A dynamical approach, rather than the usual statistical approach, is taken to explore the physical mechanisms underlying the nonlinear transfer of energy, the damping of the turbulent fluctuations, and the development of coherent structures in kineti
c plasma turbulence. It is argued that the linear and nonlinear dynamics of Alfven waves are responsible, at a very fundamental level, for some of the key qualitative features of plasma turbulence that distinguish it from hydrodynamic turbulence, including the anisotropic cascade of energy and the development of current sheets at small scales. The first dynamical model of kinetic turbulence in the weakly collisional solar wind plasma that combines self-consistently the physics of Alfven waves with the development of small-scale current sheets is presented and its physical implications are discussed. This model leads to a simplified perspective on the nature of turbulence in a weakly collisional plasma: the nonlinear interactions responsible for the turbulent cascade of energy and the formation of current sheets are essentially fluid in nature, while the collisionless damping of the turbulent fluctuations and the energy injection by kinetic instabilities are essentially kinetic in nature.
The interpretation of single-point spacecraft measurements of solar wind turbulence is complicated by the fact that the measurements are made in a frame of reference in relative motion with respect to the turbulent plasma. The Taylor hypothesis---tha
t temporal fluctuations measured by a stationary probe in a rapidly flowing fluid are dominated by the advection of spatial structures in the fluid rest frame---is often assumed to simplify the analysis. But measurements of turbulence in upcoming missions, such as Solar Probe Plus, threaten to violate the Taylor hypothesis, either due to slow flow of the plasma with respect to the spacecraft or to the dispersive nature of the plasma fluctuations at small scales. Assuming that the frequency of the turbulent fluctuations is characterized by the frequency of the linear waves supported by the plasma, we evaluate the validity of the Taylor hypothesis for the linear kinetic wave modes in the weakly collisional solar wind. The analysis predicts that a dissipation range of solar wind turbulence supported by whistler waves is likely to violate the Taylor hypothesis, while one supported by kinetic Alfven waves is not.
Turbulence in space and astrophysical plasmas is governed by the nonlinear interactions between counterpropagating Alfven waves. Here we present the theoretical considerations behind the design of the first laboratory measurement of an Alfven wave co
llision, the fundamental interaction underlying Alfvenic turbulence. By interacting a relatively large-amplitude, low-frequency Alfven wave with a counterpropagating, smaller-amplitude, higher-frequency Alfven wave, the experiment accomplishes the secular nonlinear transfer of energy to a propagating daughter Alfven wave. The predicted properties of the nonlinearly generated daughter Alfven wave are outlined, providing a suite of tests that can be used to confirm the successful measurement of the nonlinear interaction between counterpropagating Alfven waves in the laboratory.
Howes et al. Reply to Comment on Kinetic Simulations of Magnetized Turbulence in Astrophysical Plasmas arXiv:0711.4355
This letter presents the first ab initio, fully electromagnetic, kinetic simulations of magnetized turbulence in a homogeneous, weakly collisional plasma at the scale of the ion Larmor radius (ion gyroscale). Magnetic and electric-field energy spectr
a show a break at the ion gyroscale; the spectral slopes are consistent with scaling predictions for critically balanced turbulence of Alfven waves above the ion gyroscale (spectral index -5/3) and of kinetic Alfven waves below the ion gyroscale (spectral indices of -7/3 for magnetic and -1/3 for electric fluctuations). This behavior is also qualitatively consistent with in situ measurements of turbulence in the solar wind. Our findings support the hypothesis that the frequencies of turbulent fluctuations in the solar wind remain well below the ion cyclotron frequency both above and below the ion gyroscale.
