Richard D. Milroy

A numerical study of rotating magnetic fields as a current drive for field reversed configurations

A fixed ion model has been developed to study the use of a Rotating Magnetic Field (RMF) as a current drive mechanism in a Field Reversed Configuration (FRC). This model is used to investigate the physics of RMF current drive in a parameter range of interest to two experiments at the University of Washington. Empirical expressions are found to characterize the critical RMF magnitude required for full penetration and the rate of RMF penetration. It is shown that in the presence of a strong anisotropic plasma resistivity, the direction and magnitude of the axial bias field can have a strong influence on the penetration of an RMF. Calculations that include the effects of realistic RMF antennae at finite radius are used to find the effects of coil spacing and positioning.

A magnetohydrodynamic model of rotating magnetic field current drive in a field-reversed configuration

A numerical model has been developed to study the use of a Rotating Magnetic Field (RMF) as an electron current drive mechanism for the formation and sustainment of a field-reversed configuration (FRC). Previous models assumed a fixed ion model, but here a full two-dimensional (r-θ) magnetohydrodynamic model has been developed. The model has been applied to two classes of problems: (1) For the sustainment problem, a RMF is applied to a preexisting FRC. (2) For the formation problem, a RMF is applied to a plasma column with an initially uniform axial magnetic field and background plasma density. The RMF-induced current reverses this bias field, forming a FRC. The code employs an option to include some three-dimensional effects to satisfy the average β condition and equalize pressure and density between inner and outer field lines, when it is applied to sustainment simulations.

Maintaining the closed magnetic-field-line topology of a field-reversed configuration with the addition of static transverse magnetic fields

The effects on magnetic-field-line structure of adding various static transverse magnetic fields to a Solov’ev-equilibrium field-reversed configuration are examined. It is shown that adding fields that are antisymmetric about the axial midplane maintains the closed field-line structure, while adding fields with planar or helical symmetry opens the field structure. Antisymmetric modes also introduce pronounced shear.

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...

A model for inferring transport rates from observed confinement times in field‐reversed configurations

A one‐dimensional transport model is developed to simulate the confinement of plasma and magnetic flux in a field‐reversed configuration. Given the resistivity, the confinement times can be calculated. Approximate expressions are found which yield the magnitude and gross profile of the resistivity if the confinement times are known. These results are applied to experimental data from experiments, primarily TRX‐1, to uncover trends in the transport properties. Several important conclusions emerge. The transport depends profoundly, and inexplicably, on the plasma formation mode. The inferred transport differs in several ways from the predictions of local lower‐hybrid‐drift turbulence theory. Finally, the gross resistivity exhibits an unusual trend with xs (separatrix radius rs divided by the conducting wall radius rc ), and is peaked near the magnetic axis for certain predictable conditions.

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.

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...