"Modeling SSX Spheromak Plasmas: Internal Physics from External Measurements"
Vyacheslav S. Lukin

Summary:

The Swarthmore Spheromak Experiment (SSX) is a laboratory device designed to model processes such as solar flares on the sun, particularly focusing on the reconnection of oppositely oriented magnetic structures. Spheromaks (donut-shaped magnetic structures with diameter less than 0.5 m) are created by ionizing hydrogen gas in two magnetized coaxial plasma guns at opposite ends of the SSX vacuum chamber. Once ejected from one of the guns, a spheromak reaches a nearly force-free equilbrium with a lifetime of about 100 μs, unless it runs into an oppositely oriented spheromak coming from the other gun, in which case the magnetic field lines change their topology and reconnect. Information about plasma properties before, during, and after reconnection can be obtained by inserting magnetic probes into the plasma; however, this method reveals little about the large-scale structure of the inhomogenous plasma and may even disrupt the very processes it intends to reveal. As a results, external measurements of photons and high-energy ions emitted by the plasma are also necessary. These measurements only provide values for plasma parameters averaged over a narrow cone around the line-of-sight; in order to ascertain information about three-dimensional structure, computer simulations can be used.

One diagnostic used in SSX is a vacuum ultraviolet (VUV) monochromator, which collects real-time data on photon emission at one wavelength at a time. Calibrating the monochromator proved difficult because using a known plasma source would be too costly, and calibrating through the quartz window on the opposite side of the flux conserver was only possible for wavelengths greater than 250 nm. Making an absolute intensity calibration was even more difficult than the wavelength calibration--so the number of conclusive statements that could be made about plasma properties from VUV monochromator data was limited.

Appendix A contains a table of impurity ion emission lines (and the corresponding level transitions) that might plausibly be seen. Reliable data was collected for four lines: CIII 97.7 nm, CIII 124.7 nm, CIII 229.7 nm, and CIV 155.0 nm [actually a duplet]. Slava wrote a code to identify the magnitude and timing of peaks in the emission data (see Appendix B). Two peaks were identified for each emission line, for the CIII lines the first peak was around 33 μs and the second peak was around 49 μs, and for the CIV line the first peak was around 35 μs and the second peak was around 49 μs. The likely interpretation of these results is that the initial peaks in the CIII lines appear and then decay as the carbon quickly "burns through" the CIII ionization level (more electrons are stripped off the atoms), while the second peak appears as the plasma cools and electrons are re-captured. The first peak of the CIV line, on the other hand, probably decays due to the hottest part of the plasma leaving the line of sight of the instrument.

H.R. Greim has calculated a condition for determining whether or not a plasma has reached LTE--applying this rule yields the result that SSX would have to have an electron density greater than 10^16 cm^-3, while the actual electron density is one to two orders of magnitude less than this. Therefore Slava's simulation code resorts to the time-dependent coronal equilibrium approximation, in which the time evolution of different ionization stages of a given atom is considered, while steady-state equations are solved for the population of different excitation levels of a given ion. A matrix method is used to solve the system of differential equations for the ionization level populations. The end result is a code that can calculate the intensity of various spectral lines for a given plasma electron temperature and density. Comparing the data from the VUV monochromator with model calculations should then allow yield the values of these parameters in SSX. However, the analysis is complicated by the difficulty in knowing the initial ionization fractions that should be used for simulations, and by the relatively noisy SSX data for certain spectral lines.

The observed 2 μs time delay between the initial peaks in the CIII lines and the initial peak in the CIV line made it possible to use the simulation code to constrain the possible values of the actual SSX electron temperature and density to an almost linear relationship in parameter space. Simulation results showed that the ratio of the 229.7 nm line intensity to the 97.7 nm line intensity should be nearly independent of temperature for electron densities below 6 x 10^20 m^-3, and in the parameter range of interest, the ratio should be about 1:40. However, the experimental data suggested a ratio closer to 1:4. No satisfying explanation for this discrepency was found; the lack of absolute calibration of the monochromator was not expected to influence the intensity data by more than a factor of two.

Slava also ran a set of 2-D resistive MHD simulations using a code known as TRIangular Magnetohydrodynamics (TRIM) to simulate the time evolution of electromagnetic fields, momentum density, and plasma density in SSX. Since these simulations do not directly relate to my project, I will not describe them in detail. He was able to successfully produce simulation runs that closely matched the picture of spheromak formation painted by data from magnetic probes. Future studies should continue simulations with TRIM or another MHD code and combine these results with the predictions of Slava's impurity emission code to yield a much clearer picture of plasma properties.

Applications to my research:

My project this summer will build on Slava's in using computer simulations to constrain SSX plasma properties from photon-based external measurements. Although I will be using the commercial software PrismSPECT for my emission line modeling, his code will be extremely useful for understanding how such simulations work. Much of the information in his appendices, such as the table of relevant impurity ion atomic transitions, will likely be useful for my work. My initial simulations have focused on the same CIII 229.7 nm and CIV 155.0 nm lines that Slava considered, and I may look at the CIII 97.7 nm line as well. Slava's background information about SSX and MHD will also be useful references.