Theta Pinch Research Articles

Toroidal magnetic field generation during compact toroid formation in a field-reversed theta pinch and a conical theta pinch

The influence that the Hall and ∇Pe terms, in a generalized Ohm’s law, have on the formation of a compact toroid in a field-reversed theta pinch and a conical theta pinch has been examined. The inclusion of these terms leads to the spontaneous generation of toroidal magnetic fields and toroidal velocities. The toroidal fields in the end regions reach peak values of almost 50% of the external poloidal field during the early stages of formation. When the coil geometry is the same at each end of the theta pinch, equal and opposite toroidal fields are generated by the Hall effect, so that no net toroidal flux is generated. When the geometry is not the same at each end, the Hall effect can lead to a net toroidal flux. Calculations for both a conical theta pinch experiment and a field-reversed configuration translation experiment demonstrate the generation of net toroidal flux, as observed experimentally.

Theta pinch discharge designed for emission spectrochemical analysis: spectral characterization

The high-temperature plasma generated by a theta pinch discharge was studied as an emission source for solid samples. Both sample geometry and the discharge fill gas affect plasma formation and subsequent plasma/sample interaction. Ablation and emission from solid samples have been demonstrated for aluminum, tungsten, and stainless steel samples exposed to the plasma. Time-resolved emission data show neutral emission occurring well after cessation of ion and continuum emission. Time resolution therefore removes the limitations of high background and ion line interference, which are associated with high energy discharges. 15 references, 9 figures, 1 table.

Theta pinch discharge designed for emission spectrochemical analysis: design and electrical characterization

A theta pinch discharge was designed and constructed as a high-temperature plasma source for application to the emission spectrochemical analysis of solid samples. This source has been operated up to 32 kV (1.33 kJ), with a peak discharge current of 60 kA. The peak magnetic field generated by this discharge through a double helical coil is 28 kG, resulting in a calculated peak plasma current of 32 kA. Thorough electrical characterization and design specification are reported. 55 references, 11 figures, 1 table.

Helical Quadrupole Field Stabilization of Field-Reversed Configuration Plasma

The n = 2 mode rotational instability, which appears on a field-reversed configuration plasma produced by a theta pinch, is stabilized by a helical quadrupole field. The critical strength of the field to stabilize the instability is obtained as a function of pitch angle of the helical coil a rad/m. Typically, the plasma in the α = 6 winding field is stabilized by about one-fifth of α = 0 field strength. To physically explain such a good effectiveness of the helical field, the rotation speed of the plasma iso measured by a Doppler shift of a carbon V 2270.9-Å line. However, the clear explanation to the helical effect is not yet given.

Review of the Los Alamos FRX-C Experiment

The FRX-C device is a large field-reversed theta pinch experiment with linear dimensions twice those of its FRX-A and FRX-B predecessors. It is used to form field-reversed configurations (FRCs), wh...

Magnetically Tailored, Atmospheric-Pressure Plasmas for Atomic Spectroscopy

Three magnetic field-plasma configurations are used to study the interaction of external magnetic fields with analytically useful, atmospheric-pressure plasmas. A magnetic field normal to the electric field in the plasma produced by the capacitive discharge vaporization of a thin Ag film is used to obtain an ExB drift motion of the plasma. Photographs show that this drift motion can drastically alter the size, shape, and location of the plasma. The same plasma-generation technique is combined with a nonuniform magnetic field to obtain an adiabatic magnetic-mirror ion trap. Finally, the cylindrically symmetric plasma produced by the capacitive discharge vaporization of a thin metal wire or a bundle of graphite fibers is combined with an axial magnetic field to obtain a theta pinch of the plasma. In all cases, the plasma current is used to generate the magnetic field in a large air-core inductor surrounding the plasma. Radiative and electrical properties of these magnetically modified plasmas will be presented.

Physics requirements for an attractive magnetic fusion reactor

The plasma parameters beta ⟨β⟩ and thermal diffusivity χE required for a self-sustained deuterium-tritium (D-T) reactor plasma may be written in terms of the geometry and technological requirements of the reactor. While there are, separately, constraints on each parameter, it is instructive to combine them in a single parameter ⟨β⟩/χE to characterize the reactor region. In a separate study of a generic toroidal magnetic fusion reactor it has been found that, for a fusion reactor to be competitive with alternative sources of electricity, it must have a fusion island weight of not more than half that of the Starfire and Mars reference reactors. A simple model, based upon this result, is used to determine the region of minimum ⟨β⟩/χE and the self-consistent physics and technology requirements for a reactor as a function of its plasma geometry. The requirements are compared with experimental achievements and theoretical predictions for the parameters ⟨β⟩, χE, and ⟨β⟩/χE, for a varietY of magnetic configurations – tokamak, stellarator, reversed-field pinch, bumpy torus, tandem mirror, and field-reversed theta pinch. It is shown that all these configurations are, ‘classically’, capable of reaching the attractive reactor region and that good progress is being made experimentally towards that goal.

Preliminary results on the equilibrium position in a figure-eight stellarator with variable rotational transform

To investigate how torsion of a magnetic axis influences the equilibrium of high beta plasmas the authors have built a figure-eight stellarator consisting of four half tori. The connection angles of the half tori can be altered, so that the angle of the rotational transform of the magnetic field lines can be changed from 0 degrees to 160 degrees . If the angle of the rotational transform is small, the plasma column, produced by a theta pinch, drifts away and finally is reflected at the tube wall. In contrast, for a larger angle of the rotational transform there are indications that an equilibrium state may be obtained after a certain degree of radial drift. This difference may be qualitatively explained by the fact that magnetic surfaces exist only in the latter case.

Magnetic flux trapping during field reversal in the formation of a field-reversed configuration

The flow of plasma and magnetic flux toward a wall is examined in a slab geometry where the magnetic field is parallel to the wall. Magnetohydrodynamic (MHD) flow with a quasisteady approximation is assumed that reduces the problem to three coupled ordinary differential equations. The calculated behavior shows that a thin current sheath is established at the wall in which a variety of phenomena appear, including significant resistive heating and rapid deceleration of the plasma flow. The sheath physics determines the speed at which flux and plasma flow toward the wall. The model has been applied to the field-reversal phase of a field-reversed theta pinch, during which the reduced magnetic field near the wall drives an outward flow of plasma and magnetic flux. The analysis leads to approximate expressions for the instantaneous flow speed, the loss of magnetic flux during the field reversal phase, the integrated heat flow to the wall, and the highest possible magnetic flux retained after reversal. Predictions from this model are compared with previous time-dependent MHD calculations and with experimental results from the TRX-1 [Proceedings of the 4th Symposium on the Physics and Technology of Compact Toroids, 27–29 October 1981 (Lawrence Livermore National Laboratory, Livermore, CA, 1982), p. 61] and TRX-2 [Proceedings of the 6th U.S. Symposium on Compact Toroid Research, 20–23 February, 1984 (Princeton Plasma Physics Laboratory, Princeton, NJ, 1984), p. 154] experiments.

Reconnection studies in field-reversed configurations

Internal magnetic field measurements are used to study the reconnection process near the ends of a low-compression field-reversed theta pinch. The measurements indicate that the addition of independently driven magnetic mirror coils at the ends are effective in inducing rapid reconnection and in minimizing plasma losses out the ends. Fast reconnection leading to the formation of a chain of magnetic islands along the length of the coil is observed on a time scale of a 100 nsec. These islands coalesce on a time scale of 1–2 μsec. Measured values of the resistivity are two orders of magnitude greater than classical during the implosion phase. The resistivity during the equilibrium phase is four times the classical value. Axial contraction and the n=2 rotational instability are not observed to occur in these experiments. Sudden termination of the configurations is thought to be caused by rapid loss of the internal field. This flux dissipation may be a consequence of electron cooling by the crossing of a radiation barrier. An oxygen impurity concentration of 2% is enough to account for the power dissipated during the collapse.

Temperature prediction and control in pulsed fusion-hybrid neutron multipliers

A numerical algorithm was developed for the one-dimensional unsteady-conduction heat-transfer equation to model the effects of volume heating in fusion hybrid-system neutron multipliers of slab geometry for any fusion-core pulsing scenario. The algorithm was shown to be highly accurate in all cases where it could be compared to the exact solution. The algorithm was compared to a previously developed simple analytic expression for predicting average multiplier temperatures over a wide range of fusion-core pulsing parameters. For most pulsed fusion-core scenarios, the analytic expression agreed with the numerical algorithm results to within a few percent or less. In the worst case, which corresponded to theta pinch-type operation (where the heat-pulse length is small relative to the multiplier thermal time constant and the time between pulses is large relative to the time constant), the analytic expression was accurate to within 10–15%. Thus, for most applications of temperature estimation and prediction, the analytic expression is adequate. A simple nomogram was developed to allow the average slab temperatures to be calculated easily as functions of the heat-pulse length, cooling time, and slab thermal time constant. As the computations showed, for those cases in which high slab average temperatures were due to short pulse lengths and long times between pulses, large average temperature decreases required slab thermal time constants that were small relative to the heating-pulse length and, therefore, very thin slabs. Finally, it was shown that, for long-pulsed systems, allowing high-intensity volume heating of the slab near the faces only, with no internal heat generation over the bulk of the interior, permitted the average temperature to be reduced by an order of magnitude relative to the uniform volume heating with the same total slab power generation. For short-pulsed systems with a large energy input per pulse (such as impact fusion and theta pinch), where the heat generated does not have time to diffuse throughout and from the slab during the heating pulse and where the temperature profiles at the end of the heating pulse would thus mirror the heat generation profiles, minimum peak temperatures are obtained by heating the volume uniformly.

Measurement of the Ti X ion density in a theta pinch plasma utilizing a laser interferometer (abstract)

The increase in the radial line integral of the electron density in the NBS theta pinch plasma due to the ionization of titanium impurity has been measured with the use of a He–Ne laser heterodyne quadrature interferometer. Titanium is injected as an impurity into the base gas of hydrogen with the use of a coaxial gun discharge with titanium electrodes. The abundance of the Ti X ion density in the plasma is deduced in each discharge from the measured increase in electron density by knowing the temporal charge state distribution of Ti ions obtained by spectroscopic methods.

Special Section Authors

Special Section Authors

Evolution of the Rayleigh–Taylor instability driven by a magnetic field gradient

It is shown here that the Rayleigh–Taylor instability in a device like a theta pinch has two different stages. The first stage is during the implosion phase of the theta pinch, and the second stage initiates after the formation of the plasma column. Termination of the first stage and evolution of the second stage from growth to a highly nonlinear stage and eventual wave breaking is presented by holographic interferometry. Though the instability in the first stage has been investigated before, here by employing microscopic theory it is shown that the magnetic field gradient is the driving mechanism of the instability in the latter stage.

A study of high-beta ballooning modes

Ballooning instabilities are studied in the Berkeley multiple mirror experiment. Counterstreaming theta pinch and Marshall gun source hydrogen plasmas are used to achieve a high beta ( β>25%), where β is the ratio of plasma to magnetic pressure at temperatures Te=Ti≊15 eV. Four magnetic field configurations are investigated, each at varying mirror ratios, to explore a range of drive and connection length parameters. In two of these the magnetic field is pulsed from a stable to a locally unstable configuration for initiation of ballooning activity. The other two (static) configurations are a weakly unstable local field region, and the standard linked quadrupole multiple-mirror configuration. Depending on the configuration, critical β’s are found for the onset of ballooning that vary from 5% for the most unstable configuration to greater than 25% for the standard multiple-mirror configuration. The m=1 azimuthal mode is predominant, with some admixture of m=2. The experimental results are compared with predictions from a magnetohydrodynamic theory. In the model the pressure is taken to be isotropic and constant along the axis, except in the diverging field regions at the device ends where the pressure falls to maintain beta constant, consistent with experimental observations. The theoretical results generally predict somewhat higher critical betas for the m=1 mode than those observed. Estimates of the effect of finite Larmor radii, nearby conducting walls, axially nonuniform pressure profiles and resistivity, are also given.

Flux and particle life-time measurements in field-reversed configurations

Flux and particle life-times of field-reversed configurations (FRC) have been measured in the TRX-1 field-reversed theta pinch. These measurements have been correlated with detailed numerical transport calculations based on classical and lower-hybrid-drift (LHD) resistivity. The data appear to imply spatially uniform resistivity profiles with a magnitude somewhat lower than that given by the wave energy bound of LHD fluctuations. Using a programmed formation technique it has been possible to form FRCs with large amounts of poloidal flux, and thus large separatrix radii. The particle confinement time has been found to scale approximately linearly with the amount of poloidal flux, and 150 μs particle confinement times have been achieved in 3 X 1015 cm−3 density FRCs with separatrix radii of only 7 cm. The linear scaling with poloidal flux is highly encouraging for scaling to higher-field, larger-size devices.

The Spectrum and Term System of Cl VII

The spectrum of six times ionized chlorine, Cl VII, has been investigated in the wavelength interval 100-6000 Å. The region below 270 Å has been studied by means of theta pinch and open spark spectrum recordings while above 270 Å we have used the beam-foil method and a sliding spark light source. 133 lines have been identified of which about 85 are new. The observed term system has been recalculated and extended to include 52 terms. The ionization limit, as derived from the polarization formula, is 921 096 ± 5 cm-1.

Simultaneous ionization and excitation of argon in an ionization wave

Abstract We report observations of an overpopulation, among the 3p44p configuration, of some doublet levels of Ar+ ions compared with quartet levels. The effect has been observed in an ionization wave produced in a small theta pinch device. The effect is explained as a result of electron impacts which lead to simultaneous ionization and excitation of Ar atoms in the ground state.

Multipole-field stabilization of the rotational instability in a theta pinch. I

A theoretical analysis based on the magnetohydrodynamic approximation is carried out on the effect of multipole-field suppression of the rotational instabilities excited in a high-β plasma column. The multipole field is assumed not to penetrate into the plasma column but to exert magnetic pressure on its boundary surface in order to suppress the distortion of the plasma column. Analytical theory, which takes into account only the effects of the fundamental wave, gives the stability criterion for the n=2 mode as Bs≥Bs,c= 1/2 (m−1)−1/2rs‖Ω‖(μ0 ρ0)1/2, where rs, ρ0, and Ω are the radius, mass density, and rotational angular velocity of the plasma column, respectively, 2m the order of the multipole field, Bs the field strength at radius rs in the vacuum state, and μ0 the permeability of vacuum. Numerical calculations including the effects of the waves parasitic to the fundamental wave support the stability criterion for hexapole (m=3) and octopole (m=4) fields. For quadrupole (m=2) fields, it is shown that the stable range of Bs is limited between 0.841 Bs,c and 0.856 Bs,c, where Bs,c is the analytical threshold for m=2.

Particle-confinement criteria for axisymmetric field-reversed magnetic configurations

Based on two constants of motion, H and Pθ, where H is the total energy of a particle and Pθ is its canonical angular momentum, particle confinement criteria are derived which impose constraints on H and Pθ. With no electric field at the ends of field-reversed magnetic configurations, confinement criteria for closed-field and absolute confinements are obtained explicitly, including both lower and upper bounds of Pθ/q, where q is the charge of the species considered, for a class of Hill's vortex field-reversed magnetic configurations. The commonly used criterion for the Hamiltonian, H < −ω0Pθ, where ω0 ≡ qB0/mc, is deduced from a more general form as a special case. In this special case, it is found necessary to impose a new criterion, , where Rw is the wall radius and B0 is the vacuum field, which reduces the confinement region in (H, Pθ) space. With the presence of electric fields at the ends of field-reversed magnetic configurations, confinement criteria are obtained for two interesting cases. In addition to lower and upper bounds of H, both lower and upper bounds of Pθ/q are found. For axially confined particles, the lower bound of Pθ/q reduces the confinement region in (H, Pθ) space and represents a new criterion. These results can be applied to calculations for field-reversed mirrors and field-reversed theta pinches.