The Legacy of Masahiro Wakatani

J. Plasma FusionFusion Res.Res. SERIES,SERIES, Vol. Vol. 6 6(2004) (2004) 100–106 000–000 The Legacy of Masahiro Wakatani VAN DAM James W. and HORTON C. Wendell, Jr. Institute for Fusion Studies, The University of Texas, Austin, Texas 78712, USA (Received: 18 February 2004 / Accepted: 7 April 2004) Abstract As a memorial to Masahiro Wakatani, late professor of plasma physics at Kyoto University, a review is given of his legacy of achievements in scientific research, international collaborations, university administration, student guidance, and personal life. Keywords: Hasegawa-Wakatani equation, turbulent transport, helical system stability, drift wave, reduced MHD equation 1. Introduction Division (1976-1978). The international community of fusion plasma physicists In 1978 he joined the Plasma Physics Laboratory at was deeply saddened by the unexpected loss of one of its Kyoto University as an Associate Professor. He was promoted most respected members, Prof. Masahiro Wakatani, of Kyoto to full Professor in 1985. In 1996 he became a Professor in University, who died from a cerebral hemorrhage on 9 the Department of Fundamental Energy Science and the January 2003. This paper, based on a talk [1] presented during Department of Nuclear Engineering. a special memorial session at the 13th International Toki He was elected a Fellow of the American Physical Conference (9-12 December 2003), is offered as a tribute in Society in 1990. his memory. He died on 9 January 2003. Two obituaries about him Professor Wakatani had a brilliant career as a scientific have been published [2,3]. researcher, international collaborator, university leader, and teacher. In this paper, after providing a brief biographical 3. Legacy of innovative research sketch, we will describe each of these aspects of his very Without question Wakatani was one of the very best significant legacy and also offer some personal comments theoretical and computational plasma physicists in the world. about him. He published many influential papers. His creative and original work on nonlinear MHD, drift wave instabilities, 2. Capsule biography stellarator confinement, and ion-temperature-gradient mode Here we briefly list some selected biographical details dynamics is famous. Here we provide a brief description of and important dates in his career. This list will serve as a his major contributions to several areas of theoretical plasma chronological framework for the description of his many physics research. accomplishments. According to Prof. Tokuhiro Obiki’s obituary [2], He was born on 15 May 1945, in Osaka, Japan. Wakatani’s scientific talent and brilliance were already He attended Kyoto University for his undergraduate and obvious in his student days. He had the highest marks of any graduate education. He graduated with a B.Sc. degree (1968) student ever in nuclear engineering. For his Ph.D. thesis, he and a Master’s degree (1970) in nuclear engineering. He then carried out the first application of neoclassical theory to the obtained a Dr.Eng. degree in electrical engineering (1973) toroidal pinch confinement device. He used the neoclassical with a thesis entitled “Magnetohydrodynamic Equilibrium and theory of Roald Sagdeev and Alec Galeev, which was brand Stability of Toroidal Pinches” under the guidance of his thesis new at that time, to calculate the collisional diffusion advisor, Prof. Ryohei Itatani. coefficients in a toroidal pinch [4]. After graduation, he was first employed at the Japan After graduation, he continued his work on stability and Atomic Energy Research Institute as a Research Associate in transport, switching his attention first to the tokamak device, the Division of Thermonuclear Research (1973-1976). which had much better confinement than the toroidal pinch, Subsequently he went to the Institute of Plasma Physics, and (when he joined the faculty at Kyoto University) also to Nagoya University, as a Research Associate in the Theory ©2004 by The Japan Society of Plasma Corresponding author’s e-mail: [email protected] Science and Nuclear Fusion Research 1001 Van Dam J.W. et al., The Legacy of Masahiro Wakatani helical confinement devices, especially the Heliotron/torsatron used in some recent experimental work [10] to explain shear line. A major scientific accomplishment, published in the year flow-induced transport barriers. that he moved back to Kyoto, was his derivation of reduced Wakatani was clearly a world leader in the studies of MHD equations for helical systems [5]. These equations were drift wave and resistive-g mode turbulence. He was unique in derived by means of an averaging approach, based on the that he not only developed a simple paradigm model (namely, “stellarator expansion technique.” They are a simplified the two-dimensional Hasegawa-Wakatani equations with one version of the full MHD equations, but yet retain the essential parameter), but also constructed technically complete models helical physics and – quite importantly – are amenable to for three-dimensional helical systems. He gained an nonlinear numerical simulations. These reduced equations are international reputation for his work on drift wave instabilities still today the popular standard model, used worldwide for in toroidally confined plasmas. His studies of anomalous MHD analysis and machine design. transport induced by ion temperature gradient (ITG) and Perusal of his extensive list of publications leads to an electron temperature gradient (ETG) instabilities are well appreciation of how much work he did on analyzing Heliotron known. One of us had the privilege of co-authoring a series experimental results. He was a co-author on many papers of ITG and ETG papers with Wakatani and also several of dealing with pellet injection, heating, equilibrium, stability, his students (especially Dr. Hideo Sugama) [11]. transport and confinement, etc., in Heliotron experiments [6]. Wakatani and his students skillfully used large-scale Furthermore, he, with his students, carried out studies of a computing for attacking complex systems. A rather recent Helias-Heliac hybrid stellarator [7] and helped with the design example was his work on simulating the dangerous plasma of the Heliotron-J device, which was subsequently constructed transport due to electron-temperature-gradient turbulence in and is now operating at Kyoto University. Heliotron-J is a reversed-shear, nearly collisionless toroidal systems with a helical axis device, based on the quasi-isodynamic (i.e., quasi- record number of representative electrons per cell in a self- omnigenous) optimization approach to the helical-axis consistent field [12]. Heliotron line. In addition to doing original research, he somehow found In the early 1980’s, shortly after the launch of the U.S.- time to publish five books. He co-authored two textbooks with Japan fusion theory exchange activities (to be described in Prof. Kyoji Nishikawa. The first, Physics of Continuous Sec. 4), Wakatani began to study anomalous transport due to Fluids [13], unfortunately available only in Japanese, covers turbulence arising from micro-instabilities, a major obstacle material from low-temperature quantum fluids to high- to improved plasma confinement. In 1983, working with Dr. temperature plasmas. Their other jointly written book, Plasma Akira Hasegawa (then at Bell Lab), he derived a set of Physics: Basic Theory with Fusion Applications [14], was nonlinear evolution equations that describe strong turbulence used by us as a graduate-level text at the University of Texas caused by resistive drift-wave instability at the edge of a and has been reprinted in three editions so far. Two of plasma [8]. Using these equations, they showed the existence Wakatani’s other books were related to U.S.-Japan exchange of an inverse cascade of energy from short to long activities. One was a conference proceedings, U.S.-Japan wavelengths in plasma turbulence. They also found a Workshop on Ion Temperature Gradient-Driven Turbulent prototype mechanism for generating large-scale poloidal flow Transport, Austin, TX, 1993 [15]. Another arose out a series structures (e.g., zonal flows and streamers in tokamaks). of U.S.-Japan workshops, which he helped to organize, and These “Hasegawa-Wakatani equations” for nonlinear scientific exchange visits, in which he participated (mostly drift waves have become extremely well known and hence with scientists at New York University), concerning the deserve special notice in any description of Wakatani’s development of the BETA equilibrium, stability, and transport accomplishments. We speculate that perhaps because he lived codes and their application for stellarator design [16]. in the ancient cultural region of Kyoto and Nara, he liked Unquestionably his magnum opus was his final book, theories that were simple, orderly, and yet elegant, like a Zen Stellarator and Heliotron Devices [17]. This text is extremely garden. Thus, the Hasegawa-Wakatani theory created a highly well written, providing both physical pictures as well as simplified formulation of the drift wave equations, in which detailed descriptions, and covering not only MHD and two coupled nonlinear partial differential equations provide a resistive MHD physics but also drift wave physics (very powerful paradigm for studying the transition from collisional important for helical plasmas) – in short, a veritable “bible” drift wave turbulence to collisionless drift waves, all in terms of stellarator theory. of a single parameter. These equations immediately became An impressive

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