Plasma Turbulent Transport and Fine-Scale Structures of Phase Space Distribution Function

T.-H.Watanabe and H.Sugama

National Institute for Fusion Science, Toki, Gifu 509-5292, Japan

The one-body velocity distribution function f in a collisionless plasma turbulence is stretched and folded by the Hamiltonian flow in the phase space while preserving its amplitude. This is known as the phase mixing which leads to continuous generation of fine-scale fluctuations of f, and is closely related to the paradoxical argument how the collisionless turbulence described by the kinetic equation with the time-reversal symmetry causes the steady transport flux with no dissipation mechanism. If the steady transport driven by constant density and/or temperature gradients is observed through coarse-graining of f with fine-scale structures, a ''quasisteady'' state of the collisionless turbulence should be realized, where high-order velocity-space moments of f continue to grow while keeping low-order ones constant in average [1,2]. Existence of the quasisteady state in the ion temperature gradient (ITG) driven turbulence is confirmed by an Eulerian kinetic simulation with high resolution for the velocity space [3]. The numerical accuracy in dealing with the time-reversible plasma dynamics has been verified by the plasma echo simulation. It is also noteworthy that the kinetic simulation result agrees fairly well with that of the collisionless fluid simulation with the nondissipative closure model that can preserve the time-reversibility of linearly unstable eigenmodes [4]. From a viewpoint of practical applications to prediction of the transport flux in magnetically-confined plasmas, it is also required that an asymptotic behavior of the transport coefficient in a low-collisionality limit agrees with the collisionless one, and is recently examined by simulations on the ITG turbulence with weak collisionality. The finite collisionality is indispensable to realizing the real statistically steady states for the all order-moments of f, where the entropy variable associated with fluctuations is produced by the turbulent transport on a macro scale, is transfered in the phase space by the E×B nonlinearity and the phase mixing, and is, finally, damped by the collision term acting on a micro scale. This process is investigated in detail by a spectral analysis with the Hermite-polynomial expansion of f [5]. Our recent progress in the toroidal ITG simulation will also be reported.

[1] J.A.Krommes and G.Hu, Phys.Plasmas 1 (1994) 3211.
[2] H.Sugama, M.Okamoto, W.Horton, and M.Wakatani, Phys.Plasmas 3 (1996) 2379.
[3] T.-H.Watanabe and H.Sugama, Phys.Plasmas 9 (2002) 3659.
[4] H.Sugama, T.-H.Watanabe, and W.Horton, Phys.Plasmas 10 (2003) 726.
[5] H.Sugama and T.-H.Watanabe, ''Spectrum of the Velocity Distribution Function in the Slab Ion Temperature Gradient Driven Turbulence'', presented in this conference.