetic reconnection between the CT plasmoid and the toroidal field. The CT,including much of the trailing plasma, may be able to move across the external magnetic field more easily in the drift region of the injector owing to the Hall effect.

Nonlinear stability of field-reversed configurations with self-generated toroidal field

The field-reversed configuration (FRC) is a high-beta compact toroidal plasma confinement scheme in which the external poloidal field is reversed on the geometric axis by azimuthal (toroidal) plasma current. A quasineutral, hybrid, particle-in-cell (PIC) approach [Y. A. Omelchenko and R. N. Sudan, Phys. Plasmas 2, 2773 (1995)] is applied to study long-term nonlinear stability of computational FRC equilibria to a number of toroidal modes, including the most disruptive tilt mode. In particular, a self-generated toroidal magnetic field is found to be an important factor in mitigating the instability and preventing the confinement disruption. This is shown to be a unique FRC property resulting from the Hall effect in the regions of vanishing poloidal magnetic field. The instability-driven toroidal field stabilizes kink formation by increasing the magnetic field energy without destabilizing curvature-driven plasma motion. Finally, the tilt instability saturates due to nonlinear, finite Larmor radius (FLR) effects and plasma relaxation to a quasisteady kinetic state. During this transition the FRC is shown to dissipate a substantial amount of initially trapped flux and plasma energy. These effects are demonstrated for kinetic and fluid-like, spherical and prolate FRCs.

Observation of pinching in the compact toroid injection experiment: Implications for a plasma opening switch

A compact toroid inductively stores the energy released by a capacitor bank as it is being accelerated. This energy can be stored for a period of more than ten microseconds and then transferred to a load on a much shorter time scale. This article presents framing camera images of the radial compression of plasma trailing behind a compact toroid as the compact toroid leaves its inner electrode. This compression illustrates the basic principles of a compact toroid plasma opening switch which could be used to drive fast z pinches.

Effect of helical coils on the magnetic field and the stability ofa compact toroidal plasma

The helical distortion of a compact tokamak plasma with currents in modularFurth-Hartman type coils is investigated with respect to the impact on themagnetic field structure and to the ideal magnetohydrodynamic stability. Asequence of configurations, in which the current in the helical coils isincreased up to the level of that of the main toroidal coils, is generated.The magnetic field structure acquires a ripple along the field lines when thecurrents in both sets of coils becomes comparable. The magnitude of thisripple depends on the modulation of the Furth-Hartman coils on their windingsurface. The local ideal ballooning stability properties deteriorate with theincreasing helical deformation of the plasma shape because the normal magneticfield line curvature becomes larger in regions where the helical contributionenhances the toroidicity component while the local magnetic shear vanishes.The global external kink stability properties, in contrast, improvebecause the normal curvature on average does not change while the localmagnetic shear acquires a noticeable helical modulation.

Kinetic simulations of the formation and stability of the field-reversed configuration

The Field-Reversed Configuration (FRC) is a high-beta compact toroidal plasma confined primarily by poloidal fields. In the FRC the external field is reversed on axis by the diamagnetic current carried by thermal plasma particles. A three-dimensional, hybrid, particle-in-cell (zero-inertia fluid electrons, and kinetic ions), code FLAME, previously used to study ion rings [Yu. A. Omelchenko and R. N. Sudan, J. Comp. Phys. 133, 146 (1997)], is applied to investigate FRC formation and tilt instability. Axisymmetric FRC equilibria are obtained by simulating the standard experimental reversed theta-pinch technique. These are used to study the nonlinear tilt mode in the “kinetic” and “fluid-like” cases characterized by “small” (∼3) and “large” (∼12) ratios of the characteristic radial plasma size to the mean ion gyro-radius, respectively. The formation simulations have revealed the presence of a substantial toroidal (azimuthal) magnetic field inside the separatrix, generated due to the stretching of the poloidal field by a sheared toroidal electron flow. This is shown to be an important tilt-stabilizing effect in both cases. On the other hand, the tilt mode stabilization by finite Larmor radius effects has been found relatively insignificant for the chosen equilibria.

「コンパクトトーラス磁気閉じ込め研究」にあたって

「コンパクトトーラス磁気閉じ込め研究」にあたって

Design and Operation of a Passively Switched Repetitive Compact Toroid Plasma Accelerator

The design and operation of a spheromak-like compact toroid (SCT) plasma accelerator is described. As an example application, some principles are presented for using the device as a plasma injector to fuel a tokamak plasma. The device forms and accelerates an SCT plasma. The SCT is a self-contained structure of plasma with embedded poloidal and toroidal magnetic fields and their associated currents that provide plasma confinement and structural integrity. The SCT is formed in a magnetized coaxial plasma gun and then accelerated within coaxial electrodes. The typical mass of an SCT for tokamak fueling is from several tens to several hundreds of micrograms and is accelerated up to a velocity of ~2 × 105 m/s. Larger-mass SCTs can be produced, and higher velocities are possible. This is important for other applications such as space propulsion, X-ray generation, fast-opening plasma switches, and low-temperature high-density plasma simulators.The novel features of the device are as follows: (a) it can be operated in a repetitive mode, (b) the high-energy capacitor bank to form the SCT is switched by initiating breakdown with fast gas injection, (c) the required delay between formation and acceleration is achieved passively with saturable inductors that switch the high-energy accelerator capacitor bank, and (d) a drift section has been added within the toroidal field region to study cross-field propagation prior to tokamak penetration.With the device installed on the Davis Diverted Tokamak (DDT), measurements are taken to study tokamak fueling. Typical rep-rated parameters are as follows: the SCT poloidal magnetic field at the outer electrode = 0.4 T, the stored formation bank energy = 1600 J, and the stored accelerator bank energy = 3600 J. The lower bound on SCT kinetic energy leaving the accelerator = 40 J (inferred from electron line density measurements). Typical SCT velocity is 15 to 20 cm/μs. The maximum rep-rate achieved so far with the device is 0.2 Hz and is currently limited by vacuum pumping capacity. Reliable operation has been demonstrated for 1000 consecutive shots. Higher-energy single shots have also been taken to study SCT propagation through an open guide tube and to study penetration of the SCT into the DDT tokamak vessel with both tokamak plasma discharges and vacuum toroidal magnetic field only.

Optimization of soft x-ray emission from stagnating compact toroidal plasmas: A computational study

Computational simulations aimed at optimizing the high-energy, high-power, multikilovolt electromagnetic radiation emitted by a rapidly moving compact toroidal (CT) plasma which stagnates against a stationary “wall” are performed for argon, krypton, and xenon plasmas over a range of CT parameters. CT kinetic energies vary from 2–10 MJ, impact speeds vary from 50–200 cm/μs, and CT masses vary from 5–11 mg. It is found that a 2 MJ Ar CT optimally emits 1–1.5 MJ of essentially K-line radiation (>3 keV) for impact speeds of about 60–90 cm/μs; a 10 MJ Kr CT optimally emits about 1 MJ of essentially K-line radiation (>12.5 keV) for impact speed of about 135 cm/μs; and a 10 MJ Xe CT optimally emits about 3 MJ of essentially L-line radiation (>5 keV), about 0.5 MJ of continuum radiation above 10 keV, and about 0.1 MJ of continuum radiation above 20 keV, all also for impact speed of about 135 cm/μs. Pulse widths vary for the above optima from 7 ns at 135 cm/μs to 30 ns at 60 cm/μs.

Review of Experimental Investigations on Compact Toroids and Compact Tokamaks Using TS-3 Device

The TS-3 device at the University of Tokyo has been used to produce tree boundary spheromaks or spheromak-like compact toroids. Plasma production is accomplished either by Z-θ discharges or by means of magnetized coaxial plasma guns installed at both ends of the device. The plasmas produced have a minor=major radius of about 15 to 20 cm with a natural decay time of about 30 to 50 μs and a toroidal plasma current of about 30 to 60 kA. A unique feature of TS-3 device is the possession of production regions at both ends of the device, and concequently the ability of producing two adjacent compact toroids which can be merged through magnetic reconnection. Another feature of TS-3 device is the possibility of external application of a toroidal field with the aid of an optional center conductor assembly that can carry an axial current ranging from 0 to ±80 kA. This construction enables us to produce compact toroidal plasmas of various types from reversed field pinch(RFP) to tokamak in terms of the difference in q profile. The variation of both poloidal plasma current and external toroidal field current permits the change in magnetic configuration of merging plasmas, enabling the reconnection angle to continuously vary from about 20° (tokamak merging) through 90° (cohelicity spheromak merging) to 180° (counter-helicity spheromak merging to produce field reversed configurations(FRC)). When the coaxial guns are installed at both ends of the device in place of the center conductor, a center plasma current can be injected to form flux-core spheromaks (or bumpy z-pinches). Novel research subjects that have emerged from TS-3 experiments are; (1) the investigation of three dimensional effects of magnetic reconnection in laboratory plasmas. (2) the formation of FRC plasmas by a counter-helicity spheromak merging, (3) non-OH production and merging of tight aspect ratio tokamaks, (4) the stabilization of tilt motions of tight aspect ratio tokamaks, and (5) the formation and compression (flux amplification) of free-boundary tilt stabilized flux-core spheromaks.

A long conduction time compact torus plasma opening switch

Experiments to form and accelerate compact toroid (CT) plasmas have been performed on the 0.4-MJ Shiva Star fast capacitor bank at Phillips Laboratory. Theoretical investigations of employing a CT as a very fast opening switch are reported. A particular axisymmetric, geometrically complex switch design is studied with the help of 2-1/2-dimensional magnetohydrodynamic computer simulations. This design, called a magnetically-confined-plasma opening switch (McPOS), accumulates magnetic energy in an inductive store. Because of its intrinsic stability, the switch can conduct current for ten or more microseconds and can open in less than 100 ns-substantially less than the risetime of the capacitively produced electric current. A long conduction time compact torus plasma opening switch. >

High-power magnetic-compression heating of field-reversed configurations

Magnetic compression heating experiments at the 1 GW level on field-reversed configuration (FRC) compact toroid plasmas are reported. FRC’s formed in a tapered theta-pinch coil have been translated into a single-turn compression coil, where the external magnetic field is slowly raised up to seven times its initial value. Significant electron and ion heating consistent with the expected B4/5 adiabatic scaling is observed, despite significant particle diffusion, which is enhanced during compression. The n=2 rotational instability is enhanced during compression, but has been controlled to an extent by the application of an external quadrupole field. The particle and flux confinement times, τN and τφ, remain approximately equal and decrease roughly with the square of the plasma radius R during compression, implying a constant nonclassical field-null resistivity. The observed τN and τφ magnitudes and scalings are compared with classical and anomalous transport theories, and existing empirical models. Particle diffusion dominates the energy confinement, accounting for three-fourths of the total losses. Upper bounds on the electron thermal diffusivities are estimated.

THE SPHEROMAK AS AN AXISYMMETRIC SPHERICAL DYNAMO: CLARIFICATION OF AN OLD AMBIGUITY

An elementary result in magnetostatics clarifies a fundamental ambiguity in the theory of the Spheromak (which is a compact toroidal plasma without the external poloidal windings of a Tokamak). A free Spheromak (without an external equilibrium field) is shown to possess intrinsic rotational self-forces that amplify its toroidal current, and hence its poloidal magnetic field. This result explains the experimentally observed increase of toroidal current in free compact toroidal plasmas. The possibility of an axisymmetric spherical dynamo that generates its own dipole-like self-field is mentioned.

Linear stability analysis of compact toroidal plasmas using particle simulation

A technique is presented for the linear three-dimensional stability analysis of plasmas in which ion kinetic effects are important. This technique is appropriate for the analysis of compact toroidal plasmas such as spheromaks, field-reversed mirrors and theta pinches, field-reversed configurations, and ion rings and layers. The plasma is modeled by the hybrid quasineutral model, in which the ions are represented by particles. An initial value approach is used to find the most rapid instabilities, in conjuction with the numerical integration of the equations. The model is verified against known analytic and numerical results for the linear stability of ion layers and theta pinches. The tilt instability in the spheromak is investigated, and comparison is made to magnetohydrodynamic (MHD) stability results for an equilibrium with a low ion beta.

An Experimental Investigation of Low Power, Long Duration Rotamak Discharges

A rotamak device is described in which compact torus plasmas are generated using relatively low RF input powers (~ a few kW). Compact torus configurations are generated in both argon and hydrogen plasmas and are sustained for ~ 9 ms. These configurations appear to be grossly stable and show no tendency to disrupt even when subjected to large amplitude forced oscillations. A configuration incorporating a toroidal field is also investigated.

Magnetohydrodynamic Equilibrium Models for Rotamak Plasmas

A semi-analytic method is used to solve the Grad-Shafranov equation for a range of compact torus plasma configurations which have ellipsoidal separatrices, zero toroidal magnetic field and pressure P proportional to the square of the poloidal flux function 1[1. The equilibria are compared with the analytic solutions of the Solov'ev model, for which P ex 1[1.

The use of a preconditioned bi-conjugate gradient method for hybrid plasma stability analysis

Abstract The numerical stability analysis of compact toroidal plasmas using implicit time differencing requires the solution of a set of coupled, 2-dimensional, elliptic partial differential equations for the field quantities at every timestep. When the equations are spatially finite-differenced and written in matrix form, the resulting matrix is large, sparse, complex, non-Hermitian, and indefinite. The use of the preconditioned bi-conjugate gradient method for solving these equations is discussed. The effect of block-diagonal preconditioning and of incomplete block-LU preconditioning on the convergence of the method is investigated. For typical matrices arising in our studies, the eigenvalue spectra of the original and preconditioned matrices are calculated as an illustration of the effectiveness of the preconditioning. We show that the preconditioned bi-conjugate gradient method converges more rapidly than the conjugate gradient method applied to the normal equations, and that it is an effective iterative method for the class of non-Hermitian, indefinite problems of interest.

Special Section Authors

Special Section Authors

Adiabatic compression and interchange stability of rotating compact toroid plasmas

The adiabatic compression of plasmas with mass rotation is formulated as a variational principle based on some constants of the motion. A numerical code is constructed and Grad’s alternating dimensions method is used. The calculations simulate compression either by increasing the flux outside the plasma or by liner compression. Changes in Mach number and some stability criteria during compression are monitored. Interestingly, the Mach number remains almost constant despite a spin up of the plasma. An extension of the interchange stability criterion for rotating plasmas is developed. Interchange stable equilibria exhibit very high current density near the separatrix and tend to be more elongated. Interchange instability offers a mechanism to generate rotation throughout the plasma.

A 28 ?m water-vapor laser interferometer for plasma diagnostics

A high-power CW 27.972 μm water-vapor laser has been developed for interferometric and polarimetric measurements of plasmas. The maximum output power and the power density in the cavity of the laser with 2.0 cm bore and 220 cm length reach 85 mW and 109 μW/cm3, respectively. An interferometer using this laser is constructed and its performance is examined as a study on polarimetric method of magnetic field measurement. Preliminary interferometric experiments are also carried out on a compact toroidal plasma with field-reversal configuration.