The dynamics of high-temperature magnetically confined plasma is characterized by the interactions of widely spaced time and space scales — that is, the behavior of macroscale phenomena is intrinsically coupled to and facilitated by kinetic dynamics at the smallest spatial scales. The historical compartmentalization of physics issues in the Fusion Energy Sciences program into macro- and micro-scale phenomena has inhibited the development of techniques to attack these problems, to the detriment of the program. In this section we describe several critical multiscale phenomena and describe our strategy for building new algorithms that can adequately treat them. In the table below, the numbers quoted are approximate values for ITER based on the design parameters. It is apparent from this table that the range of interacting scales is enormous. Much of current fusion research has exploited the separation of scales. For example, gyrokinetic modeling exploits two scale separations:

• The turbulence and the resultant fluxes are calculated in a stationary equilibrium, exploiting the separation of the fast turbulence time scale and the slow discharge evolution time scale.
• The small perpendicular turbulence scale makes it possible to ignore the perpendicular variations of the equilibrium gradients when computing local turbulence — the validity of this approach has recently been confirmed for small rho/a.

However, relatively little has been done to couple dynamical calculations at different scales. The table below lists some the important time scales of phenomena relevant to the proposed ITER experiment. Transport barriers, for example, form over time scales of 0.1-1.0 s while their dynamics is controlled by the turnover of small-scale eddies that may have time scales of 100's of microseconds or smaller. Sawteeth cause an expulsion of the core plasma energy on time scales of 100's of microseconds but the observational data suggests that the core energy escapes not by macroscopic convection, as had been believed in earlier theories, but due to the rapid development of turbulence that may spread from the q=1 surface as magnetic reconnection develops. Thus, the sawtooth crash involves the complex interaction of MHD scale phenomena and kinetic scale phenomena. Similarly, the slow growth (over several seconds) of neoclassical tearing modes depends sensitively on the pressure gradients around magnetic islands, which in turn are controlled by local turbulent eddies produced by these same gradients. The range of temporal scales is therefore extreme.

Physics	Spatial scale	Temporal scale
Electron energy transport from ETG modes	Scale perp. to B ~ 0.001 cm-0.1 cm Scale parallel to B is qR ~ 15 m	ω* ~ 0.5-5 MHz
Ion energy transport from ITG modes	Scale perp. to B ~ 0.1 cm-8 cm Scale parallel to B is qR ~ 15 m	ω* ~ 10-100 kHz
Transport barriers	Unknown scaling of perpendicular scales. Measured scales suggest width ~ 1-10 cm	Lifetime 100 seconds or more in core? Relaxation oscillations for edge barrier with unknown frequency
Magnetic islands, tearing modes and NTM's	Island width ~ 1 cm Eigenfunction extent ~ 100 cm Turbulent correlation length near island ~ 1 cm (?)	Growth time ~ 1-100 seconds Island frequency ~ 0.1-1 kHz Turbulent frequency near island ~ 100 kHz
Sawteeth	Reconnection layer width ~ 0.05 cm Eigenfunction extent ~ 100 cm	Crash time ~ 50-100 microseconds Real frequency ~ 0.1-1 kHz Ramp time 1-100 seconds
Discharge evolution	Profile scales ~ 100 cm	Energy confinement time 2-4 seconds Burn time unknown

Properly treating the range of scales in these critical problems is essential to predict, interpret and enhance the performance of current and future experiments. Despite the rapid advance of modern computers, a brute force approach (including all scales simultaneously) is not practical in any time frame of interest. A central theme of this proposal is therefore the development of multiscale algorithms for plasma physics. Each physical problem has a particular scale separation and clearly no single method will suffice for all problems. However, the development of innovative techniques to address similar problems in engineering and applied mathematics suggests that solutions of these important problems in plasma physics may be attainable.