Dissipation Range Turbulent Cascades in Plasmas

Recent spectral measurements of turbulence in the interstellar medium, solar wind, and laboratory experiments reach small scales where dissipation likely plays a role. The spectra show breaks in power laws and steepening of spectral indices from either small-scale inertial effects or dissipation. These observations motivated formulation of the first theoretical description of dissipation range cascades in MHD turbulence, with generalizations to other types of dissipation range plasma turbulence with scalable dissipation rates, including tokamak micorturbulence. The central construct is the scaled attenuation in wavenumber space of the spectral energy transfer rate. With closure, this yields spectra characterized by the product of a power law and exponential fall-off. Both functional forms apply to all scales. Spectral indices of the power law and exponential fall-off depend on the scaling of the dissipation, the strength of the nonlinearity, and alignment of vector fields. The theory describes three very different spectral measurements. Turbulence at low magnetic Prandtl number in the liquid metal Madison Dynamo Experiment has a magnetic dissipation range/flow inertial range dominated by power law behavior, well matched by the MHD dissipation range theory. Magnetic turbulence in the MST reversed field pinch plasma has spectra that are exponential or power law, depending on propagation direction and scale. The dominant small-scale turbulence fits a product of a power law and exponential, but the implied dissipation is larger than expected for classical dissipation, hinting at kinetic effects. Gyrokinetic ion- temperature-gradient turbulence has a spectrum in which the exponential component and dissipation become weaker at small scale, giving a power law asymptotically. Strong dissipation at large scale and the asymptotic power law are observed in simulation.