SYSTEMS

By Steve Fisher, Editor In Chief -- It was announced last Friday that a team of researchers at Oak Ridge National Lab, MIT, and Princeton University have received over $1 million dollars from the Department of Energy to fund their efforts to better understand and control fusion machines. For an insider’s perspective, Supercomputing Online turned to Donald B. Batchelor, Head of the Plasma Theory Section at Oak Ridge National Laboratory. Supercomputing: Congratulations on the recent SciDAC funding. What does this influx of funds mean to your research and that of your colleagues? BATCHELOR: I'd like to say that it means we are going to bring on some young new staff or post docs. But it doesn't because of budget losses in other areas and increased operating costs. It means that we will be able to continue our work and we will have access to powerful computers, and we will have support for our colleagues in computer science. But no new faces. Supercomputing: I understand that you already have SciDAC results off your machines. You folks have been busy! Can you share a little bit about the results and the systems and software used to attain them? BATCHELOR: Last year we had a very significant breakthrough in developing acomputational technique we call the All Order Spectral Algorithm in two dimensions. This algorithm eliminates a number of restrictive mathematical approximations to the theory which were previously necessary. Simultaneously it enables us to study essentially arbitrarily small scale wave phenomena, limited only by the size and speed of the computer, not the approximations in the theory. Using 576 processors on the Eagle IBM SP computer at ORNL we were able to obtain the first converged wave solutions in 2D for an important wave process in fusion called 'fast wave to ion Bernstein wave mode conversion'. It required a massively parallel solution of 120,000 dense equations using the ScaLAPAC package, running at greater than 0.6 teraflops. We developed this technique with the idea that it might be extensible to full 3D calculations. As soon as we heard about the SciDAC award we pressed ahead as rapidly a possible to implement a three dimensional version of the all All Order Spectral Algorithm. We have found that the algorithm is indeed extensible, and have initial result for fast wave propagation and absorption in a complicated type of fusion device called a stellarator. We are far from being able to resolve the very short wavelength Bernstein wave in 3D, but the fast wave (a much longer wavelength phenomenon) looks do-able. Supercomputing: Last week's release mentions that one specific goal of your fusion research project is to increase the dimensionality of computer models. Can you tell the readers a bit about how you'll be going about that? BATCHELOR: See above. In physics it is often useful to simplify problems by neglecting variations in some directions, thereby reducing the dimensionality. Consider a simple heat conduction problem. Suppose you had a thin wire that you held on one end and heated the other end with a blow torch. The wire exists in three dimensional space. But for most purposes it would be a good approximation to neglect the temperature variation across the diameter and develop an equation to predict the temperature in one dimension, along the wire, including heat sources, conduction and heat loss. On the other hand if you placed a large skillet on a small burner and wished to predict the evenness and cooking rate for an egg you would probably need to treat it as a fully 3D problem. In early studies of waves in plasmas it was helpful to neglect all spatial variations of the plasma medium. We call this a zero dimensional model. Such models can usually be solved exactly and give information about the different kinds of waves which can exist in the plasma, such as the fast wave and the ion Bernstein wave mentioned above. The next step is to consider plasmas which vary in only one spatial direction. We call this a one dimensional model. Within such a model we find qualitatively new physics relative to the zero dimensional case. For example we find that when the plasma varies, different kinds of waves can interact with one another as in the case of fast waves converting to ion Bernstein waves. Still this is a very idealized picture and to get an accurate view of what is happening in a real fusion experiment it is necessary to solve the equations across at least in a plasma cross section (i.e. in 2 dimensions) or in some cases for the entire plasma volume (i.e. in 3 dimensions). Each added dimension of the solution raises the difficulty and computational work by something like to a power of two times the number of dimensions. So to solve a 3D model could be something like a million times more computer intensive than to solve it in zero dimensions. One of the goals of our project is to be able to solve problems in 2D or 3D which are presently only feasible in 1D or marginally in 2D, and simultaneously to include more physics content within the equations. Supercomputing: Once the enhanced computer models are developed, how do you and your team plan to use them? BATCHELOR: We will use the computer models to study the basic physics of plasma waves in higher dimensions. I mentioned above that qualitatively new phenomena appear when one extends a zero dimensional theory to one dimension. What happens when that is extended to 2D or 3D? As a specific example we will be trying to understand certain effects of quantum chaos on a type of modes called lower hybrid waves. We will try to understand how this chaos affects the ability of lower hybrid waves to drive electric currents in fusion machines. The great problem of fusion is to heat the fuel material to temperatures hotter than the sun, thus turning the material into an ionized state of matter called plasma, and to hold the plasma with magnetic fields until sufficient fusion reactions occur to produce net energy. Electromagnetic waves are used to heat plasmas to these kinds of temperatures, but they can also be used control the plasma by driving electric currents and by forcing the plasma fluid to flow relative to the magnetic field. We will be using our computer models to develop practical techniques for this heating and control and to understand the results from experiments in which these techniques are used. ---------- Supercomputing Online wishes to thank Don Batchelor for his time and insights. It would also like to thank ORNL’s Betsy Riley for her assistance. ----------