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Review of Stellarator Research: in Search of the "Magic Magnetic Bottle"

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-Tt» «MM mna im oma [ REVIEW OF STELLARATOR RESEARCH: IN SEARCH OF THE "MAGIC MAGNETIC BOTTLE" NICOLAS DOMINGUEZ CCNF-920728-2 Fusion Energy Division, Oak Ridge National Laboratory, Oak Ridge, 77V 37831-8071, USA DE92 019045 ABSTRACT We summarize the current work on stellarators being carried out out in fusion research laboratories around the world. The theoretical aspects of the stellarator research are emphasized. *'~ 1. Introduction The steadily increasing need for energy makes it imperative to look for new sources of energy for the future. Fusion energy is one of the most promising posibilities. One of the main approaches to harnessing fusion energy is magnetic confinement. In this approach, the thermonuclear plasma containing the fuel to be fused is confined in a magnetic trap, where it can be heated to the high temperatures necessary for nuclear processes to occur1. Confining a plasma involves the creation of gradients of density, temperature and pressure. The presence of those gradients implies the creation of free energies. These free energies have the potential to destroy the magnetic confinement through magnetohydrodynamic (MHD) instabilities and microinstabilities. The central issue for magnetic confinement is to create a magnetic bottle that confines the plasma in such a way that the free energies are not too dangerous for confinement. It is fair to say that the history of fusion research for more than 30 years has been the search for a "magic magnetic bottle" -one with excellent confinement properties at low cost. A number of concepts have been developed as part of this search. Among them we can list the Model C stellarator, the mirror machines, the pinches, the tandem mirrors, the bumpy torus, the reversed-fisld pinches (RFPs), the tokamaks, the spherical tokamaks, and the advanced stellarators. Experimental devices based on these concepts have been constructed serving as valuable plasma containers in which different plasma physics theories have been tested. Most of them are no longer in operation, not because the physics of the plasma they contained was fully understood, but mainly because of budget constraints. Different countries have played important roles in the search for fusion devices. In the United States, Oak Ridge National Laboratory (ORNL) has been one of the most innovative leaders, with research on mirror machines, the bumpy torus, tokamaks, spherical tokamaks and stellarators. At present, the tokamak is by far the reigning concept, but a number of new stellarators are in operation, under construction or being designed. OF THfS QOCUMENT IS UNLIMITED Several of the new stellarator concepts look quite complicated but very attractive. In the world of stellarator devices, one notable characteristic is the propensity for designing machines with different number of field periods: 3 (Australia), 4 (Kharkov. Ukraine; Spain), 5 (Germany; Auburn, USA), 6 (ORNL; Spain), 7 (Wisconsin, USA), 8 (Japan;, 9 (Kharkov, Ukraine), 10 (Japan), 12 (ORNL), 14 (Moscow, Russia) and 19 (Japan). The stellarator, a concept first proposed some time ago,2 can be seen as an alternative to the tokamak. The principal characteristics that differentiate stellarators from tokamaks are that stellarators . are three-dimensional (3-D) geometries . are free of disruptions, and . have the capability for steady-state operation. The stellarator should be able to operate, in a steady state and the disruptions that tokamaks can suffer are absent in stellarators because the toroidal net current is zero. The experimental results from tokamaks look a lot better than those from the stellarators because the tokamaks are a lot bigger. The tokamaks have enjoyed a lot of popularity and economic support for the last several decades. However, the experimental results show that the plasma performance in stellarator plasmas is comparable to that in tokamak plasmas of similar size. Because stellarators are inherently 3-D configurations an obvious question arises From the infinite number of possibilities, which 3-D geometries are the best? The question cannot be answered by intuition alone. The first step in trying to answer the question is to carry out optimization studies to determine the best configurations in a space of parameters. The step is followed by realization of a plasma device and finally by carrying out the experiment. The information from the experiments can be used to propose promising new configurations, and so on. The optimization studies are constrained by two factors: . The engineering problems, such as the capability to build the complicated coils and the cost. It has been proven at ORNL, at the Max Planck Institute for Plasma Physics in Garching, Germany, and at other research institutes in many countries that the engineering difficulties can be overcome. Despite the latest engineering feats we have the cost of the devices. The cost of the devices constrains the size of the machines. It is well known nowadays mat the bigger the machines, the better the results, but big machines are very expensive. Plasma physics. Stellarators must be designed in such a way to obtain the highest possible stable plasma betas and the minimum transport of energy and particles. A great deal of work has been devoted to addressing the second constraint, not only because it is important and interesting to understand the plasma behaviour in magnetic traps but also because reducing the constraints imposed by the plasma physics can help to reduce the engineering constraints, the cost, and the number of possibilities examined in searching for new confinement devices. In addition, an understanding of stellarator plasmas can help to improve the understanding of the plasma behaviour of the most popular toroidal confinement configuration, the tokamak: so the exploration of plasma physics in stellarators c^n also be seen as complementary to tokamak research. Thus, the study of stellarator plasmas is a promising tool for indicating directions towards innovations for tokamak devices. The construction of the Advanced Toroidal Facility (ATF) and the Wendelstein VII-AS (W VII-AS) is proof that the engineering required to build stellarators exists, and there has been some economic support. Construction of TJ-II and the Large Helical Device (LHD) is currently under way, and a proposal for the construction of W VII-X is being considered. In this paper we address studies of stellarator plasmas in progress all around the world with the aim of obtaining the best plasmas in 3-D geometry. Stellarator researchers have been very imaginative, exploring ways to attain flexibility in the 3-D configurations and taking different approaches to increasing the beta limits and to reducing the plasma transport. The physics point of view regarding stability has been to understand the importance of particular stabilizing mechanisms, and to study the mechanisms which can reduce the destabilizing contributions. In the optimization studies there is always a tension between the configuration with the best stability properties and the configuration with the minimum plasma transport; thus, there have been trade-offs regarding some of the equilibrium quantities. Theoretical optimization studies have been done analytically and numerically using reduced two-dimensional (2-D) geometries and lately numerically considering full 3-D geometries. In the last five years there has been a lot of progress in developing tools to consider the 3-D stellarator geometries. This has been possible with the advent of powerful codes and fast computers. New codes to study equilibrium and stability of these 3-D configurations are being used in different parts of the world; much of this effort is concentrated at the Centre de Recherche en Physique des Plasmas, Ecole Polytechnique Federale de Lausanne, Switzerland3*4. Most of the codes are based on the VMEC code.5"7 The main conclusion regarding the MUD stability studies is that stellarator configurations must be studied without several approximations used in the past.8"10 The Helias concept can be realized in W VII-X, which is based on the quasi-helically symmetric configurations proposed by Nuehrenberg.21'12 The bootstrap current has been measured in ATF,13 and its effects for the devices of the next generation have been calculated. An empirical scaling law for energy confinement time has recently been proposed; it is mainly based on Heliotron-E experimental data.14 This LHD scaling law agrees very well with the gyro-Bohm scaling.15-16 The agreement between the ATF experimental data and the LHD scaling gives confidence in the empirical scaling and makes it possible to predict confinement times for devices under design. Density and temperature profiles are also being calculated in computer simulations, and the results are consistent with the LHD scaling.15 In Section 2 we give definitions and rudiments of MHD equilibrium and stability. In Section 3 the latest studies carried out in different parts of the world are summarized. Section 4 presents our final remarks. 2. Basics of Equilibrium and Stability 2.1. Definitions and Equilibrium Relations M, number of toroidal field periods A multipolarity R, major radius of the configuration a, average minor radius v, collision frequency A = R/a, aspect ratio of the configuration In this section we assume that nested flux surfaces exist. 0, magnetic toroidal flux divided by 2 K X, magnetic poloidal flux divided by 2n s, flux label (normalized toroidal flux in this work) 0b, value of 0 at the boundary p ~ I—, average radius of a flux surface .., tdl . „ V = j—, magnetic well *, rotational transform c di di . , 5 oc oc — t magnetic shear P, plasmd0 a pressurds e /, J plasma poloidal and toroidal net currents, respectively B, magnetic field [in Tesla (T)] J, plasma current Equilibrium which has to be satisfied in each point of the flux surface a = —y» parallel current 2u P , peak beta, where B is the magnitude of the magnetic field at the magnetic = ° ° o axis for the particular value of beta considered and Po is the plasma pressure at the magnetic axis.
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