Simplifying complexity: Reduced fluid models of low-collisionality, long-mean-free-path systems
Fluid equations are used in many different fields of physics because they can often provide a reduced but powerful description of complex many-body systems, by expressing important conservation laws (for conservation of particles, momentum, thermal energy, etc.) which the (nonlinear) dynamics of the system must satisfy. The usual Chapman-Enskog/Braginskii derivations of fluid equations are valid only in the limit of very frequent collisions (and short mean-free-path). This requirement fails in some important systems in plasma physics, astrophysics, semiconductors, etc. In plasmas, this leads to the fascinating phenomena of Landau-damping and wave-particle interactions, which are important for an accurate simulation of turbulence in tokamak fusion energy experiments. Attempting to derive fluid equations in the collisionless limit leads to an infinite hierarchy of coupled moment equations, and most previous closure approximations miss Landau-damping, leading to the usual assumption that a full Vlasov/Boltzmann/Liouville kinetic equation must be solved (often with a Particle-in-Cell code). Instead, the authors have found a new class of closure approximations based on the rate at which structures in phase space are linearly sheared (a.k.a. phase-mixing), {nu}{sub shear} {approximately}{vert_bar}k{sub {parallel}}{vert_bar}/v{sub t}. This provides an n-pole Pade` approximation to the linear propagator. It can be thought of as a lower bound to the effective collision frequency {nu}, thus extending the Chapman-Enskog thermal conductivity v{sup 2}{sub t}/{nu} to a non-local integral operator. There are some types of problems where an excessive number of moments are needed for sufficient convergence, but, for the types of strong-turbulence regimes typical of tokamaks, it seems sufficient to keep only a few low moments.
- DOE Contract Number:
- AC02-76CH03073
- OSTI ID:
- 375695
- Report Number(s):
- CONF-9304297-; ISSN 0003-0503; TRN: 96:004080-0297
- Journal Information:
- Bulletin of the American Physical Society, Vol. 40, Issue 2; Conference: 1993 joint meeting of the American Physical Society and the American Association of Physics Teachers, Washington, DC (United States), 12-15 Apr 1993; Other Information: PBD: Apr 1995
- Country of Publication:
- United States
- Language:
- English
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