Plasmas are the most common form of baryonic matter, which is currently believed to constitute about 4% of the universe (the rest being dark matter and dark energy). Plasmas surround the Earth (ionosphere and magnetosphere), permeate the solar system, and pervade interstellar and intergalactic space.

With a growing understanding of plasmas over the past century, researchers have found dozens of practical applications for them. The most familiar applications are fluorescent lights, neon signs, and plasma display screens for televisions and computers; the most promising application is nuclear fusion as a renewable energy source. Recent discoveries from numerical simulations are advancing both the basic science of plasmas and fusion energy experiments.

Understanding magnetic explosions

On December 6, 2006, Global Positioning System (GPS) devices suddenly started malfunctioning all over the Earth. The culprit: a solar flare. Solar flares can eject a billion tons of charged particles into space at a speed of 1 million km per hour, disrupting navigation and communications satellites, and sometimes even electrical grids on Earth, while producing bright auroras in the polar regions.

How so much energy can be released so quickly has perplexed scientists for decades. In 1946 Ronald Giovanelli conceived the idea of magnetic reconnection to explain solar flares. The basic idea is that the churning of ionized gas amplifies the magnetic fields in a plasma by twisting and folding them—kinetic energy being converted into magnetic energy. When the magnetic field lines touch or cross, they break, reconnect, and reverse direction (Figure 1). The process may take months or, in the case of a solar flare, as little as 30 minutes, in which case vast amounts of magnetic energy are converted back to kinetic energy with explosive force.

“Magnetic reconnection differs from a conventional explosion in that the energy is not released equally in all directions,” explained James F. Drake, Professor of Physics at the University of Maryland, whose recent research has focused on this subject. “Instead, the plasma flows in from one direction and flows out in another.

“Magnetic reconnection has broad importance for almost all areas of plasma physics, including solar flares, storms in the Earth’s magnetosphere, and disruptions in laboratory fusion experiments,” Drake added. “It’s a fascinating topic and a challenging research area.”

Figure 1. (A) Glowing loops of plasma illuminate the magnetic field structure around a sunspot. The planet Earth would easily fit under one of these loops. (B) Constantly in motion, the field lines sometimes touch or cross and reverse direction in a process called magnetic reconnection. Open field lines instead of loops show that plasma is being ejected outward as a solar flare. (Click on images to enlarge.) (Images courtesy of NASA)

One of the puzzles in this sudden release of massive energy is how that much energy could have built up in the first place. If reconnection were always fast and occurred frequently, the magnetic fields would never be strong enough to reach explosive force. A long period of slow reconnections might allow the magnetic energy to accumulate. But why would reconnection happen at two different speeds?

The first mathematical model for magnetic reconnection, known as the Sweet-Parker model, was developed in the late 1950s. This model generates a slow and steady release of energy, but not the explosive events that the theory is supposed to explain. In this model the electrons and ions move together, and the heavier ions slow down the plasma flow. The more recent Hall reconnection model suggests that the movements of ions become decoupled from electrons and magnetic fields in the boundary layers where magnetic field lines reconnect. The result is much faster plasma flow. The signatures of the Hall model have been confirmed by satellite measurements in the magnetosphere and by laboratory experiments, but this model still does not explain the origin of the magnetic explosion.

In two recent papers by Paul Cassak, Drake, and Michael Shay, the two models have converged in a self-consistent model for the spontaneous onset of fast reconnection.¹ The researchers’ calculations showed that slow reconnection can continue for a long time, during which magnetic stresses continue to build up. As progressively stronger magnetic fields are drawn into the reconnection region, when the available free energy crosses a critical threshold, the system abruptly transitions to fast reconnection, manifested as a magnetic explosion.

This new model is consistent with solar flare observations. For example, extreme-ultraviolet observations of the sun’s corona have shown one instance of slow reconnection lasting for 24 hours, followed by fast reconnection lasting for 3 hours. The change was sudden, with no visible trigger mechanism, and the energy released during fast reconnection was comparable to the energy accumulated during slow reconnection.

Solar observations have suggested that at least 50% of the energy released during flares is in the form of energetic electrons, and energetic electrons have also been measured during disruptions in laboratory nuclear fusion experiments. The source of these energetic electrons has been a puzzle. Large numbers of these low-mass particles travel at speeds far higher than can be explained by the energy of the moving magnetic field lines that propel them. Drake and Shay, along with Michael Swisdak and Haihong Che, proposed an answer to this question in a paper published in Nature.²

Figure 2. Computer simulations of island formation and electron acceleration during magnetic reconnection. The electron current is shown at two time steps in (a) and (b); (c) shows the electron temperature, with intense heating caused by electron acceleration along the rims of the islands.

In their simulations of magnetic reconnection, the process is more turbulent than it was once thought to be—magnetic islands form, grow, contract, and merge as the field lines converge (Figure 2). The electrons gain speed by reflecting off the ends of contracting islands, just as a ball would gain speed if it were bouncing off two walls that were moving toward one another. But as the temperature in an island goes up, back pressure slows down the shrinking, thus slowing down reconnection and converting more of the magnetic energy into electron acceleration. The repeated interactions of electrons with many islands allow them to be accelerated to high speeds.

“Ours is the first mechanism that explains why electrons gain so much energy during magnetic reconnection,” said Drake. “From a practical standpoint, these new findings can help scientists to better predict which solar storms pose the greatest threat to communications and other satellites. And they may give us a better understanding of how to control plasmas in fusion reactors.”

Drake explained that the strongest confirming evidence for the new theory was the surprising agreement between the model and data from NASA’s WIND satellite. “We were as surprised as the WIND scientists when the distribution of energetic electrons seen by their spacecraft popped right out of our model. Such a match isn’t something you see very often,” he said.

Drake computes at NERSC under the project “Turbulence, Transport and Magnetic Reconnection in High Temperature Plasma,” led by William Dorland. In addition to magnetic reconnection, this project also studies the mechanisms by which plasma particles, energy, and momentum are transported across, rather than along, magnetic field lines—the so-called “anomalous transport” problem.

Modeling microturbulence in fusion plasmas

Most people do not think about turbulence very often, except when they are flying and the captain turns on the “Fasten Seat Belts” sign. The kind of turbulence that may cause problems for airplane passengers involves swirls and eddies that are a great deal larger than the aircraft. But in fusion plasmas, much smaller-scale turbulence, called microturbulence, can cause serious problems—specifically, instabilities and heat loss that could stop the fusion reaction.

In fusion research, all of the conditions necessary to keep a plasma dense and hot long enough to undergo fusion are referred to as confinement. The retention of heat, called energy confinement, can be threatened by microturbulence, which can make particles drift across, rather than along with, the plasma flow. At the core of a fusion reactor such as a tokamak, the temperatures and densities are higher than at the outside edges. As with weather, when there are two regions with different temperatures and densities, the area between is subject to turbulence. In a tokamak, turbulence can allow charged particles in the plasma to move toward the outer edges of the reactor rather than fusing with other particles in the core. If enough particles drift away, the plasma loses temperature and the fusion reaction cannot be sustained.

The growth of the microinstabilities that lead to turbulent transport has been extensively studied over the years. Understanding this process is an important practical problem, and it is also a true scientific grand challenge which is particularly well suited to be addressed by modern terascale computational resources. One of the leading research groups exploring this issue is the SciDAC-funded Center for Gyrokinetic Particle Simulations of Turbulent Transport in Burning Plasmas and Multiscale Gyrokinetics (GPSC), headed by Wei-li Lee of the Princeton Plasma Physics Laboratory. This team developed the Gyrokinetic Toroidal Code (GTC) to simulate instabilities in tokamak plasmas using the particle-in-cell (PIC) method.

“Particle-in-cell simulation, which began in the late sixties, uses finite size particles on a grid to dramatically reduce the numerical noise associated with close encounters between the particles, while leaving intact their long range interactions outside the grid,” Lee explained. “This approximation reduced the number of calculations for particle interactions and greatly reduced the computational time.

“For simulations of magnetic fusion plasmas,” he continued, “further improvements came in the eighties and nineties with the development of the gyrokinetic particle simulation and perturbative particle simulation methods. Briefly, under the gyrokinetic approximation, the spiral motion of a charged particle is represented as a charged ring centered around its gyro-center; and perturbative methods are used to greatly reduce the discrete particle noise.”

Over the past dozen years, these simulation methods have produced some impressive discoveries, including the identification of ion temperature gradient (ITG) drift turbulence as the most plausible process responsible for the thermal transport observed in tokamak experiments; the reduction of such transport by self-generated zonal flows; and the confinement scaling trends associated with the size of the plasma and also with the ionic isotope species.³

With the availability of terascale computers in recent years, the GPSC team has been able to carry out simulations of experiment-sized plasmas with improved physics fidelity. Typical global PIC simulations of this type have used one billion particles with 125 million grid points over 7000 time steps to produce significant physics results. Simulations of this size would not be feasible on smaller computers.

Figure 1. Particle number convergence studies for the ITG simulation: thermal diffusivity and the time rate of change of entropy for 10, 100, 400, and 800 particles per cell. The only numerical noise comes from the 10 particle run. (Click on images to enlarge.)

With nearly two orders of magnitude increase in particle numbers, the GPSC project has been able to resolve longstanding uncertainty about the effect of discrete particle noise on the long-term transport predictions of turbulent gyrokinetic PIC simulations. The “noise” referred to here involves not just particle interactions that are not relevant to energy transport, but primarily numerical sampling noise, because PIC simulations involve Monte-Carlo sampling of a collection of “marker” particles. Recent work shows that this numerical noise has little effect on the resulting energy transport when a reasonable number of particles is used (Figure 1).³,⁴

Figure 2. Turbulence spreading (left to right) as depicted by the perturbed potentials of ITG turbulence on the poloidal plane as they follow the magnetic field lines around the torus.

When the GTC code was applied to a geometry similar to the ITER experiment, an interesting new phenomenon was discovered: the turbulence spreads radially from a localized region to eventually cover most of the poloidal plane (Figure 2).³,⁵ This discovery was made possible by a simulation volume that is large enough to allow a clear scale separation between the turbulence eddy size and the device size.

“The simulation clearly shows that small-scale turbulence eddies are typically generated in the unstable region and flow along the streamers to the stable region,” Lee said. “In addition, the streamers are found to break and reconnect, resulting in a very complex dynamical evolution. These new results have raised intense interest in the fusion theory community on the fundamental physics of turbulence spreading.”

Clearly, there is a lot more work to be done in modeling tokamak plasmas, and with petascale computers coming online and the addition of more detailed physics to the GTC code, the GPSC team is eager to continue. With trillion particle simulations, they hope to find detailed solutions to problems such as electron thermal transport, the scaling of confinement with plasma size, and the effects of different ionic isotope species such as tritium on plasma burning.

“Our long-range goal is to carry out integrated simulations for ITER plasmas for a wide range of temporal and spatial scales, including high-frequency short-wavelength wave heating, low-frequency meso-scale transport, and low-frequency large-scale magnetohydrodynamic physics,” Lee said.

The success of these efforts will depend on close collaboration with other SciDAC centers, including the Terascale Optimal PDE Simulations (TOPS) Center, the Scientific Data Management (SDM) Center, the Ultrascale Visualization Center, and the Visualization and Analytics Center for Enabling Technologies (VACET).

This article written by: John Hules, Berkeley Lab.

1 P. A. Cassak, M. A. Shay, and J. F. Drake, “Catastrophe model for fast magnetic reconnection onset,” Physical Review Letters 95, 235002 (2005); P. A. Cassak, J. F. Drake, and M. A. Shay, “A model for spontaneous onset of fast magnetic reconnection,” Astrophysical Journal 644, L145 (2006).

2 J. F. Drake, M. Swisdak, H. Che, and M. A. Shay, “Electron acceleration from contracting magnetic islands during reconnection,” Nature 443, 553 (2006).

3 W. W. Lee, S. Ethier, W. X. Wang, and W. M. Tang, “Gyrokinetic particle simulation of fusion plasmas: Path to petascale computing,” Journal of Physics: Conference Series (SciDAC 2006) 46, 73 (2006).

4 Thomas G. Jenkins and W. W. Lee, “Fluctuations and discrete particle noise in gyrokinetic simulation of drift waves,” Physics of Plasmas 14, 032307 (2007).

5 W. X. Wang, Z. Lin, W. M. Tang, W. W. Lee, S. Ethier, J. L. V. Lewandowski, G. Rewoldt, T. S. Hahm, and J. Manickam, “Gyro-kinetic simulation of global turbulent transport properties in tokamak experiments,” Physics of Plasmas 13, 092505 (2006).