"Sustained spheromak coaxial gun operation in the presence of an n = 1 magnetic distortion "
C.T. Holcomb et al.

Summary:

A spheromak is defined as "a simply connected magnetic equilibrium that approaches a force-free state described by del × B = λB." The helicity of a spheromak is conserved on a time scale comparable to the Alfvén and reconnection times but decays on the resistive diffusion time scale. One way to sustain a spheromak equilibrium is to "inject helicity" by connecting a magnetized coaxial gun to the flux conserver. One can write an equation describing the helicity balance necessary to sustain equilibrium, but the exact relaxation mechanisms that lead to equilibrium are complicated, with various magnetic dynamo mechanisms thought to be responsible. During spheromak experiments, magnetic probes nearly always observe a departure from toroidal symmetry of the form exp(i(ωt+nφ)), with n=1. This "n=1 mode" is believed to be responsible for the relaxation current. Three assumptions are usually made to simplify the analysis of spheromaks driven by coaxial helical injection: (1) B field and current remain axisymmetric to first order; (2) Relaxation is rapid, so that the current density distribution on the electrodes and open flux is uniform; (3) after formation, all of the gun flux remians connected to the electrodes while linking the magnetic axis of the spheromak.

In this paper, the authors discuss measurements that bring into question the validity of these assumptions. Data was taken from the Sustained Spheromak Physics Experiment (SSPX) at the Lawrence Livermore National Laboratory. Three arrays of six radial, six axial, and six toroidal magnetic field probes were used for the measurements (comparisons of electron temperature, gun voltage and edge mechanics for consecutive runs with and without probes showed that the perturbation of the plasma was negligible). Shots lasted about 4 ms, and a coherent n=1 mode was visible during the middle 2 ms of each shot. Probe measurements were expected to show 100% of the gun flux anchored to the outer wall, but instead the average over many shots was about 80%. The open flux current density was also found to be non-uniform.

The amount of current leaving the gun at a given location is shown to differ from the amount of current returning to the gun at that probe array, implying that current must flow across magnetic field lines somewhere below the array. This means that the current is not force-free, as in an ideal spheromak. The presence of cross-field current would tend to generate a toroidal J × B force on the plasma, causing it to rotate. A toroidal ion flow was observed using IDS in earlier experiments with a different discharge configuration, but no impurity ion velocity measurements were available for this study.

In conclusion, the coaxial gun used to sustain the SSPX spheromak was shown to break many of the usual assumptions for this sort of experiment. The amount of gun flux varies, and a large n=1 mode causes the flux and current within the gun to become asymmetric, leading to the presence of cross-field currents. These measurements make progress toward determining whether the closed-flux current profile can be controlled by adjusting the gun flux and current--a critical element for spheromak sustainment.

Applications to my research:

The SSPX is somewhat different than SSX in that the goal is to sustain a spheromak configuration for a relatively long period of time (the ability to create sustainable equilibrium plasma structures is essential for achieving practical magnetic confinement fusion), while SSX is intended to study magnetic reconnection using high time resolution measurements, with shots lasting only about .1 ms. However, this paper is a good example of how magnetic probe measurements can be used to calculate complex plasma properties. Like we do at SSX, the experimentalists at SSPX will want to use IDS or other external diagnostics to measure ion velocity during their shots--combining these data with the magnetic probe results will lead to a greater understanding of the processes at work.