# Center for Magnetic Self Organization

## in Laboratory and Astrophysical Plasmas

# MHD dissipation range turbulence

Measurements of magnetic turbulence in laboratory, space, and astrophysical plasmas are accessing small scales where dissipation can become dynamically important. To help interpret spectra measured at such scales, a theory for dissipation range MHD turbulence has been derived for the first time. Like hydrodynamic dissipation range turbulence the spectra consist of a product of a power law and an exponential falloff that scales with the dissipative (Kolmogorov) wavenumber. Unlike hydrodynamics, the values of exponential and power law indices depend on whether the turbulence is aligned or unaligned, and on the ratio of viscous to magnetic diffusivity, or magnetic Prandtl number. There are also multiple dissipative wavenumbers. (See P.W. Terry and V. Tangri, Phys. Plasmas 16, 082305 (2009).]

* The magnetic turbulence spectrum measured in the Madison Symmetric Torus, as a function of toroidal wavenumber k⊥ (in green), in the direction with maximum fluctuation power. The spectrum is well fit (overlying blue curve) by a theoretical model only if both power law and exponential factors are included. The exponential decay becomes important at smaller k⊥ than expected for classical dissipation, hinting at a kinetic dissipation process. *

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