Field-reversed Theta Pinch Research Articles

Improvement and test of high-voltage pulsed power supply for HFRC

Field-reversed theta-pinch (FRTP) is commonly used to form high-performance field-reversed configuration (FRC) plasmas, and it is employed for the initial plasma formation in the HFRC device. The high-voltage pulsed power supply which is used to feed the θ-pinch coils in HFRC has already demonstrated its importance for initial plasma formation. This paper presents two attempts to improve the performance of the high-voltage pulsed power supply. To reduce the space occupation and increase the accuracy of the triggers of hydrogen thyratron, a newly designed high-voltage floating trigger is proposed in this paper. Experimental tests show that the optimized trigger can work stably under a floating voltage of 35 kV with a voltage rising rate of about 12 kV/μs and a total jitter time of less than 60 ns. Besides, a high-voltage laminated busbar is proposed to reduce the stray parameters. Experimental tests show that it can withstand a voltage of 34 kV. The peak current and frequency of each branch of the power supply are increased by at least 10%. Tests of the entire power supply show that the power supply can work stably under a voltage of 34 kV. The oscillation frequency of the Pre-Ionization (PI) branch can reach 152.0 kHz and the peak current of the Main branch can reach 78.3 kA. The results show the validity and reliability of the improvements.

Experimental evidence for super-Alfvénic acceleration of the field-reversed configuration due to a magnetic pressure gradient

The super-Alfvénic acceleration of an extremely high beta plasmoid due to a magnetic pressure gradient is evidenced in translation experiments involving the field-reversed configuration (FRC) in the FRC amplification via the translation-collisional merging (FAT-CM) device. Inside the FRC, there is a population of unmagnetized particles that forms a volume with extremely high beta. Formed using the field-reversed theta pinch method, the FRC is accelerated and injected into a quasi-static confinement magnetic field that is weaker than the formation and acceleration fields. Because the FRC is injected with nonzero axial translation speed and cannot slow down, its speed exceeds the Alfvénic and sonic speed upon entering the confinement field. This phenomenon is predicted from two-dimensional resistive magnetohydrodynamic simulations, and experimental results that are consistent with the magnetohydrodynamic approximation show that the FRC acceleration process is due mainly to magnetic pressure on the thin magnetized layer.

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.

Addressing Short Trapped-Flux Lifetime in High-Density Field-Reversed Configuration Plasmas in FRCHX

The objective of the field-reversed configuration heating experiment (FRCHX) is to obtain a better understanding of the fundamental scientific issues associated with high-energy density laboratory plasmas (HEDLPs) in strong, closed-field-line magnetic fields. These issues have relevance to such topics as magneto-inertial fusion, laboratory astrophysical research, and intense radiation sources, among others. To create HEDLP conditions, a field-reversed configuration (FRC) plasma of moderate density is first formed via reversed-field theta pinch. It is then translated into a cylindrical aluminum flux conserver (solid liner), where it is trapped between two magnetic mirrors and then compressed by the magnetically driven implosion of the solid liner. A requirement is that, once the FRC is stopped within the solid liner, the trapped flux inside the FRC must persist while the compression process is completed. With the present liner dimensions and implosion drive bank parameters, the total time required for implosion is ${\sim}{\rm 25}~\mu{\rm s}$ . Lifetime measurements of recent FRCHX FRCs indicate that trapped lifetimes following capture are now approaching ${\sim}{\rm 14}~\mu{\rm s}$ (and therefore, total lifetimes after formation are now approaching ${\sim}{\rm 19}~\mu{\rm s}$ ). By separating the mirror and translation coil banks into two so that the mirror fields can be set lower initially, the liner compression can now be initiated 7–9 $\mu{\rm s}$ before the FRC is formed. A discussion of FRC lifetime-limiting mechanisms and various experimental approaches to extending the FRC lifetime will be presented.

Development of a compact tomography camera system using a multianode photomultiplier tube for compact torus experiments

A compact tomography camera system consisting of a photomultiplier tube, a multislit optical system, and a band-pass interference filter has been developed. The viewing area and spatial resolution can be configured by the arrangement of the slit system. The camera system has been specially designed for self-organized compact torus experiments having strong magnetohydrodynamics events with a submicrosecond time-scale. The developed system has been tested on a field-reversed configuration formed by the field-reversed theta-pinch. Performance evaluation of the system has been performed by comparison to the former optical system.

High-density field-reversed configuration plasma for magnetized target fusion

Field reversed theta pinch technology is employed with programmed cusp fields at the theta coil ends to form high-density field-reversed configuration (FRC) plasmas. The well-formed FRC plasmas have volume-averaged density of 2-4/spl times/10/sup 22/ m/sup -3/, total temperature (T/sub e/+T/sub i/) of 300-500 eV, and plasma lifetime between 10-20 /spl mu/s in 50-70 mtorr of deuterium static gas fill. The achieved FRC parameters are very close to the desired target plasma requirements for magnetized target fusion.

Recent Results on Field Reversed Configurations from the Translation, Confinement and Sustainment Experiment

The field-reversed configuration (FRC) offers an attractive alternative approach to magnetically confined fusion because of its extremely high β, simple linear geometry, and natural divertor for helium ash removal. Multi-hundred eV and high density FRCs have been produced using the standard Field Reversed Theta Pinch (RFTP) method, with a confinement scaling that leads to fusion conditions. These FRCs are, however, limited to only tens of mWb fluxes and sub-msec lifetime. Recent progress has been made in building up the flux and sustaining the FRC current using Rotating Magnetic Fields (RMF) in the Translation, Sustainment, and Confinement (TCS) facility at the University of Washington. TCS has demonstrated formation and steady-state sustainment of standard, flux-confined, prolate FRCs. The RMF also provides stability for the n = 2 rotational mode, which is the dominant global instability observed experimentally. Simple calculations show that a strong radially inward force imposed by the RMF increases proportionally to any local outward deformation of the plasma cross section. Evidence of this has been experimentally demonstrated, and the effects of various RMF antenna geometries studied. High temperature FRCs could also be produced in TCS by translating high energy plasmoids formed in the normal theta pinch manner into the confinement chamber containing the RMF antennas. Extremely interesting results were obtained for this translation and capture process. The plasmoids can survive the violent dynamics of supersonic reflections off magnetic mirror structures, producing a stable high-β, near-FRC state with substantial flux conversion from toroidal to poloidal. This is a tribute not only to the robustness of FRCs, but also to the tendency of an FRC to assume a preferred state for a magnetized plasma. The magnetic helicity, as inferred by a simple interpretive model, is approximately preserved, possibly conforming to a high-β relaxation principle.

Transport, energy balance, and stability of a large field-reversed configuration

Experiments have been conducted on the Large s Experiment (LSX) [Phys. Rev. Lett. 69, 2212 (1992)] field-reversed theta pinch, where plasmas confined in a field-reversed configuration (FRC) have exhibited record energy, particle, and configuration lifetimes. By careful control of the formation process, it was possible to form symmetric, quiescent FRCs with s values (the number of ion gyroradii from the field null to the separatrix of the FRC) as large as 5. LSX particle confinement showed a strong scaling with s. The inferred particle diffusivity, Ds, at large s approached ∼2 m2/s, which, along with previous experimental results, indicate a favorable Ds∼s−1/2 scaling. At large s, both electron and ion cross-field thermal conduction losses become negligible compared to convective losses, with the inferred χ⊥e∼4 m2/s, which was near classical values. Data from several diagnostics employed on the LSX device were analyzed to seek correlation between distortions in the plasma shape and the confinement properties of the FRCs formed. No clear correlation between the quality of confinement and distortion was observed. Experiments conducted over a large range of s (1<s<8) appeared to be grossly stable to low-order modes, such as the internal tilt.

Current Sustainment of a Field-Reversed Configuration by Rotating Magnetic Field

The sustainment of a field-reversed configuration by means of a rotating magnetic field (RMF) is studied by the numerical simulation. In has been shown that the RMF applied externally on an FRC immediately after the production by a field-reversed theta pinch is penetrated into the plasma to drive a steady current, before the FRC fades out. There is a threshold value of the RMF which can maintain the FRC by the method. Since the RMF used in the present study is fairly large, we should optimize the parameters of the RMF to reduce the magnitude of the RMF required for sustaining the FRC. The method of applying the RMF to the FRC, however, may be effective for sustaining the hot and dense FRC in a steady state. 7 refs., 4 figs.

Axial dynamics in field-reversed theta pinches. II: Stability

Detailed stability studies are made with new diagnostics in the FRX-C/LSM field-reversed theta pinch [Plasma Physics and Controlled Nuclear Fusion Research (IAEA, Vienna, 1989), Vol. II, p. 517]. These studies seek the origin of a degradation of the confinement properties of field-reversed configurations (FRC’s) that appears associated with strong axial dynamics during plasma formation. Several instabilities are observed, including rotational modes, interchanges, and tilt instabilities. Only the latter are strongly correlated with FRC confinement. Tilt instabilities are observed for FRC’s with larger average number of ion gyroradii (s∼3–5) and smaller separatrix elongations (e∼3–4). Coincidently, strong axial dynamics occurs for cases with larger s and smaller e values, through increases in either reversed bias field or fill pressure. These data provide some understanding of FRC stability. In agreement with finite Larmor radius theory, there is a regime of gross stability for the very kinetic and elongated FRC’s with s/e<0.2–0.3. This is the regime that has been studied in most FRC experiments. However, tilt and other instabilities are observed for FRC’s with s/e∼1. Additional stabilization techniques will be required for future large-size FRC’s.

Axial dynamics in field-reversed theta pinches. I: Formation

Bias field scans are performed at various fill pressures in the FRX-C [Fusion Technol. 9, 13 (1986)] and FRX-C/LSM [Plasma Physics and Controlled Nuclear Fusion Research (IAEA, Vienna, 1989), Vol. II, p. 517] field-reversed theta pinches. These data show a systematic degradation of the confinement properties of field-reversed configurations whenever strong axial implosions occur during plasma formation. This limitation prevents access to the desired regime of large-size and long-lived field-reversed configurations. The cause of the confinement degradation must be due to some formation or gross stability problem. Here many studies are reported that attempt to correlate confinement degradation with some formation characteristic. These investigations remain inconclusive and suggest further stability studies presented in a companion paper.

Formation studies of field-reversed configurations in a slow field-reversed theta pinch

Field-reversed configurations (FRC’s) have been successfully formed in a field-reversed theta pinch in a regime where there was little or no radial shock heating. It has been observed that even with the elimination of radial shock heating there remains sufficient resistive and compressional heating to burn through any radiation barriers caused by the low Z contaminates introduced during formation. The equilibrium behavior of the FRC was not influenced by the loss of radial shock heating other than yielding a lower equilibrium flux for a given initial reverse flux. With the slower reversal of the axial field, it was possible to exert considerable control over the formation dynamics through the use of end control coils. Two modes of formation have been identified wherein either the equilibrium flux was maximized (slingshot mode), or, plasma heating was maximized and formation dynamics were minimized (bubble mode).

A semiempirical formation model for field-reversed configurations

Recent data from the FRX-C [Proceedings of the 7th Symposium on the Physics and Technology of Compact Toroids (Los Alamos National Laboratory, Los Alamos, NM, 1986), p.142] and FRX-C/LSM [Proceedings of the 14th European Conference on Controlled Fusion and Plasma Physics (European Physical Society, Madrid, 1987), p. 485] field-reversed theta pinches are presented concerning heating, internal flux, and particle retention after formation. These results extend the data base of field-reversed configuration plasmas to larger dimensions. Good agreement is found for collisionless plasmas with some existing formation laws [Fusion Technol. 9, 48 (1986)] and the main result is confirmation of improved internal flux retention for plasmas of larger radius. Some simple semiempirical laws are proposed, which allow a global analytical formation model. This model should provide reasonable estimates of the equilibrium parameters of field-reversed configurations formed in theta pinches.

Flux, energy, and particle lifetime measurements for well formed field reversed configurations

Experimental flux, energy and particle lifetimes are reported for a wide range of plasma conditions (Ti = 100–800 eV, rs = 3.5–7 cm) in the slow risetime TRX-2 field reversed theta pinch. The lifetimes exhibit a scaling with the parameter rs/ρi01/2 to an exponent of between 2.7 and 3.6. This favourable scaling, especially for the flux lifetime, implies an average plasma resistivity which scales as the drift parameter vE/vi to some power greater than unity. For present small devices, typical flux diffusion coefficients are about 4 m2·s−1 and, based on the above scaling, would decrease rapidly in larger devices with smaller pressure gradient scalelengths. The above scaling is obtained only for well formed FRCs with low levels of formation turbulence, and it remains to be seen if this low turbulence level can be maintained in larger, less kinetic, FRCs.

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.

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...

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.

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.

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.