Computer and theoretical modeling has become an essential partner with experiment in developing techniques to improve the confinement and stability of high performance fusion science experiments. Important concepts such as the bootstrap current, radio-frequency current drive, and second stability arose from efforts to describe and predict the complex behavior of confined plasmas. These ideas have fundamentally transformed our picture of how a future fusion reactor might work and have become integral and essential parts of efforts to explore the burning plasma regime in a laboratory experiment. The development of new confinement concepts such as the spherical torus and the quasi-axisymmetric stellarator arose from the efforts to model and improve techniques for manipulating plasma containment.

Because of the large cost of the most advanced plasma confinement systems, especially those that can approach and enter a regime in which a burning plasma can be achieved, it is essential that we have the scientific understanding to predict the performance of planned devices. The program has made great strides in this direction. For example, modeling the nonlinear dynamics of very small scale turbulence across the core region of a nearly collisionless plasma in a complex shaped magnetic geometry is an enormous achievement. There are still significant areas, however, where success has proved elusive. These areas are typically where the traditional separation of the dynamics of plasma systems into microscale and macroscale processes breaks down. The sawtooth crash, neo-classical magnetic island growth and the formation and collapse of transport barriers are examples of such problems. At large scale, these problems involve the dynamics of magnetic fields and flows while the kinetic dynamics of turbulence, particle acceleration, and energy cascade dominate the smallest spatial scales. The interaction between these vastly disparate scales controls the evolution of the system. The enormous range of temporal and spatial scales associated with these problems renders direct simulation intractable even in computations using the largest existing parallel computers. In the absence of new multiscale simulation techniques which exploit the separation of scales while still allowing dynamical interactions between scales, these problems will remain unsolved for the foreseeable future.

The growth of magnetic islands through the development of the pressure-driven bootstrap current in a toroidal system — the neo-classical tearing mode — illustrates the difficulty of addressing these critical multiscale problems. The growth of these islands is thought to limit the accessible β of many confined plasmas, including the proposed ITER experiment. Its stability is thus a critical issue for the program. Neoclassical tearing modes grow on a long resistive time scale (about 0.2 seconds on DIII-D) while rotation of the magnetic islands gives a real frequency of about 5-8 kHz (in the frame moving with the ExB rotation). The pressure and current profiles around the island determine island growth and these profiles are themselves determined by the turbulent transport in the vicinity of the island. However, the local turbulence will be strongly perturbed by the island itself and it is not sufficient to model the transport with turbulent transport coefficients deduced from the bulk plasma. The turbulence has a frequency of 100-500 kHz — thus the range of important time scales covers nearly five decades. The spatial scales of interest range from millimeters (turbulence and reconnection layer scales) to meters — the size of the device. To understand this phenomenon, we must simultaneously model the turbulence and the island growth. This cannot be done without the development of a new class of computational algorithms that can treat both the kinetics at very small spatial scales as well as the macroscopic dynamics at the largest scales available to the system.

The scaling of turbulent transport in the complex, nearly-collisionless environments of high performance fusion plasmas remains one of the premier grand challenge topics in fusion science. Great progress has been made in developing an understanding of transport due to electrostatic fluctuations, including the interplay between zonal flows and this turbulence. The exploration of electromagnetic turbulence and magnetic transport in the finite β regime of greatest interest to future confinement systems is also rapidly progressing. However, the development of a full understanding of the feedback between large scale temperature and density gradients and poloidal and toroidal rotation profiles is not complete. Of particular importance are the onset conditions for the formation of internal and edge transport barriers — particularly what controls the threshold for this onset. It is not clear that we can guarantee that these important barriers, which can greatly enhance confinement, will continue to be accessible in planned burning plasma experiments such as ITER. Current projections are based on extrapolations from the databases of present machines. Such databases, however, are less reliable in projecting the performance of some of the new classes of innovative concept machines currently under construction. The possibility that changes in scaling may take place even in the tokamak line cannot be completely discounted. Again, the exploration of barrier formation, which may require in excess of 100 milliseconds, compared with the time scales of turbulent fluctuations, which are several microseconds, is not possible with presently available algorithms.

Problems that require the meshing of kinetic and fluid dynamics with disparate time scales have gained widespread interest recently in the engineering and applied mathematics communities. Significant progress has been made in the development of novel algorithms to address such problems. This work has attracted much interest and has been recognized recently by the J. D. Crawford Prize of the Society for Industrial and Applied Mathematics (SIAM). The basic idea is to take existing timestepping routines that advance the small-scale, kinetic physics, and use them to develop novel coarse-grained algorithms to calculate specific quantities of interest. The techniques work best when there are clear separations in space and time scale in a problem of interest. The growth of neo-classical islands with self-consistent turbulence driven transport, for example, seems well suited to this approach. (fusion examples) The application of these ideas in fusion science has the potential to facilitate the solution of a variety of the most challenging problems facing the program.

The Center for Multiscale Plasma Dynamics brings together a critical mass group of scientists with expertise in applied mathematics, computer science, theoretical and computational plasma physics and basic and performance dominated plasma experiments to address the most important multiscale issues facing fusion science. The Center is located at two primary institutions, the University of Maryland and UCLA. Bill Dorland and Steve Cowley are the principal investigators at their respective institutions.

The focus areas of the Center research program are three problems of central and immediate importance to fusion: sawteeth, neoclassical island growth and transport barrier formation. Research leaders for these topics are Dorland, Drake, and Cowley and Waelbroeck. All of the three topics are complex issues that have resisted resolution. For each of these problems we have formulated a research strategy that involves the close interplay of theory, advanced computation, and a detailed comparison with experimental observations. The designated leaders of each of these research projects, along with the team of scientists who are most involved are listed in the table below. Extensive benchmarking of theoretical and computational results will involve three of the most advanced confinement experiments in the US portfolio, DIII-D, CMOD and NSTX, as well as the JET experiment in the UK (coordinated with Dr. Richard Buttery, the JET MHD task force leader).

Projects	Leaders	Senior team members
Transport barrier bifurcation analysis	Dorland	Kevrekidis, Rogers, Hassam, Drake, Hammett, Waltz
Sawtooth physics	Drake	Gombosi, Cowley, Waelbroeck, Glasser, Rogers, Waltz, Shay, La Haye, Buttery, Peebles
NTM physics	Cowley, Waelbroeck	Waltz, Gombosi, Leboeuf, Glasser, Wilson, La Haye, Buttery, Peebles, Antonsen, Dorland
Multiscale gyrokinetic algorithm development (Eulerian)	Kevrekidis, Dorland	Stone, Hammett, Tadmor
Multiscale PIC algorithm development (PIC)	Gear, LeBoeuf, Shay	Swisdak, Drake, Gombosi
Kinetic Alfven waves (Expt)	Carter	Gekelman, Dorland, Cowley, Quataert
Identify ETG fluctuations (Expt)	Peebles, Porkolab	Synakowski, Dorland, Hammett
Streaming instabilities and anomalous resistivity in VTF (Expt)	Egedal	Porkolab
Streaming instabilities and anomalous resistivity in LAPD (Expt)	Gekelman	Carter, Pribyl, Judy, Stillman, Kintner
Streaming instabilities and anomalous resistivity (theory)	Shay	Carter, Swisdak, Cowley, Drake, Rogers
Kinetic Alfven waves (theory)	Quataert, Cowley	Morales, Dorland, Hammett, Chandran
ETG/TEM interactions	Hammett	Synakowski, Dorland
Kinetic/Ultra high-β MHD/LB-MHD	Leboeuf	Cowley, Macnab, Dorland, Wiley
Astrophysical applications	Quataert	Arons, Stone, Hammett, Cowley, Dorland, Lathrop, Chandran

To address the three fusion specific problems listed above, important basic physics issues linked to magnetic reconnection and turbulence and transport in the finite-β regime of advanced confinement systems must be resolved. Small scale fluctuations and their role in electron transport will be studied on DIII-D and NSTX using data from the UCLA group under Tony Peebles. A focused experimental program led by Troy Carter and Walter Gekelman on LAPD at UCLA and Prof. Miklos Porkolab and Jan Egedal on CMOD and VTF at MIT will address issues related to the fundamentals of reconnection and the dissipation of Alfven waves, including the development of anomalous resistivity and particle energization. Since these experiments can be diagnosed in considerable detail they will provide stringent tests of the numerical modeling of the nearly collisionless plasmas that are relevant to fusion.

Two leaders of the newly emerging effort in the applied mathematics community will assist in the development of new techniques for treating multiscale systems: Yannis Kevrekidis and Bill Gear from Princeton University. Both the fundamental science issues that are being addressed as part of the Center research program as well as the development of novel algorithms have broad applications to space and astrophysics, where there is wide recognition of the need to move beyond the MHD description. Four prominent members of the astrophysics community, Eliot Quataert (UC-Berkeley), Jonathon Arons (UC-Berkeley), Jim Stone (PU) and Ben Chandran (Iowa), and a member of the space science community, Tamas Gombosi (U.\ Michigan), are active participants.

While the research program is the primary goal of the center, a strong secondary goal is to provide advanced plasma physics education beyond the usual post-graduate course in plasma physics. This will consist of three elements: (1) advanced courses taught at one location and available via video conference to both locations and to the community; (2) a winter school for the whole community held every year and aimed at post-docs and above; and (3) weekly video conference seminars.

In College Park, the Center is hosted by the Center for Scientific Computation and Mathematical Modeling (CSCAMM). This March, CSCAMM co-sponsored a workshop with Princeton University's Institute for Computational Science and Engineering on the development of novel algorithms for plasma astrophysics problems.

The Center also has strong links with the NSF-funded Institute for Pure and Applied Mathematics (IPAM) at UCLA. IPAM will host a workshop on Multiscale Fusion Physics in January 2005.