Field-reversed Configuration Experiment Research Articles

Field Reversed Configuration Translation and the Magnetized Target Fusion Collaboration

After considerable design and construction, we describe the status of a physics exploration of magnetized target fusion (MTF) that will be carried out with the first flux conserving compression of a high pressure field-reversed configuration (FRC). The upgraded Los Alamos (LANL) high density FRC experiment FRXL has demonstrated that an appropriate FRC plasma target can be created and translated on a time scale fast enough to be useful for MTF. Compression to kilovolt temperature is expected to form a Mbar pressure, high energy density laboratory plasma (HEDLP). Integrated hardware on the new Field Reversed Compression and Heating Experiment (FRCHX) at the Air Force Research Laboratory Shiva Star facility, has formed initial FRC’s and will radially compress them within a cylindrically symmetric aluminum “liner”. FRXL has shown that time scales for FRC translation to the target region are significantly shorter than the typical FRC lifetime. The hardware, diagnostics, and design rationales are presented. Pre-compression plasma formation and trapping experimental data from FRXL and FRCHX are shown.

Power balance in a high-density field reversed configuration plasma

A global power balance analysis has been performed for the Field Reversed Experiment with Liner high density (>5×1022m−3) field reversed configuration (FRC) plasma. The analysis was based on a zero-dimensional power balance model [D. J. Rey and M. Tuszewski, Phys. Fluids 27, 1514 (1984)]. The key findings are as follows. First, the percentage of radiative losses relative to total loss is an order of magnitude lower than previous lower density FRC experiments. Second, Ohmic heating was found to correlate with the poloidal flux trapping at FRC formation, suggesting that poloidal flux dissipation is primarily responsible for plasma heating. Third, high density FRCs analyzed in this work reinforce the low-density adiabatic scaling, which shows that particle confinement time and flux confinement time are approximately equal.

Analysis of magnetic probe signals including effect of cylindrical conducting wall for field-reversed configuration experiment

A confinement field is disturbed by magnetohydrodynamic (MHD) motions of a field-reversed configuration (FRC) plasma in a cylindrical conductor. The effect of the conductor should be included to obtain a spatial structure of the disturbed field with a good precision. For this purpose, a toroidal current in the plasma and an eddy current on a conducting wall are replaced by magnetic dipole and image magnetic dipole moments, respectively. Typical spatial structures of the disturbed field are calculated by using the dipole moments for such MHD motions as radial shift, internal tilt, external tilt, and n=2 mode deformation. Then, analytic formulas for estimating the shift distance, tilt angle, and deformation rate of the MHD motions from magnetic probe signals are derived. It is estimated from the calculations by using the dipole moments that the analytic formulas include an approximately 40% error. Two kinds of experiment are carried out to investigate the reliability of the calculations. First, a magnetic field produced by a circular current is measured in an aluminum pipe to confirm the replacement of the eddy current with the image magnetic dipole moments. The measured fields coincide well with the calculated values including the image magnetic dipole moments. Second, magnetic probe signals measured from the FRC plasma are substituted into the analytic formulas to obtain shift distance and deformation rate. The experimental results are compared to the MHD motions measured by using a radiation from the plasma. If the error included in the analytic formulas and the difference between the magnetic and optical structures in the plasma are considered, the results of the radiation measurement support well those of the magnetic analysis.

Adiabatic model and design of a translating field reversed configuration

We apply an adiabatic evolution model to predict the behavior of a field reversed configuration (FRC) during decompression and translation, as well as during boundary compression. Semi-empirical scaling laws, which were developed and benchmarked primarily for collisionless FRCs, are expected to remain valid even for the collisional regime of FRX-L experiment. We use this approach to outline the design implications for FRX-L, the high density translated FRC experiment at Los Alamos National Laboratory. A conical theta coil is used to accelerate the FRC to the largest practical velocity so it can enter a mirror bounded compression region, where it must be a suitable target for a magnetized target fusion (MTF) implosion. FRX-L provides the physics basis for the integrated MTF plasma compression experiment at the Shiva-Star pulsed power facility at Kirtland Air Force Research Laboratory, where the FRC will be compressed inside a flux conserving cylindrical shell.

FRC Simulations using the NIMROD Code

The Plasma Science and Innovation Center (PSI-Center) is benchmarking and refining the NIMROD code for simulations of field-reversed configurations (FRCs). The NIMROD code can resolve highly anisotropic heat conduction and viscosity (Sovinec et al., JCP 195:355, 2004). This combined with its ability to include two-fluid effects, allows us to capture more detailed physics than previous calculations. Recent modifications to the radial boundary conditions capture most of the effects of multiple discrete coils found in many FRC experiments. When the tangential electric field on the end boundaries (open field lines) is set to zero and the Hall term is included in the calculation, the open field-line plasma spins up due to end-shorting effects, which in turn couples to the main FRC plasma through shear viscosity. The spin-up rate is found to be sensitive to the open field-line plasma profile. We are also investigating recent observations (Guo et al., Phys. Rev. Lett. 95:175001, 2005] that imply that a small toroidal field could help stabilize the n = 2 rotational instability. We find that a combination of a relatively weak toroidal magnetic field and the inclusion of the Hall term in the calculation can lead to a change in the character of the mode and a dramatic reduction to its growth rate.

Experimental profile evolution of a high-density field-reversed configuration

A field-reversed configuration (FRC) gains angular momentum over time, eventually resulting in an n=2 rotational instability (invariant under rotation by π) terminating confinement. To study this, a laser interferometer probes the time history of line integrated plasma density along eight chords of the high-density (∼1017cm−3) field-reversed configuration experiment with a liner. Abel and tomographic inversions provide density profiles during the FRC’s azimuthally symmetric phase, and over a period when the rotational mode has saturated and rotates with a roughly fixed profile, respectively. During the latter part of the symmetric phase, the FRC approximates a magnetohydrodynamic (MHD) equilibrium, allowing the axial magnetic-field profile to be calculated from pressure balance. Basic FRC properties such as temperature and poloidal flux are then inferred. The subsequent two-dimensional n=2 density profiles provide angular momentum information needed to set bounds on prior values of the stability relevant parameter α (rotational to ion diamagnetic drift frequency ratio), in addition to a view of plasma kinematics useful for benchmarking plasma models of higher order than MHD.

Visible bremsstrahlung tomographic diagnostic for the pulsed high density field-reversed configuration experiment

A diagnostic suite for the source section of the pulsed high density field-reversed configuration (FRC) experiment has been constructed to investigate the equilibrium and stability of FRC plasmas. In particular, a visible bremsstrahlung tomographic system has been designed and implemented. Three types of tomographic analyses for FRCs are performed: a Fourier fit method (Cormack-Granetz), a maximum entropy method, and a minimum Fisher method utilizing code developed for the TCV tokamak experiment in Switzerland [Anton et al., Plasma Phys. Controled Fusion 38, 1849 (1996)]. Results from the different methods and end-on imaging from the fast-framing camera are compared showing relative agreement of FRC internal structures between all measurements.

Twenty-channel bolometer array for studying impurity radiation and transport in the TCS field-reversed configuration

A bolometer array diagnostic has been developed for the University of Washington Translation, Confinement, and Sustainment (TCS) field-reversed configuration (FRC) experiment in order to measure radially resolved total radiated power per unit length of the FRC. This will provide radiation energy loss information, useful in power balance and impurity studies. The 20-element photodiode bolometer will be mounted at the midplane of the TCS cylindrical vacuum chamber to view the rotating magnetic field (RMF) generated FRC plasma. Key features of this new bolometer array are (1) extensive electrical shielding against the RMF, (2) robust electrical isolation, (3) trans-impedance amplifiers using a microcoax interface at the array and a fiber optic interface to the screen room, and (4) a custom glass-on-metal socket for the 20-element photodiode chip to ensure high vacuum compatibility. The bolometer array can be retracted behind a gate valve using a stepper motor to protect it during vacuum chamber bakeout. The slit assembly housing is interchangeable to provide flexibility for the viewing sightlines.

Modeling of field-reversed configuration experiment with large safety factor

The Translation-Confinement-Sustainment facility has been operated in the “translation-formation” mode in which a plasma is ejected at high-speed from a θ-pinch-like source into a confinement chamber where it settles into a field-reversed-configuration state. Measurements of the poloidal and toroidal field have been the basis of modeling to infer the safety factor. It is found that the edge safety factor exceeds two, and that there is strong forward magnetic shear. The high-q arises because the large elongation compensates for the modest ratio of toroidal-to-poloidal field in the plasma. This is the first known instance of a very high-β plasma with a safety factor greater than unity. Two-fluid modeling of the measurements also indicate several other significant features: a broad “transition layer” at the plasma boundary with probable line-tying effects, complex high-speed flows, and the appearance of a two-fluid minimum-energy state in the plasma core. All these features may contribute to both the stability and good confinement of the plasma.

Confinement analyses of the high-density field-reversed configuration plasma in the field-reversed configuration experiment with a liner

The focus of the field-reversed configuration (FRC) experiment with a liner (FRX-L) is the formation of a target FRC plasma for magnetized target fusion experiments. An FRC plasma with density of 1023m−3, total temperature in the range of 150–300 eV, and a lifetime of ≈20μs is desired. Field-reversed θ-pinch technology is used with programed cusp fields at θ-coil ends to achieve non-tearing field line reconnections during FRC formation. Well-formed FRCs with density between (2–4)×1022m−3, lifetime in the range of 15–20μs, and total temperature between 300–500 eV are reproducibly created. Key FRC parameters have standard deviation in the mean of 10% during consecutive shots. The FRCs are formed at 50 mTorr deuterium static fill using 2 kG net reversed bias field inside the θ-coil confinement region, with external main field unexpectedly ranging between 15–30 kG. The high-density FRCs confinement properties are approximately in agreement with empirical scaling laws obtained from previous experiments with fill pressure mostly less than 20 mTorr. Analyses in this paper reveal that reducing the external main field modulation and∕or extending the θ-coil length in the FRX-L device are critical in achieving higher FRC parameters for application in magnetized target fusion.

Stabilization of global movement on a field-reversed configuration due to fast neutral beam ions

Experimental evidence for the global stabilization effect of neutral beam injection on field-reversed configuration (FRC) plasma has been found for the first time. The translation of FRC plasma, i.e., transferring the formed plasma into another vessel along a gradient of guiding magnetic field, is an important technique for both the current FRC experiments and a future fusion reactor to separate formation and confinement regions. However, the translation’s dynamic process causes global wobble movement of the plasma column. The stabilization effect induced by obliquely injected neutral beams on this global movement has been observed by both interferometry and magnetic measurement. The behavior of injected beam ions has been calculated numerically and suggests that the injected beam ions confined under a strong mirror field could produce effective ring-current at both ends of the plasma column. The stabilization effect of this ring-current on the global movement has been discussed by using a rigid body model.

Spontaneous and artificial generation of sheared-flow in oblate FRCs in TS-3 and 4 FRC Experiments

Spontaneous formation of toroidal flow was measured for the first time in oblate field-reversed configurations (FRCs) produced in TS-3 and TS-4 experiments. The toroidal ion flow (Vi ≈ 10 km s−1) was found to peak around the magnetic axis, indicating that the FRC had a peaked ion current in sharp contrast to its hollow electric current. The peaked ion flow also indicated the formation of high flow shear inside the separatrix. The toroidal flow was observed to deform the magnetic field lines of the FRC, producing bipolar toroidal field profile. In high-s FRC (averaged number of ion gyro-radii in the separatrix: `s' = 4.5) with slow flow, its n = 1 mode kept growing, causing collapse of the whole configuration. However, in low-s FRC (s = 3) with fast flow, the rotating n = 2 mode (saturated) became dominant after n = 1 mode saturation. The spontaneous formation of flow-shear possibly transformed the n = 1 mode into the n = 2 mode, suggesting a new sheared-flow stabilization of the n = 1 mode. The flow-shear was also generated artificially using the `sling shot' effect of the counterhelicity reconnection. The n = 1 and 2 mode amplitudes were reduced to (1/5)–(1/10) due to the generated flow-shear. A new method for continuous sheared-flow generation was proposed for stabilization and heating of FRC by the use of intermittent merging of spheromaks with opposing toroidal field.

Linear gyroviscous stability of field-reversed configurations with static equilibrium

A discrepancy persists between field-reversed configuration experiments, which are generally stable, and theoretical predictions of instability. The common consensus has been that the stability is the result of finite Larmor radius (FLR) effects. An FLR analysis is presented that finds the self-consistent displacement functions and complex frequency. This is done using the linear gyroviscous model, a fluid-based representation of FLR that allows a wide range of equilibria and modes to be examined with modest computations. The conclusion is that FLR in static FRC fails to explain the observed stability. The cause of stability must lie elsewhere.

Tilt mode stability scaling in field-reversed configurations with finite Larmor radius effect

The marginal stability of a static plasma with finite-Larmor-radius (FLR) effects depends on a combination of the FLR effect and the ideal magnetohydrodynamic (MHD) potential energy. For the tilt mode in a field-reversed configuration (FRC) previous computations of these two factors led to a prediction of stability for S*⩽(3−5)E where S* is the macroscale parameter (separatrix radius/ion skin depth) and E is the elongation (separatrix half length/separatrix radius). This prediction explained the observed stability of most experiments. However, recent computations of actual MHD eigenfunctions indicate that the MHD growth rate has a much weaker scaling with elongation than previously believed. As a consequence, most of the long-lived, stable FRC experiments lie in the region predicted to be unstable. It appears then that the stability of FRC experiments is not explained by FLR effects in a static equilibrium.

Flux buildup in field reversed configurations using rotating magnetic fields

Rotating magnetic field (RMF) current drive is a very attractive method for both increasing the flux and sustaining the current in field reversed configurations (FRC). It has been demonstrated in low temperature, low field rotamaks, and will now be applied to a new translation, confinement, and sustainment (TCS) experiment attached to the LSX/mod (Large s field-reversed configuration Experiment) facility [Hoffman et al. Fusion Technol. 23, 185 (1993)]. Previous RMF calculations have been concerned primarily with the plasma currents and particle orbits produced in one-dimensional cylinders with the rotating field strength of near equal magnitude to the confining axial field. Both fluid current and particle orbits are calculated here in the more interesting regime appropriate to TCS and reactors where the confinement field far exceeds the rotating field strength. New insight is gained into both the flux buildup requirements for two-dimensional equilibria and into the limits on ion rotation in this high confinement field regime.

Damping of lower hybrid waves by low-frequency drift waves

The conditions under which a spectrum of lower hybrid drift waves will decay into low-frequency drift waves (LFD) are calculated. The purpose is to help understand why lower hybrid drift waves are not seen in all field-reversed configuration (FRC) experiments in which they are predicted. It is concluded that if there is in the plasma a LFD wave amplitude above a critical level, lower hybrid waves will decay into low-frequency drift waves. The critical level required to stabilize TRX-2 [Phys. Fluids 30, 1497 (1987)] is calculated and found to be reasonably consistent with theoretical estimates.

Electron temperature in field reversed configurations and theta pinches with closed magnetic field lines

Field-reversed configurations (FRC) and theta pinches with trapped reversed bias field are essentially the same magnetic confinement systems using closed magnetic field lines inside an open-ended magnetic flux tube. A simple model of joule heating and parallel electron thermal conduction along the open flux lines to an external heat sink gives the electron temperature as Te(eV) ≅ 0.05 B2/3(G) L1/3(cm), where B is the magnetic field and L is the coil length. This model appears to agree with measurements from present FRC experiments and past theta-pinch experiments which cover a range of 40–900 eV. The energy balance in the model is dominated by (a) parallel electron thermal conduction along the open field lines which has a steep temperature dependence, , and (b) the assumed rapid perpendicular transport in the plasma bulk which, in experiments to date, may be due to the small number of ion gyroradii across the plasma.

Inadequacies of finite Larmor radius treatments of the internal tilting instability in field-reversed configurations

A finite Larmor radius treatment of the tilting instability for field-reversed configurations is presented. It is shown on two accounts that such a treatment is inappropriate. First, the finite Larmor radius terms become infinite at the field null of the magnetic axis, because of the breakdown of the small Larmor radius assumption. Second, numerical computations using realistic parameters show that the magnetic moments of the ions are very poorly conserved at the tips of the flux surfaces in field-reversed configuration equilibria. Therefore finite Larmor radius theories cannot be used reliably to explain the observed stability to tilting of field-reversed configuration experiments.

The origin of rotation in field-reversed configurations

The stable lifetimes of many field-reversed configuration (FRC) experiments have been observed to be limited by the onset of the m = 2 rotational instability. The origin of the rotation which drives this instability is investigated with the aid of hybrid simulation methods. The loss of particles with guiding centres on open field lines is found to lead to localized rotation near the separatrix and this effect is found to be enhanced by end-shorting of the radial electric field outside the separatrix. In simulations allowing azimuthal variation the velocity shear is eventually relaxed so that the bulk of the plasma begins to rotate. These simulations also show that the m = 2 instability does not appear as long as rotation is localized near the separatrix. It is found that by increasing the separatrix radius it is possible to significantly delay the transfer of rotation from the separatrix, hence delaying the onset of the m = 2 instability.

Electron temperature measurements in the field-reversed configuration experiment FRX-C

Electron temperature data are presented from Thomson scattering measurements performed on field-reversed configuration plasmas generated in the FRX-C experiment. Two experimental conditions have been investigated, corresponding to initial deuterium fill pressures of 5 and 20 mtorr. At 5 mtorr, Te values of (175±25) eV are observed, which are nearly independent of time and radial position inside the separatrix. An electron power loss of approximately 80 MW is inferred. At 20 mtorr, Te values of 70–120 eV are measured and good agreement with radial pressure balance is obtained. This agreement indicates that radiation from low-Z impurity ions does not dominate the observed energy confinement.