Mathematical Modeling and Control of Plasmas in Magnetic Fusion

Lehigh University, Bethlehem PA

Investigators

Abstract

The objective of this workshop is to initiate a dialogue between tokamak fusion physicists and engineers, and specialists in mathematical control theory, with the intended outcome of starting collaborative efforts to solve some of the many mathematical modeling and control problems that will arise in the International Thermonuclear Experimental Reactor (ITER) over the next 5-10 years. The ITER tokamak, an international $5 billion project that includes the European Union, the People's Republic of China, the Republic of Korea, the Russian Federation, Japan, and the United States, will confine a mixture of ionized isotopes of hydrogen, also known as plasma, at a temperature of around 100 million degrees centigrade, fusing the isotopes of hydrogen into helium and converting some of the matter involved in the reaction into a much larger amount of energy. Control researchers will receive a good general overview of the major objectives of fusion research and obtain a basic understanding of the many control problems that must be solved to achieve those objectives. Fusion scientists will obtain an improved understanding of available control technologies and expertise with some feeling for how applicable these techniques are to their own control problems. Both communities will learn what is needed to initiate a collaborative activity. The workshop will consist of two days of presentations and discussion. Day 1 will provide an overview of tokamak fusion and the associated control problems. Day 2 will provide a selected cross-section of state-of the art mathematical control theories, which may be beneficial in fusion control problems. A tour of the DIII-D tokamak and fusion facility will be provided to enhance the learning experience for control researchers. At the present rate of energy use, and considering the estimate of world population growth, experts predict an energy shortfall in less than fifty years. Although the accuracy of this prediction can be discussed, it is a fact that fossil fuel energy is becoming more expensive and polluting. The need for new sources of energy to supply this shortfall will become a critical problem in the near future. As a source of energy, fusion would have many advantages: abundant fuel supply, no risk of nuclear accident, no air pollution, no high-level nuclear waste, and no generation of nuclear weapon materials. There is consensus in the fusion community that active control will be one of the key enabling technologies. With further advancements in reduced-order fusion modeling, advances in control systems for fusion will continue, including vertical and shape control, kinetic and current profile control, MHD (magnetohydrodynamic) stabilization and plasma transport reduction. The visibility that this workshop will give to the problem of fusion plasma control will attract high quality mathematicians and engineers to work on this important topic. As one outcome of this workshop, a large number of challenging problems will become known to graduate students in mathematics, physics, and controls. The large number of problems, their importance to the welfare of society as a whole, and their challenging nature can provide a focused objective for development of many new and interesting mathematical control techniques.