The Fusion and Astrophysical Plasma Physics Group within the Physics Department and the Center for Astrophysics and Space Sciences at the University of California, San Diego is led by Professor Patrick H. Diamond, Distinguished Professor of Physics, and consists of two research scientists-- Mikhail Malkov, Fred Hinton, and four graduate student researchers-- and is managed by an administrative assistant.

**Nonperturbative mean-field theory for minimum enstrophy relaxation** - *Pei-Chun Hsu, P.H. Diamond and S. Tobias*

The dual cascade of enstrophy and energy in quasi-two-dimensional turbulence strongly suggests that a viscous but otherwise potential vorticity (PV) conserving system decays selectively toward a state of minimum potential enstrophy. We derive a nonperturbative mean field theory for the dynamics of minimum enstrophy relaxation by constructing an expression for PV flux during the relaxation process. The theory is used to elucidate the structure of anisotropic flows emerging from the selective decay process. This structural analysis of PV flux is based on the requirements that the mean flux of PV dissipates total potential enstrophy but conserves total fluid kinetic energy. Our results show that the structure of PV flux has the form of a sum of a positive definite hyperviscous and a negative or positive viscous transport of PV. Transport parameters depend on zonal flow and turbulence intensity. Turbulence spreading is shown to be related to PV mixing via the link of turbulence energy flux to PV flux. In the relaxed state, the ratio of the PV gradient to zonal flow velocity is homogenized. This homogenized quantity sets a constraint on the amplitudes of PV and zonal flow in the relaxed state. A characteristic scale is defined by the homogenized quantity and is related to a variant of the Rhines scale. This relaxation model predicts a relaxed state with a structure which is consistent with PV staircases, namely, the proportionality between mean PV gradient and zonal flow strength.

To the memory of Professor Marshall N. Rosenbluth - an American plasma physicist and member of the National Academy of Sciences - who passed away on September 23, 2003.

We are working primarily on the theory of fusion plasma including:

- Nonlinear dynamics of plasmas and fluids
- Anomalous transport
- Self-organized criticality in confined plasma
- L-H transition, transport barrier physics
- Dynamo theory
- Nonlinear waves in space plasma

Our work is primarily funded by the Office of Fusion Energy Sciences of the U.S. Department of Energy.

Grant No. DE-FG02-04ER54738.