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Transition between Saturation Regimes of Gyrokinetic Turbulence

D. R. Hatch, F. Jenko, A. Bañón Navarro, V. Bratanov

2013
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Physical Review Letters
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A gyrokinetic model of ion temperature gradient driven turbulence in magnetized plasmas is used to study the injection, nonlinear redistribution, and collisional dissipation of free energy in the saturated turbulent state over a broad range of driving gradients and collision frequencies. The dimensionless parameter L T =L C , where L T is the ion temperature gradient scale length and L C is the collisional mean free path, is shown to parametrize a transition between a saturation regime
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... ion regime dominated by nonlinear transfer of free energy to small perpendicular (to the magnetic field) scales and a regime dominated by dissipation at large scales in all phase space dimensions. Introduction.-Gyrokinetic theory is the predominant formalism for describing low-frequency microturbulence in magnetized plasmas [1], with a wide range of applications from magnetic confinement fusion [2,3] to space and astrophysics [4] [5] [6] . Despite its importance, a coherent overall picture regarding the fundamental nature of gyrokinetic turbulence has yet to emerge. In this context, it is key to understand the injection, nonlinear redistribution, and collisional dissipation of free energy-which is the ideal quadratic invariant in gyrokinetics-in the saturated turbulent state. Because of the diffusive terms (secondorder velocity space derivatives) inherent in realistic collision operators, collisional dissipation is often associated with small scales in velocity space. This is roughly analogous to the link between dissipation and small spatial scales in Navier-Stokes turbulence, with the (normalized) collision frequency playing the role of the inverse Reynolds number. Two main mechanisms have been identified for developing small scales in velocity space: linear phase mixing (Landau damping) [7, 8] , associated with small scales in parallel (to the magnetic field) velocity space, and nonlinear phase mixing [9,10], which becomes important at k ? i > 1 (k ? is the perpendicular wave number and i is the ion gyroradius) and is linked to small scales in perpendicular velocity and real space. In contrast with the latter, a large fraction of the collisional dissipation is often observed to occur at large (real space) perpendicular scales in gyrokinetic simulations [11, 12] . This large-scale dissipation has been interpreted using the so-called damped eigenmode paradigm [11-13]-saturation via nonlinear excitation of linearly stable structures at phase space scales comparable to those of the driving microinstabilities. To date, there exists no framework reconciling large-scale and small-scale dissipation scenarios. At issue is the relative importance of each of these mechanisms, the processes by

doi:10.1103/physrevlett.111.175001
pmid:24206497
fatcat:rbbloztkizbc3lgljeifhmkeoa