Stability and nonlinear dynamics of plasmas: A symposium celebrating Professor Robert Dewar's accomplishments in plasma physics

To celebrate Professor Robert Dewar's 65th birthday, a Symposium was held on 31 October 2009 in Atlanta, Georgia, just before the 51st Annual Meeting of the Division of Plasma Physics of the American Physical Society. The Symposium was attended by many of Bob's colleagues, friends, postdoctoral colleagues and students (present and former). Boyd Blackwell, Anthony Cooper, Chris Hegna, Stuart Hudson, John Krommes, Alexander Pletzer, Ellen Zweibel, and I gave talks that covered various aspects of Bob's wide-ranging scholarship, and his leadership in the Australian and the US fusion program. At the Symposium, Bob gave an insightful talk, published in this issue as a paper with D Leykam. This paper makes available for the first time unpublished results from Bob's M Sc Thesis on a general method for calculating the potential around a `dressed' test particle in an isotropic and collisionless plasma. The paper is interesting not only because it provides a glimpse of the type of elegant applied mathematics that we have come to associate with Bob, but also because he discusses some leitmotifs in his intellectual evolution since the time he was a graduate student at the University of Melbourne and Princeton University. Through his early encounter with quantum field theory, Bob appreciated the power of Lagrangian and Hamiltonian formalisms, which he used with great effectiveness in nonlinear dynamics and plasma physics. A question that animates much of his work is one that underlies the `dressed' particle problem: if one is given a Hamiltonian with an unperturbed (or `bare') part and an interaction part, how is one to obtain a canonical transformation to `the oscillation centre' thatwould reduce the interaction part to an irreducible residual part while incorporating the rest in a renormalized zeroth-order Hamiltonian? One summer in Princeton, I worked with Bob on a possible variational formulation for this problem, and failed. I was daunted enough by my failure that I turned to MHD relaxation theory for my PhD thesis under Bob's supervision. It was a good decision because Bob showed me how beautiful MHD theory can be, but he did not himself give up the problem of formulating optimal oscillation-centre transformations. He has a singular ability to hold difficult problems like this in in his mind for many years until they crack open (or even if they do not!), a trait that many of us find altogether admirable. The impact of such thinking on plasma turbulence theory over the last four decades is described in the article by John Krommes in this issue. Stuart Hudson's article touches on some of the same themes in the pursuit of fully three-dimensional relaxed states in toroidal stellarators. Zensho Yoshida has contributed an interesting article on the interplay of Lagrangian and Eulerian representations of collective motions in a fluid, a theme that appears in Bob's work in several contexts. Underlying much of Bob's work on Hamiltonian systems is his deep knowledge and appreciation of Lie perturbation theory, and the article by Steven Richardson and John Finn, which discusses an example of symplectic integrators and their numerical implementation, reflects that interest. It is impossible to do justice to all of Bob's contributions to theoretical plasma physics in this short section. Bob's WKB theory of ballooning modes in three-dimensional toroidal systems (with Alan Glasser) is a classic paper that was in some ways years ahead of its time, especially in its exploration of the deep connections between KAM theory and the nature of the spectrum. In later work, he developed these ideas further by establishing connections with the phenomenon of Anderson localization in condensed matter physics. His papers on the subject of ballooning modes are gems of the plasma physics literature, and are unsurpassed in their mathematical elegance, insight, and their development of broad connections with other fields of theoretical physics. Some of this was covered in the talks at the Symposium. The paper by David Barmaz and coworkers published in this issue discusses the problem diamagnetic stabilization of ballooning instabilities in stellarators. It is not surprising that Bob's work on ballooning modes shows an accomplished master of WKB theory at work, for it is the culmination of a process that began many years earlier. His involvement in applications of WKB theory to problems involving instability and turbulence began in 1970, when he was a graduate student. At this time he wrote a very influential paper, discussed at the Symposium, on the interaction between hydromagnetic waves and a timedependent inhomogeneous medium. This paper is widely cited, especially in the astrophysical and space plasma literature, for it gives a rigorous method of evaluating the effects of lowfrequency hydromagnetic fluctuations on a slowly varying background medium. The method has found use in problems as diverse as the self-sustainment of molecular clouds, the heating and acceleration of the solar wind, and the effect of cosmic rays on the interplanetary medium. Attentive readers will note that Bob has been drafted as a co-author and participant in about half of the publications in this issue. This is a reflection of Bob's continued and tireless involvement in a wide spectrum of research problems that have their genesis in his fundamental contributions to plasma physics, as well as the eagerness with which we all welcome his involvement in our own projects. We hope to have this continue for many years to come.