Models for Plasma Control in Fusion Reactors Aitor J. Garrido, Izaskun Garrido, Oscar Barambones, F. Javier Maseda and Patxi Alkorta * Abstract— The control of plasma in nuclear fusion has revealed as a promising application of Control Engineering, with increasing interest in the control community during last years. In this paper it is outlined a control-oriented linear model for the control of plasma current. For this purpose, it is firstly provided a summary of the background necessary to deal with control problems in tokamak-based nuclear fusion reactors as it is the case of the future ITER tokamak. Besides, it is also given a review of the most used simulators and plasma models, with the aim of providing an adequate background for control engineers to derive their own control- oriented model or to choose the appropriate existing one. Finally, a simple linear model based on loop control voltage is derived. Keywords— Fusion Control, Plasma Physics, Tokamak Modeling. I. INTRODUCTION A. Motivation N the last years, substantial effort and resources are being devoted to the development of a clean nuclear technology based upon fusion processes. This effort materializes in a large number of research papers published, specially in the field of Control Engineering applied to fusion processes (see [1] and [2]), establishing an area of novel application for Control Theory, after some timid efforts in the 50s and beginning of the 90s. Nowadays the control of plasma in fusion processes is an area of increasing interest, involved in ambitious international projects as the ITER - International Thermonuclear Experimental Reactor [3]. B. Background on nuclear fusion magnetic confinement: tokamak When two light nuclei fuse into a heavier and more stable nucleus, the nuclear rearrangement results in a reduction in total mass and a consequent release of energy in the form of kinetic energy of the reaction products. The idea relays in heating the fuel up to a sufficiently high temperature so that the thermal velocities of the nuclei are high enough to fuse. Manuscript received February 29, 2007; Revised version received June 4, 2007. This work has been supported in part by UPV/EHU and MEC through project EHU 06/88 and projects DPI2006-01677 and DPI2006-00714, respectively. It was also partially supported by Basque Government through the research project S-PE06UN10. Aitor J. Garrido, Izaskun Garrido, O. Barambones and F. J. Maseda are with the Department of Automatic Control and Systems Engineering of the University of the Basque Country, Bilbao, Spain (corresponding author tel: +34 94 601 4469; fax: +34 94 601 4300; e-mail: aitor.garrido@ehu.es ). P. alkorta is with the Department of Automatic Control and Systems Engineering of the University of the Basque Country, Eibar, Spain. This process that takes place continuously in the Sun and stars. In order to obtain nuclear fusion on Earth, the most suitable reaction at present takes place between the nuclei of deuterium and tritium. Nevertheless, to achieve and maintain the reaction for a substantial period of time (a pulse), temperatures of the order of 100 ·10 6 ºC (10 4 [eV]) and a density of about 10 20 m −3 are required. Under these conditions the fuel changes its state from gas to plasma, in which the electrons are separated from the atoms, becoming these atoms charged ions (see [4]). This technology has nowadays reached the point in which the experimental reactors can produce almost as much energy as they consume. In this sense, the future ITER reactor is desired to generate ten times as much energy as it consumes (see [1]). For this purpose, being nuclear reactors inherently pulsed devices due to the limited main transformer magnetic flux availability (see [5] and [6]), the objective is to control the plasma so as to maintain its stability in order to achieve a pulse duration of the order of minutes instead seconds. As indicated above, the plasma consists of two types of charged particles, ions and electrons, so that it may be contained within a region away from the vessel walls by means of magnetic fields [5-6], namely, using magnetic confinement. The most common magnetic confinement structure is denominated tokamak, acronym of TOroidalnaya KAmera i MAgnitnaya Katushka that means “toroidal camera with magnetic coils”, which is also the design that will be used in ITER. In a tokamak, the plasma is heated in the toroidal vessel and kept away from its walls by applying two combined magnetic fields: The toroidal field, around the torus, which is maintained by the toroidal field coils surrounding the vacuum vessel (see Figure 1), providing the primary mechanism of confinement of the plasma particles. And a smaller poloidal field (about 10% of toroidal field), around the plasma cross section, that keeps the plasma away from the walls and contributes to maintain the plasma's shape and position. The poloidal field is induced both internally, by the current driven in the plasma, and externally, by the outer poloidal field coils that are positioned around the perimeter of the vessel (see Fig. 1). In turn, the main plasma current is induced in the plasma by the action of a large transformer (inductive current drive): A changing current in the primary winding formed by the inner poloidal field coils located around a large iron core induces a current in the plasma, which acts as the transformer secondary circuit. I Issue 1, Volume 1, 2007 12 INTERNATIONAL JOURNAL of ENERGY and ENVIRONMENT