"High Resolution Flow and Ion Temperature Measurements with Ion Doppler Spectroscopy at SSX"
Jerome Fung

Summary:

Plasmas are defined as ionized gases that have enough mobile charge carriers to permit macroscopic currents and magnetic fields. They do not contain large-scale electrostatic fields because of Debye shielding (electrons tend to congregate around positive ions and shield their electrical influence). Understanding plasmas is of great importance in astrophysics (since they are the dominant state of luminous matter in the Universe) and nuclear physics (if we ever hope to create commercially viable fusion reactors we'll need a better understanding of plasma physics). The most promising theory for understanding plasmas is magnetohydrodynamics (MHD), which combines fluid mechanics and electrodynamics. In ideal MHD, the plasma is assumed to be perfectly conducting, and magnetic field lines are frozen into the plasma. In reality, however, when regions of oppositely directed fields approach each other, the fields lines can change their topology and reconnect. The simplest modification to ideal MHD is the Sweet-Parker model, which allows for a resistive plasma. The Sweet-Parker framework is useful for thinking about reconnection dynamics, but the model significantly underestimates the reconnection rate that actually observed.

Jerome includes a detailed section on MHD theory. Among the key points are: The Alfvén speed is the speed a plasma would obtain if it converted all of its magnetic energy into kinetic energy (a sort of speed limit for the plasma). In ideal MHD, magnetic field lines convect with the plasma (they are frozen in). If we deviate from ideal MHD and give the plasma a resistivity, the result is a diffusion of the magnetic field. Plasma β is the ratio of plasma pressure to magnetic pressure--it gives a measure of the extent to which plasma dynamics are dominated by magnetic forces. Other theorists such as Petschek have made modifications to Sweet and Parker's model that produce higher reconnection rates, but no model has yet been able to explain all effects observed in actual plasmas.

A key new diagnostic for the Swarthmore Spheromak Experiment (SSX) is ion Doppler spectroscopy (IDS). IDS uses Doppler shifts of spectral lines to measure plasma flow velocities and Doppler broadening of lines to measure ion temperature. The spectrometer observes spectral lines at 25th order so that the dispersion is low. This is necessary to achieve good spectral resolution because the photomultiplier tube (PMT) array used for SSX has large pixels (~1 mm). The advantage of the PMT array over other technologies such as CCD arrays is that is has good time resolution. This allows SSX to study reconnection on smaller time scales than previous experiments could. An interference filter is placed in front of the diagnostic to ensure that the desired spectral line is being observed (rather than other lines at different orders).

The other primary diagnostics used at SSX are a He-Ne quadrature interferometer and a soft x-ray detector. Magnetic probes have been used in the past to study field structure during reconnection. The SSX can produce two spheromaks from guns on either side of the main vacuum chamber. A strong potential difference applied across the inner and outer electrodes in the guns ionizes gas that has been pumped in, forming a plasma. Current flowing along the inner electrode creates a magnetic field with field lines in concentric circles in the gun--this field interacts with the plasma current running between the electrodes to push the plasma out of the gun. On its way out it runs into a "stuffing field", which is carried along with the plasma. The result is a spheromak that has both toroidal and poloidal fields. SSX can create and collide both "left-handed" and "right-handed" (defined by the directions of the two magnetic fields) spheromaks.

Previous studies at SSX showed that reconnection events were not two-dimensional (as assumed by Sweet-Parker) but had significant components perpedicular to the plane of reconnection. Counter-helicity spheromak merging was found to produce a Field Reversed Configuration (FRC)-like object. FRCs are axisymmetric plasmas that have only a poloidal magnetic field. The roughly symmetric plasmas produced by counter-helicity shots are ideal for calculations using a technique called Abel inversion, which allows one to infer three-dimensional distributions of quantities such as emissivity from a collection of line-of-sight measurements. This calculation was carried out in Jerome's research, but inverting other interesting quantities such as temperature and flow would most likely be too difficult and inaccurate to be worthwhile. Double-peaked spectra were observed on many occasions during the runs, indicating bi-directional flows. They evolved rapidly, often lasting only a few microseconds. It is likely, but difficult to prove without magnetic probes, that the bi-directional flows were caused by reconnection. Additionally, Fourier analysis of the data indicate the possibility of periodic behavior of flows.

Future measurements with IDS will study other emission lines from carbon, oxygen, nitrogen, and other impurities and compare the flows and temperatures measured to those inferred by looking at the C III 229.687 line (the focus of studies up to this point). Doping the plasma with a carbon-containing gas such as methane would allow for better control of the amount of impurities in the plasma. Reinserting magnetic probes will be necessary to identify the exact times and places where reconnection occurs. A downside of probes is that they inevitably perturb the plasma. Comparisons of observations made using IDS and other diagnostics with computer simulations will also be useful for constraining plasma properties.

Applications to my research:

I'm going to be continuing Jerome's work with IDS this summer, and his suggestion about using computer-based spectral emission models to better understand observations of the SSX is exactly what I'm going to do. I'll be using software such as PrismSPECT to simulate the spectra that should be produced by the SSX plasma; I'm starting by looking at the ratio between the strength of the CIV 155 nm line (doublet) and the CIII 229 nm line, and I will probably look at other line ratios as well. I'm also going to be working with the soft x-ray diagnostic, both through simulations and observations in the lab. Jerome's theory section will continue to be a useful resource as I learn about SSX.