Mathematical Modeling and Control of Plasmas in Magnetic Fusion

这次讲习班的目的是在托卡马克聚变物理学家和工程师以及数学控制理论专家之间展开对话，预期的结果是开始合作努力，解决国际热核实验堆(热核实验堆)在未来5-10年内将出现的许多数学建模和控制问题。ITER托卡马克是一个耗资50亿美元的国际项目，包括欧盟、中国、韩国、俄罗斯联邦、日本和美国，它将把氢的电离同位素混合物，也就是等离子体，限制在大约1亿摄氏度的温度下，将氢的同位素聚变为氦，并将参与反应的一些物质转化为更大的能量。控制研究人员将对聚变研究的主要目标有一个很好的总体概述，并对实现这些目标必须解决的许多控制问题有一个基本的了解。聚变科学家将对现有的控制技术和专业知识有更好的了解，并对这些技术如何适用于他们自己的控制问题有一些感觉。两个社区都将学习发起协作活动所需的内容。研讨会将由两天的陈述和讨论组成。第一天将概述托卡马克聚变和相关的控制问题。第二天将提供精选的最先进的数学控制理论的横截面，这可能对融合控制问题有所帮助。将提供DIII-D托卡马克和聚变设施的参观，以增强控制研究人员的学习体验。按照目前的能源使用速度，并考虑到世界人口增长的估计，专家预测不到50年内将出现能源短缺。尽管这一预测的准确性可以讨论，但化石燃料能源正变得越来越昂贵和污染越来越严重，这是一个事实。在不久的将来，需要新的能源来供应这一短缺将成为一个关键问题。作为一种能源，聚变将有许多优点：充足的燃料供应，没有核事故风险，没有空气污染，没有高水平的核废料，不会产生核武器材料。聚变界的共识是，主动控制将是关键的使能技术之一。随着降阶核聚变模型的进一步发展，核聚变控制系统的进展将继续下去，包括垂直和形状控制、动力学和电流剖面控制、磁流体稳定和减少等离子体传输。这次研讨会将为聚变等离子体控制问题提供可见性，将吸引高素质的数学家和工程师致力于这一重要主题的工作。作为本次研讨会的成果之一，大量具有挑战性的问题将成为数学、物理和控制专业的研究生所熟知的。大量的问题，它们对整个社会福利的重要性，以及它们的挑战性，可以为许多新的和有趣的数学控制技术的发展提供一个集中的目标。

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.