From numerical solutions of a gyrokinetic model for ion temperature gradient turbulence it is shown that nonlinear coupling is dominated by three-wave interactions that include spectral components of the zonal flow and damped subdominant modes. Zonal flows dissipate very little energy injected by the instability, but facilitate its transfer from the unstable mode to dissipative subdominant modes, in part due to the small frequency sum of such triplets. Although energy is transferred to higher wave numbers, consistent with shearing, a large fraction is transferred to damped subdominant modes within the instability range. This is a new aspect of regulation of turbulence by zonal flows.

A broad sample of fluid models for instability-driven plasma turbulence is surveyed to determine whether saturation involving damped eigenmodes requires special physics or is a common property of plasma turbulence driven by instability. Previous investigations have focused exclusively on turbulence in the core of tokamak discharges. The models surveyed here apply to a wide range of physical mechanisms for instability, turbulent mode coupling, and parameter regimes, with the common modeling feature that the physics has been reduced to a two-field fluid description. All the models have regimes in which damped eigenmodes saturate the instability by damping the fluctuation energy at a rate comparable to the injection rate by the unstable eigenmode. A test function derived from model parameters is found to predict when damped eigenmodes provide saturation. This confirms that a critical condition for saturation by damped eigenmodes is that the damping rate of the damped eigenmode does not greatly exceed the growth rate. For the quadratic dispersion relation of two-field models, this tends to hold in regimes of stronger instability and for regimes with strong gradients and strong diamagnetic frequency. Nonlinear coupling also matters. Strong coupling can overcome the effects of heavy damping, while weak coupling can prevent a damped eigenmode from saturating turbulence even though it is not heavily damped. This study indicates that damped eigenmodes represent a pervasive mechanism for the saturation of plasma instability in fluid descriptions, complementing recent works showing these effects in comprehensive gyrokinetic models.

We study properties of magnetohydrodynamic (MHD) eigenmodes by decomposing the data of MHD simulations into linear MHD modes-namely, the Alfvén, slow magnetosonic, and fast magnetosonic modes. We drive turbulence with a mixture of solenoidal and compressive driving while varying the Alfvén Mach number (M A), plasma β, and the sonic Mach number from subsonic to transsonic. We find that the proportion of fast and slow modes in the mode mixture increases with increasing compressive forcing. This proportion of the magnetosonic modes can also become the dominant fraction in the mode mixture. The anisotropy of the modes is analyzed by means of their structure functions. The Alfvén-mode anisotropy is consistent with the Goldreich-Sridhar theory. We find a transition from weak to strong Alfvénic turbulence as we go from low to high M A. The slow-mode properties are similar to the Alfvén mode. On the other hand, the isotropic nature of fast modes is verified in the cases where the fast mode is a significant fraction of the mode mixture. The fast-mode behavior does not show any transition in going from low to high M A. We find indications that there is some interaction between the different modes, and the properties of the dominant mode can affect the properties of the weaker modes. This work identifies the conditions under which magnetosonic modes can be a major fraction of turbulent astrophysical plasmas, including the regime of weak turbulence. Important astrophysical implications for cosmic-ray transport and magnetic reconnection are discussed.

Zonal flows are shown to regulate ion temperature gradient turbulence by enabling efficient energy transfer from the instability to a damped eigenmode in the unstable wavenumber range. The damped mode also saturates turbulence when zonal flows are not active in saturation dynamics, for example, in electron temperature gradient turbulence, but the transfer from unstable to stable mode is less efficient and requires a larger amplitude to balance the instability drive. From numerical solutions of a fluid model with a single damped eigenmode, an eigenmode decomposition of the nonlinear evolution shows that the dominant energy transfer involves the triplet correlation of the unstable mode, the zonal flow, and the stable mode at three wavenumbers satisfying k ¼ k 0 þ k 00 . In this triplet, nearly all of the energy from the instability goes to the damped mode. The very small fraction going to the zonal flow is balanced by small zonal flow damping. This combination of unstable mode, zonal flow, and stable mode minimizes the nonlinear frequency mismatch and avails itself of large coupling strengths associated with the zonal flow. V C 2012 American Institute of Physics. [http://dx.

Simulations of decaying magnetohydrodynamic (MHD) turbulence are performed with a fluid and a kinetic code. The initial condition is an ensemble of long-wavelength, counterpropagating, shear-Alfvén waves, which interact and rapidly generate strong MHD turbulence. The total energy is conserved and the rate of turbulent energy decay is very similar in both codes, although the fluid code has numerical dissipation whereas the kinetic code has kinetic dissipation. The inertial range power spectrum index is similar in both the codes. The fluid code shows a perpendicular wavenumber spectral slope of k −1.3 ⊥ . The kinetic code shows a spectral slope of k −1.5 ⊥ for smaller simulation domain, and k −1.3 ⊥ for larger domain. We estimate that collisionless damping mechanisms in the kinetic code can account for the dissipation of the observed nonlinear energy cascade. Current sheets are geometrically characterized. Their lengths and widths are in good agreement between the two codes. The length scales linearly with the driving scale of the turbulence. In the fluid code, their thickness is determined by the grid resolution as there is no explicit diffusivity. In the kinetic code, their thickness is very close to the skin-depth, irrespective of the grid resolution. This work shows that kinetic codes can reproduce the MHD inertial range dynamics at large scales, while at the same time capturing important kinetic physics at small scales.