E. B. Hooper

MHD equilibria in a spheromak sustained by coaxial helicity injection

Spheromaks sustained by coaxial helicity injection differ from unsustained spheromaks in the profiles of the ratio of current to magnetic field and of the safety factor. Ideal MHD modelling with Taylor relaxed profiles in the injector predicts that the safety factor in the confined region will generally lie between 0.5 and 1, with a divergence on the separatrix since the open field lines carry current from the injector. The safety factor can be single or double valued, depending on the current profile. The modelling predicts that there are no mode rational surfaces with m = 1 except very near the separatrix; this is expected to determine the unstable resistive tearing modes associated with the dynamo which drives the discharge current. The resulting low magnetic shear has a beta (~2%) at the Mercier limit, which can be improved by current profiles differing significantly from the Taylor state or by other effects such as plasma flow. Examples are presented for the Sustained Spheromak Physics Experiment recently constructed at LLNL.

Low‐frequency oscillations in the central cell of the TMX tandem mirror experiment

Two modes of low‐frequency oscillations have been observed in the central cell of the tandem mirror experiment (TMX). A mode at about 7 kHz has m=1 and probably drives radial transport at large radii. The mode identification is uncertain. A mode at about 13 kHz has m=0. The two end plugs oscillate 180° out of phase with each other and in phase with the amplitude (envelope) of the ion cyclotron frequency oscillations in each plug. This mode is identified as a sound wave; the frequency is apparently locked to the E×B rotation frequency, probably through an associated m=1 component. Neither mode severely limits confinement in the central cell, and both may be controllable. The lower‐frequency mode is sensitive to the density profile and to the fueling and is not always present. The higher‐frequency mode may be less important (or absent) in devices in which the plugs are stable at the plug’s ion cyclotron frequencies.

Simulation of spheromak evolution and energy confinement

Simulation results are presented that illustrate the formation and decay of a spheromak plasma driven by a coaxial electrostatic plasma gun, and model the plasma energy confinement. The physics of magnetic reconnection during formation is also illuminated. The simulations are performed with the three-dimensional, time-dependent, resistive magnetohydrodynamic NIMROD code [C. R. Sovinec, A. H. Glasser, T. A. Gianakon, D. C. Barnes, R. A. Nebel, S. E. Kruger, D. D. Schnack, S. J. Plimpton, A. Tarditi, and M. S. Chu, J. Comput. Phys. 195, 355 (2004)]. The simulation results are compared to data from the Sustained Spheromak Physics Experiment (SSPX) [E. B. Hooper, L. D. Pearlstein, and R. H. Bulmer, Nucl. Fusion 39, 863 (1999)]. The simulation results are tracking SSPX with increasing fidelity (e.g., improved agreement with measured magnetic fields, fluctuation amplitudes, and electron temperature) as the simulation has been improved in its representations of the experimental geometry, the magnetic bias coils,...

Ambipolar potential formation and axial confinement in TMX

TMX experimental data on ambipolar potential control and on the accompanying electrostatic confinement are reported. In the radial core of the central cell, measurements of electrostatic potentials of 150 V which augment axial ion confinement are in agreement with predictions using the Maxwell-Boltzmann result. Central-cell ion confinement was observed to scale according to electrostatic potential theory up to average enhancement factors of eight times over mirror confinement alone.

Radial transport reduction in tandem mirrors using end-wall boundary conditions

Results from the Tandem Mirror Experiment‐Upgrade (TMX‐U) demonstrate that radial transport in the plasma volume can be affected by the boundary conditions at the end wall. Measurements in which end‐wall plates, mapping to the plasma core, are switched from floating to grounded during plugging operation demonstrate that this floating increases the build‐up rate of the central cell plasma (by increasing the radial confinement time), steepens the core density profile, and affects the plasma throughout the entire cross section.

Energy confinement and magnetic field generation in the SSPX spheromak

The Sustained Spheromak Physics Experiment (SSPX) [Hooper et al., Nuclear Fusion 39, 863 (1999)] explores the physics of efficient magnetic field buildup and energy confinement, both essential parts of advancing the spheromak concept. Extending the spheromak formation phase increases the efficiency of magnetic field generation with the maximum edge magnetic field for a given injector current (B∕I) from 0.65T∕MA previously to 0.9T∕MA. We have achieved the highest electron temperatures (Te) recorded for a spheromak with Te>500eV, toroidal magnetic field ∼1T, and toroidal current (∼1MA) [Wood et al., “Improved magnetic field generation efficiency and higher temperature spheromak plasmas,” Phys. Rev. Lett. (submitted)]. Extending the sustainment phase to >8ms extends the period of low magnetic fluctuations (<1%) by 50%. The NIMROD three-dimensional resistive magnetohydrodynamics code [Sovinec et al., Phys. Plasmas 10, 1727 (2003)] reproduces the observed flux amplification ψpol∕ψgun. Successive gun pulses are...

Magnetic Reconnection During Flux Conversion in a Driven Spheromak

During buildup of a spheromak by helicity injection, magnetic reconnection converts toroidal flux into poloidal flux. This physics is explored in the resistive magnetohydrodynamic code, NIMROD [C.R. Sovinec, A.H. Glasser, T.A. Gianakon, D.C. Barnes, R.A. Nebel, S.E. Kruger, D.D. Schnack, S.J. Plimpton, A. Tarditi, and M.S. Chu, J. Comp. Phys., 195, 355-386 (2004)], which reveals negative current sheets with {lambda} = {mu}{sub 0}j {center_dot} B/B{sup 2}reversed relative to the applied current. The simulated event duration is consistent with magnetic diffusion on the sheet thickness and is accompanied by cathode voltage spikes and poloidal field increases similar to those seen in the Sustained Spheromak Physics Experiment, SSPX [E. B. Hooper, L. D. Pearlstein, and R. H. Bulmer, Nucl. Fusion 39, 863 (1999)]. All magnetic fieldlines are open during reconnection and their trajectories are very sensitive to their starting points, resulting in chaos. The current sheets are most intense inside the separatrix near the X-point of the mean-field spheromak, suggesting that the reconnection occurs near fieldlines which are closed in the azimuthal average.

Transport and fluctuations in high temperature spheromak plasmas

Higher electron temperature (Te>350eV) and reduced electron thermal diffusivity (χe<10m2∕s) is achieved in the Sustained Spheromak Physics Experiment (SSPX) by increasing the discharge current=Igun and gun bias flux=ψgun in a prescribed manner. The internal current and q=safety factor profile derived from equilibrium reconstruction as well as the measured magnetic fluctuation amplitude can be controlled by programming the ratio λgun=μ0Igun∕ψgun. Varying λgun above and below the minimum energy eigenvalue=λFC of the flux conserver (∇×B=λFCB) varies the q profile and produces the m∕n=poloidal/toroidal magnetic fluctuation mode spectrum expected from mode-rational surfaces with q=m∕n. The highest Te is measured when the gun is driven with λgun slightly less than λFC, producing low fluctuation amplitudes (<1%) and 1∕2<q<2∕3. Transport analysis shows a reduction in χe as Te increases, differing from Bohm or open field line transport models where χe increases with Te. Detailed resistive magnetohydrodynamic sim...

Magnetic reconnection process in transient coaxial helicity injection

The physics of magnetic reconnection and fast flux closure in transient coaxial helicity injection experiments in NSTX is examined using resistive MHD simulations. These simulations have been performed using the NIMROD code with fixed boundary flux (including NSTX poloidal coil currents) in the NSTX experimental geometry. Simulations show that an X point is formed in the injector region, followed by formation of closed flux surfaces within 0.5 ms after the driven injector voltage and injector current begin to rapidly decrease. As the injector voltage is turned off, the field lines tend to untwist in the toroidal direction and magnetic field compression exerts a radial J × B force and generates a bi-directional radial Etoroidal×Bpoloidal pinch flow to bring oppositely directed field lines closer together to reconnect. At sufficiently low magnetic diffusivity (high Lundquist number), and with a sufficiently narrow injector flux footprint width, the oppositely directed field lines have sufficient time to rec...

Controlled and spontaneous magnetic field generation in a gun-driven spheromak

In the Sustained Spheromak Physics Experiment, SSPX [E. B. Hooper, D. Pearlstein, and D. D. Ryutov, Nucl. Fusion 39, 863 (1999)], progress has been made in understanding the mechanisms that generate fields by helicity injection. SSPX injects helicity (linked magnetic flux) from 1 m diameter magnetized coaxial electrodes into a flux-conserving confinement region. Control of magnetic fluctuations (delta B/B similar to 1% on the midplane edge) yields T-e profiles peaked at > 200 eV. Trends indicate a limiting beta (beta(e)similar to 4%-6%), and so we have been motivated to increase T-e by operating with stronger magnetic field. Two new operating modes are observed to increase the magnetic field: (A) Operation with constant current and spontaneous gun voltage fluctuations. In this case, the gun is operated continuously at the threshold for ejection of plasma from the gun: stored magnetic energy of the spheromak increases gradually with delta B/B similar to 2% and large voltage fluctuations (delta V similar to 1 kV), giving a 50% increase in current amplification, I-tor/I-gun. (B) Operation with controlled current pulses. In this case, spheromak magnetic energy increases in a stepwise fashion by pulsing the gun, giving the highest magnetic fields observed for SSPX (similar to 0.7 T along the geometric axis). By increasing the time between pulses, a quasisteady sustainment is produced (with periodic good confinement), comparing well with resistive magnetohydrodynamic simulations. In each case, the processes that transport the helicity into the spheromak are inductive and exhibit a scaling of field with current that exceeds those previously obtained. We use our newly found scaling to suggest how to achieve higher temperatures with a series of pulses.