Multiscale Processes in Fusion Plasmas

January 10 - 14, 2005

Schedule and Presentations

Program Poster PDF

Pictures

Organizing Committee:

Steven Cowley, Chair (UCLA)
William Dorland (University of Maryland)
James Drake (University of Maryland)
Bjorn Engquist (University of Texas)
Alan Glasser (Los Alamos National Laboratory)
Eliezer Hameiri (New York University/Courant Institute of Mathematical Sciences)
Yannis Kevrekides (Princeton University)
Bruce Langdon (Lawrence Livermore National Laboratory)
Warren Mori (UCLA)
Carl Sovinec (University of Wisconsin)
William Tang (Princeton University)

Introduction

To achieve fusion in a magnetically confined plasma, it is necessary to hold a plasma of tens of meters cubed in a stable configuration for many seconds. Inside this plasma are physical processes on a vast range of space and time scales. Theoretical analysis of these problems has mainly focused on a single relevant space and time scale for each physical processes. For example, in the last decade the fusion community has made remarkable progress on calculating the small scale anisotropic kinetic turbulence that leads to the loss of heat from magnetically confined plasmas. It has become clear, however, that this single scale approach is inappropriate for key phenomena and that the interaction of disparate scales is nontrivial. A similar situation has arisen in inertial confinement fusion and in the relativistic interaction of beams and lasers with plasmas. In these high energy density (HED) plasmas the time scales range from the femtosecond laser period to the nanosecond plasma evolution time. While the fusion and high energy density communities have begun to develop multiple scale approaches, much needs to be done before predictive modeling of these plasmas is achieved. Clearly, the plasma community is not alone in facing such issues. Indeed, many areas have been addressing multiple scale issues for decades. The applied mathematics community has developed both specific and general techniques for the analysis of multiple scale problems. The plasma community has had limited exposure to these advances. Similarly, the applied mathematics community is largely unaware of the specific technical challenges in plasmas. This workshop aims to foster a dialogue between the fusion and applied mathematics communities.

Meeting Organization - Scientific Topics

We will organize the meeting around five physical phenomena in fusion plasmas - one per day. Each morning will start with a pedagogical review of the phenomena, the scales involved, the physical approximations and the equations to be solved. This will be followed by a series of talks on current approaches and recent progress. Each afternoon will begin with talks from applied mathematicians on techniques developed to solve similar problems. The afternoons will conclude with open discussions.

Day 1. Reconnection, Sawteeth and Kinetic Modeling

Magnetically confined plasmas in tokamak devices routinely show a periodic oscillation of the central temperature with a very characteristic sawtooth shape. The rise in the central temperature happens on a time-scale of tens to hundreds of milliseconds - in contrast the fall happens in 20-100 microseconds. This phenomena is not understood although it clearly involves reconnection of magnetic field lines in a narrow layer and possibly the triggering of fast fine-scale turbulence. Detailed global Magnetohydrodynamic modeling has yielded inconclusive results. The full kinetic equations for the plasma must be solved for the reconnection and turbulence but the macroscopic effects must be treated with averaged equations. Topics for talks include coupling of kinetic and macroscopic treatments in codes, fast scale averaging, projective methods and adaptive numerics (AMR, high order finite elements, spectral elements).

Day 2. Methods in Relativistic Laser and Beam Plasma Interaction

Today's state-of-the-art lasers and particle beams have energy densities near at 10¹⁷m^-3 or equivalently terrabars of pressure. When such beams propagate through plasmas they create large space-charge wakes that can accelerate and focus particle beams. The physics involved in such interactions has a hierarchy of time and space scales. For example in laser plasma interaction space scales range from the micron sized laser wavelength to the centimeter lengths over which the laser energy is depleted. It has become clear that to model these processes requires a set of algorithms, some of which resolve the shortest time and space scales and some of which average out the shortest scales. Writing efficient algorithms which scale to parallel computers and accurately include all the relevant physics is a great challenge. Topics to be discussed include: PIC simulation, averaged equations, projective methods, anisotropic modeling and adaptive numerics.

Day 3. Multiscale Turbulent Transport in Magnetic Confinement

Heat is lost from fusion devices via turbulent transport caused by convective instabilities. These instabilities are fine scale (centimeter eddy sizes) and fast time-scale (microseconds). The heat is transported on a time-scale of about a second over distances of order a meter. Despite the obvious difficulty of calculating turbulence in long mean free path (i.e. kinetic) plasmas recent Gyro-kinetic simulations (which average over the motion of electrons and ions around the field lines) have successfully reproduced features of the turbulence and transport in narrow domains. Patching these domains together to calculate the global transport has not yet been done. There is an urgent need to make this step from microscopic turbulence to the macroscopic transport.

Day 4. Long Time-scale Laser Plasma Interaction for Direct Drive, Indirect Drive and Fast Ignition Fusion

In inertial confinement fusion small capsules of fusion fuels are compressed by powerful lasers (like the NIF laser being built at Livermore). In "Direct Drive" laser fusion the lasers shine on the capsule to be compressed. To compress the capsule in "Indirect Drive" Fusion, however, the laser heats plasma inside a enclosure called the hohlraum - x-rays from this plasma then heat and compress the capsule. If, at the point of maximum compression the fuel is heated by an intense short pulse laser, the fusion yield is considerably enhanced - this is the principle of "fast ignition". In all scenarios the laser heating time is long compared to period of the laser. Long time-scale kinetic modeling of the interaction requires techniques to reduce noise and average over short times - such methods are being developed. Methods are also being developed to separate the thermal part of the distribution function from the non-thermal part. In fast ignition the intense short pulse laser, however, creates and interacts with a population of relativistic electrons. This is being calculated with particle-in-cell codes increasingly successfully. The heating of the electrons must be calculated over very fast time-scales and then incorporate into slower evolution of the capsule. The existing techniques to calculate the long time evolution will be discussed and new ideas on how to make the computations more realistic will be presented.

Day 5. Slow Island Growth in Tokamaks

Over a time-scale of seconds the magnetic field in tokamaks is often observed to lose its toroidal symmetry and grow non-axisymmetric islands. These islands grow in the presence of fast time-scale short spatial-scale turbulence. So far computations have treated the turbulence as providing enhanced transport in fluid/MHD modeling of the island growth - ignoring key aspects of the interaction of turbulence and islands. This problem is of great importance to the International Tokamak program where the growth of islands may limit the achievable pressure. Topics for discussion include the observations, the existing calculations, methods to calculate turbulence in the presence of the islands, methods to follow the slow evolution of the islands, projection techniques, adaptive numerical techniques and averaging methods.

Speakers

Contact Us:

Institute for Pure and Applied Mathematics (IPAM)
Attn: FUS2005
460 Portola Plaza
Los Angeles CA 90095-7121
Phone: 310 825-4755
Fax: 310 825-4756
Email: ipam@ucla.edu
Website: http://www.ipam.ucla.edu/programs/fus2005/