Theta Pinch Research Articles

Spontaneous development of toroidal magnetic field during formation of field-reversed theta pinch

The formation of an FRC (Field-Reversed Configuration) is considered by using a hybrid simulation model that treats the electrons as a zero-inertia thermal fluid and the ions either kinetically or as a simple fluid. The unexpected spontaneous generation of a substantial toroidal magnetic field Bθ near magnetic reconnection points requires explanation. Although ion kinetic effects are responsible for some of the internal reconnection, simulations with a fluid ion representation also show similar self-generation of the toroidal field. Further investigation reveals that the origin of the toroidal field can be found in some of the terms that arise from retention of the Hall term – an automatic feature of the two-component model. Conceptually, the phenomena can be understood by noting that, if the magnetic field is ‘frozen into the electron fluid’, a sheared toroidal electron flow will stretch the poloidal field to make the toroidal field.

Experimental Excitation Rate Coefficients for Ne VIII Ions

From the line emission of a pure neon plasma produced in a theta pinch discharge rate coefficients for the excitation of the n = 3 and 4 levels in Ne VIII ions are derived and compared with theoretical calculations and previous measurements. The general agreement between theory and all measurements is rather satisfactory for the excitation to the n = 3 levels, the measured rate coefficients to the 4p and 4d levels, however, being consistently too low.

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高速可飽和リアクトルをスイッチング素子として用いたテータピンチ用大電流重畳電源

高速可飽和リアクトルをスイッチング素子として用いたテータピンチ用大電流重畳電源

A study of the VUV emission from highly ionized krypton in a theta pinch plasma

The ionization rates of Kr(IX), (X), (XI), and (XII) have been measured using a fast 60-kV-60kJ theta pinch as a plasma source. The line emission from each ion stage has been identified and the time evolution observed. A coupled set of rate equations was used along with time- and space-resolved measurements of the electron density and temperature to model the plasma light emission. The ionization rates of Kunze were adjusted by multiplying the rate for each ion stage with a constant until the peak intensity of the calculated emission agreed with the time of the observed peak intensity. The constants required for best fit were 2.5, 0.15, 3.0, and 2.0 for Kr(IX), (X), (XI), and (XII), respectively. Two successive ionization stages, Kr(X) and Kr(XI), have shown the same time dependence and possible reasons for this observation are discussed. During the course of modeling the light emission, we have also found that the rate for the excitation from the 3 d n to the 3 p 53 d n+1 level in Kr(X) ( n=9) and Kr(XI) (n=8) is a factor of 5 lower than predicted by the van Regemorter excitation rate equation.

Quadrupole Stabilization of then=2Rotational Instability of a Field-Reversed Theta-Pinch Plasma

The $n=2$ rotational instability is the most dangerous gross instability in a field-reversed theta pinch. It is demonstrated for the first time that the instability is completely suppressed by superposing a quadrupole field which is much smaller than the axial confinement field at the separatrix. The experimental threshold intensity of the field for stabilization is about 2.5 times less than that predicted by theoretical stability analysis.

Survey Of Reactor Aspects Of Compact Fusion Concepts

A compact fusion reactor is one that has a higher power density and, for the same total power, is significantly smaller than a conventional magnetic fusion reactor. This survey reviews the principal physics and technology employed by compact fusion power plants. Each of these concepts has been proposed as a fusion power source and rudimentary power plant designs exist. The concepts reviewed are: compact reversed-field pinch reactors, the Ohmically Heated Toroidal Experiment reactor, TRACT, field-reversed mirror reactor, spheromak, field-reversed theta pinch, compact tokamak reactors, dense Z-pinch reactor, imploding liner reactors, and the wall-confined fusion reactor.

Experimental studies on energy transport in a reversed-field theta pinch

The transport of energy and particles from a field-reversed configuration (FRC) produced by a theta pinch has been studied experimentally under the following typical plasma parameters in the quasi-static phase: Ti ∼ 300 eV, Te∼100eV, n̄e ∼ 5 × 1015 cm−3, ⟨β⟩ ∼ 1, ⟨Zeff⟩ ∼ 3 and separatrix radius rs ∼ 1.8 cm. Energy transport through various processes has been evaluated, consistent with the observed volume-averaged quantities which are changing in time in a quasi-static manner. As a result, it has been found that the dominant energy loss mechanism is particle loss, which accounts for more than 50% of the power flow out of the FRC. The second important process is the electron thermal conduction loss, which is estimated to be roughly 30% of the total loss if impurity radiation losses other than by carbon and oxygen are not important. In contrast, the ion thermal conduction loss is observed to be so small as to be hidden by the experimental errors. Radiation loss has been estimated to play a minor role if the observed ⟨Zeff⟩ can be ascribed to contaminations of only carbon and oxygen. The inferred energy confinement time τE is 7 is μs, which compares with the observed particle confinement time τp of 17 μs. The data indicate that τp is consistent with classical diffusion theory.

Suppression of the n=2 rotational instability in field-reversed configurations

Compact toroid plasmas formed in field-reversed theta pinches are generally destroyed after 30–50 μsec by a rotating n=2 instability. In the reported experiment, instability is controlled, and the plasma destruction is avoided in the TRX-1 theta pinch through the application of octopole magnetic fields. The decay times for loss of poloidal flux and particles are unaffected by the octopole fields. These decay times are about 100 μsec based on inferences from interferometry and excluded flux measurements. The weak, rotating elliptical disturbance (controlled n=2 mode) also made possible a novel determination of the density profile near the separatrix using single-chord interferometry. The local density gradient scale length in this region is found to be about one ion gyrodiameter.

Plasma Behaviors in the Open Field Region of Reversed-Field Theta-Pinch

A characteristic behavior of the plasma in an open field region of reversed field theta pinch has been studied with the guide field (GF) which extends the field line along the axial direction. The experimental result suggests that the rotational instability may be induced after the plasma touches the wall at the ends of the open field.

Magnetic guiding, focusing and compression of an intense charge-neutral ion beam

The motion of an intense, charge- and current-neutralized ion beam propagating axially into a solenoidal magnetic field in vacuum is shown to be described by one of two models depending on whether or not the beam magnetic skin depth c/ωpe exceeds half the beam radius. For a less-intense beam having a large skin depth, a new theoretical model is presented which shows that a solenoidal field penetrates to the beam axis and acts as a lens. If a minimum beam density is exceeded, the electrons and ions are brought to a common focus as a result of quasineutrality. The collective focal length is the geometric mean of the focal lengths for the two species when traveling alone. For an intense beam having a small skin depth, the applied field is excluded from the center of the beam channel by a skin current and the resulting magnetic pressure gradient compresses the beam. This case is similar to the theta pinch and is described by a snowplow model. The two models are verified by experiments with a 150 kV, 0.5–5 A/cm2 proton beam from a magnetically insulated diode. Possible applications in magnetic fusion, inertial fusion, and magnetospheric physics are discussed.

Macroscopic plasma behavior in a high-voltage toroidal theta pinch

The behavior of the implosion and post-implosion phases of two different toroidal high-beta plasma configurations has been investigated. The plasma is produced in a nominally axisymmetric toroidal theta pinch in which a tokamak-like low-beta plasma is heated and compressed to high beta by a fast-rising toroidal field. The two plasma cases differed from each other by the direction of their initial toroidal magnetic field relative to the direction of the main implosion magnetic field. The purpose of this investigation was to determine what factors govern the development and lifetime of the magnetic configuration during the early time post-implosion phase. It was determined from the q profiles for the parallel field case that the plasma should be unstable to the m=1 kink mode, i.e., q<1, but the normal outward shift of the plasma with respect to the external conducting wall carried it into the internal vacuum chamber wall before the kink could grow to an observable level. The magnetic fields in the case with the initial toroidal field antiparallel to the main implosion magnetic field exhibited nonaxisymmetric behavior.

Measurements of collisional excitation rate coefficients for Fe x ions in a plasma

About 1% or more of iron was introduced into a hydrogen-filled theta pinch by a gun-injection method. The Fe X density in the plasma was determined from the measured intensity of the Fe X forbidden (coronal) line at 6374.5 A. Electron collisional excitation rate coefficients for Fe X were obtained from measurements of Fe X vacuum-ultraviolet line intensities, electron density and temperature, and Fe X density. The experimental rate coefficients are compared with theoretical results.

Time-and Space-Resolved Measurement of Fluctuating Electric Field during a Theta-Pinch Implosion

Time- and space-resolved observations of fluctuating electric fields are made using the plasma satellites of the HeI 492.2 nm line during art implosion phase in a small-linear theta pinch. The rapid excitation (up to ∼6 kV/cm) and decay of the fluctuating fields with the frequency smaller than the electron plasma frequency are observed except near the center of the plasma column. Measurement of the magnetic field B z indicates that the intense fluctuating fields are localized in a narrow layer just behind the imploding magnetic front. From a measurement of the ion temperature, the fast ion heating and thermalization are observed in the implosion phase. These fast heating and thermalization and the decay of the fluctuations are almost coincident in time.

Compact toroid experiments: Spheromaks and field-reversed configurations

Compact toroids (CT) containing both poloidal and toroidal magnetic field, spheromaks, are generated in the CTX experiment using a magnetized coaxial plasma gun, and are trapped and stably confined in an oblate flux conserver. Total configuration lifetimes are observed up to ∼ 0.8 ms, consistent with classical resistive decay. The field reversed configuration (FRC) is a high beta, axisymmetric, highly prolate compact toroid, containing only poloidal magnetic field, formed in a field-reversed theta pinch. A quiescent confinement period of 30 to 90 μs with T i ∼ 200–500 eV and n ∼ 5 × 10 15 cm −3 is terminated by an n = 2 rotational instability. The FRC is stable to MHD modes including the tilting instability.

Confinement of a high-beta plasma column

Hydromagnetic aspects of confinement of a high-beta linear plasma column, including the reverse field configurations, are investigated. The previous theoretically predicted diverging confinement time of a sharp-boundary plasma column as β→1 is removed by properly taking into account the magnetic tension effect near the column throats. The obtained end loss rate is tested through simulation: the present simulation results in slab geometry are in good agreement with theory and are also close to other simulation and experimental values. The confinement time τ of a plasma with thickness a and length L at β=1 is found to be τ= 3/4 (3/2π)1/2(L/2cs)(L/a)1/2. When the magnetic field inside the column is reversed, the plasma end loss much improves: the end loss induces the reconnection of the field lines near the throats, which produces closed field lines (islands). Those islands are found to be unstable against the tilting instability. The tilting-induced reconnection of the island field line and the mirror field line is a very fast process even for negligibly resistive plasmas and this helps to rapidly spill out the plasma confined in the islands. The significance of these processes for the spheromaks and reversed field (theta) pinches is discussed.

Influence of Plasma Expansion on a Spectral Line Decaying in an Ionizing Plasma in a Theta Pinch

The particle end-loss process and its influence on the intensity of the HeII 468.6 nm line are investigated in a small linear theta-pinch plasma using spectroscopic techniques. In side-on measurement at the center of the plasma column, the HeII line intensity decreases with a much larger decay rate than in end-on measurement. The side-on decay rate is due to both the ionization and the particle-end-loss processes, while the end-on decay rate is mainly due to the ionization process. The difference between the two rates is investigated by solving rate equations involving both ionization and plasma expansion. Good agreement is obtained between the experimental and theoretical results. A simple method, using both the side-on and the end-on measurements is offered for estimating the particle-end-loss rate due to the plasma expansion.

Computer modelling of theta pinch behaviour with plasma column rotation

In order to simulate a theta pinch experiment in which the rotational energy is estimated to be comparable to the thermal energy, plasma column rotation is included through the radial pressure balance equation in a zero-dimensional, time-dependent computer model with a diffuse density profile. It is found that rotational pressure results in a suppression of the internal magnetic field, leading to an increase in the rate of flux diffusion and ohmic heating. The major effect of rotation is to increase the predicted temperature. Comparison of computer simulations with experimental temperatures at mid-plane indicates that temperature predictions of the computer simulations agree better with rotation effects included. Other features of the experiment, such as effective length and particle loss rate, are consistent with the simulation.

Material testing in a linear theta pinch

The interaction of stainless steel 316 and Inconel 625 alloys has been investigated with a thermonuclear-like plasma, n = 10 16 cm −3 and T i = 1 keV, generated in the Alvand I linear theta pinch. The average power flux is 10 7 W/cm 2 and the interaction time nearly one μs. A theoretical analysis based on the formation of an observed impurity layer near the material, has been used to determine the properties of the impurity layer and the extent of the damage on the material. Although arcing has been observed, the dominant damage mechanism has been assessed to be due to evaporation. Exposure to single shots has produced very heavily defective areas and even surface cracks on the SS 316 sample, but no cracks were observed on Inconel 625 after exposure to even 18 shots. On the basis of temperature rise and evaporation a comparison is made among materials exposed to plasmas of a theta pinch, shock tube, present generation tokamak and an anticipated tokamak reactor.

Plasma heating in field-reversed theta pinches

A method is devised to simulate plasma formation and heating in a field-reversed theta pinch which accounts for implosion kinetics, resistive dissipation, and compression (both radial and axial). Although containing several simplifying features, e.g., assumed radial profiles, distinct steps in the formation process, and a single adjustable parameter, the model nevertheless conserves energy and momentum in a global sense. Dissipation of reversed flux is governed by imposing an empirical ‘‘relaxation condition’’ on the drift parameter. Despite the simplicity of the method, predicted temperatures and radii agree well with experiments in most cases. The most important trend observed is the significant increase in temperature at higher reverse bias field. This arises from resistive dissipation and axial compression. In most cases, the predicted temperature exceeds (sometimes significantly) the temperature derived for a simple bounce and compression.