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Simulating spheromak behavior in 3-D

Carl R. Sovinec

Carl R. Sovinec (large image)

New plasma simulation capabilities developed by Assistant Professor Carl Sovinec and colleagues enable plasma researchers to model more completely the behavior of a magnetic-confinement fusion experiment called a spheromak.

Unlike its toroidally shaped tokamak cousin, which drives toroidal plasma current via external transformers, a spheromak has no central column and relies on natural relaxation to generate magnetic fields that also confine the plasma. "You're letting the plasma do as much as it possibly can," he says.

Although previous spheromak simulations generated lots of information about how the experiment's magnetic fields evolved, the results didn't paint the full picture and many researchers were skeptical of them, says Sovinec. "They thought that the predicted magnetic fields wouldn't be consistent with the kinds of temperatures observed in the experiment," he says.

Simulated temperatures increasing during spheromak decay

Simulated temperatures increasing during spheromak decay. During decay, closed flux surfaces form (bottom) and the peak temperature increases (top). (t=0.63 ms, 0.76 ms, and 0.91 ms after breakdown are shown.) (large image)

The new simulations incorporate temperature evolution. "In particular, we can model thermal energy transport in our full three-dimensional simulations, including the ansiotropies and temperature-dependent coefficients that you would have in a collisional plasma," he says.

From analyzing the new simulation results, Sovinec's group has shown that while the experiment attains relatively low temperatures when driven, high temperatures researchers observed later in the discharge are a direct result of transients that occur when they remove the drive. "If we evolve the simulated drive the way that they do in the experiment, taking the transients into account, we see that when the magnetic field starts decaying a lot of things come together," he says. "It actually makes a better configuration when it's decaying."

Normally, the experiment's magnetic configuration includes wiggles and fluctuations, which don't retain the plasma's temperature well. "But then when you stop driving it and let it decay a bit, those wiggles go away and it's that process that's critical for getting the high temperatures that they see in the experiment," says Sovinec.

The new simulations also show that there's a difference between the effects of the initial drive and those produced by subsequent drives.

Now researchers can learn more than what they did by looking just at experimental results or by applying earlier analytical theories, Sovinec says. "They don't tell you all of these details that are critical for really understanding things like how large the magnetic fluctuations are and what kind of temperatures you can get," he says. "We're able to do that with the three-dimensional calculations."

The spheromak research collaboration includes PhD student Giovanni Cone and staff scientists at Lawrence Livermore National Laboratory. The group ran many of its calculations on Sovinec's 25-PC cluster in the Engineering Research Building. The Department of Energy's Office of Fusion Energy Science supports the multi-institutional code development team (, including groups at Science Applications International Corporation, San Diego; Utah State University; and the University of Colorado. It also supports the local spheromak study via Sovinec's three-year, $415,000 junior faculty award.