A. L. Hoffman

Formation and steady-state maintenance of field reversed configuration using rotating magnetic field current drive

Rotating magnetic fields (RMF) have been used to both form and maintain field reversed configurations (FRC) in quasisteady state. These experiments differ from steady-state rotamaks in that the FRCs are similar to those formed in theta-pinch devices, that is elongated and confined inside a flux conserver. The RMF creates an FRC by driving an azimuthal current which reverses an initial positive bias field. The FRC then expands radially, compressing the initial axial bias flux and raising the plasma density, until a balance is reached between the RMF drive force and the electron–ion friction. This generally results in a very high ratio of separatrix to flux conserver radius. The achievable final conditions are compared with simple analytic models to estimate the effective plasma resistivity. The RMF torque on the electrons is quickly transferred to the ions, but ion spin-up is limited in these low density experiments, presumably by ion-neutral friction, and does not influence the basic current drive process...

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.

Poloidal flux loss in a field‐reversed theta pinch

Poloidal flux loss has been measured in field‐reversed configurations and related to anomalous resistivity near the magnetic field null. The results indicate that mechanisms in addition to the lower hybrid drift instability are affecting transport.

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 properti...

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 conf...

Formation of Field-Reversed Configurations Using Scalable, Low-Voltage Technology

Field-reversed configurations are compact toroids confined solely by poloidal fields. Recent experiments and numerical calculations have demonstrated that they can be formed in field-reversed theta pinches on time scales longer than the radial Alfven time. This considerably eases the technological requirements for large devices, and permits reasonable formation schemes to be developed for future experiments. Scaling laws are developed for both flux trapping and heating effectiveness as a function of the formation time scale and poloidal flux level.

Long pulse FRC sustainment with enhanced edge driven rotating magnetic field current drive

Field reversed configurations (FRCs) have been formed and sustained for up to 50 normal flux decay times by rotating magnetic fields (RMFs) in the translation, confinement, and sustainment experiment. For these longer pulse times a new phenomenon has been observed: switching to a higher performance mode delineated by shallower RMF penetration, higher ratios of generated poloidal to RMF drive field, and lower overall plasma resistivity. This mode switching is always accompanied by, and perhaps triggered by, the spontaneous development of a toroidal field with a magnitude up to 20% of the peak poloidal field. The global data cannot be explained by previous RMF theory based on uniform electron rotational velocities or by numerical calculations based on uniform plasma resistivity, but agrees in many respects with new calculations made using strongly varying resistivity profiles. In order to more realistically model RMF driven FRCs with such non-uniform resistivity profiles, a double rigid rotor model has been developed with separate inner and outer electron rotational velocities and resistivities. The results of this modelling suggest that the RMF drive results in very high resistivity in a narrow edge layer, and that the higher performance mode is characterized by a sharp reduction in resistivity over the bulk of the FRC.

Rotating magnetic field current drive of high-temperature field reversed configurations with high ζ scaling

Greatly reduced recycling and impurity ingestion in the Translation, Confinement, and Sustainment—Upgrade (TCSU) device has allowed much higher plasma temperatures to be achieved in the field reversed configurations (FRC) under rotating magnetic field (RMF) formation and sustainment. The hotter plasmas have higher magnetic fields and much higher diamagnetic electron rotation rates so that the important ratio of average electron rotation frequency to RMF frequency, called ζ, approaches unity, for the first time, in TCSU. A large fraction of the RMF power is absorbed by an as yet unexplained (anomalous) mechanism directly proportional to the square of the RMF magnitude. It becomes of relatively lesser significance as the FRC current increases, and simple resistive heating begins to dominate, but the anomalous absorption is useful for initial plasma heating. Measurements of total absorbed power, and comparisons of applied RMF torque to torque on the electrons due to electron-ion friction under high-ζ operati...

Principal physics of rotating magnetic-field current drive of field reversed configurations

After extensive experimentation on the Translation, Confinement, and Sustainment rotating magnetic-field (RMF)-driven field reversed configuration (FRC) device [A. L. Hoffman et al., Fusion Sci. Technol. 41, 92 (2002)], the principal physics of RMF formation and sustainment of standard prolate FRCs inside a flux conserver is reasonably well understood. If the RMF magnitude Bω at a given frequency ω is high enough compared to other experimental parameters, it will drive the outer electrons of a plasma column into near synchronous rotation, allowing the RMF to penetrate into the plasma. If the resultant azimuthal current is strong enough to reverse an initial axial bias field Bo a FRC will be formed. A balance between the RMF applied torque and electron-ion friction will determine the peak plasma density nm∝Bω∕η1∕2ω1∕2rs, where rs is the FRC separatrix radius and η is an effective weighted plasma resistivity. The plasma total temperature Tt is free to be any value allowed by power balance as long as the rat...

Observations of improved confinement in field reversed configurations sustained by antisymmetric rotating magnetic fields

Rotating magnetic fields (RMF) have been employed to both form and sustain currents in field reversed configurations (FRC). A major concern about this method has been the fear of opening up magnetic field lines with even small ratios of vacuum RMF Bω to external confinement field Be. A recently proposed innovation was to use an antisymmetric arrangement of RMF, but vacuum calculations with full RMF penetration showed that very low values of Bω∕Be would still be required to provide field-line closure. Recent comparisons of symmetric and antisymmetric RMF drive on the translation, confinement, and sustainment (TCS) facility [A. L. Hoffman, H. Y. Guo, J. T. Slough et al., Fusion Sci. Technol. 41, 92 (2002)] have shown strong improvements in the basic confinement properties of the FRCs when using antisymmetric drive, even with ratios of Bω∕Be as high as 0.3. This is due to normal standard operation with only partial penetration of the RMF beyond the FRC separatrix. The uniform transverse RMF in vacuum is shie...