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Anisotropic wave turbulence in electron MHD

机译：电子MHD中的各向异性波湍流

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摘要

It is well known that the magnetic and the velocity field fluctuations in the solar wind possess many features expected of fully developed magnetohydrodynamic (MHD) turbulence. However, for frequencies higher than 0.1 Hz the situation is different and clear discrepancies have been recently observed with, for example, a steepening of the magnetic fluctuation power law spectrum. In order to give a satisfactory description of the high frequency solar wind it is necessary to adopt a new description like the electron MHD approximation in which the dynamics is entirely governed by electrons. In that context, we review and discuss recent theoretical results obtained in anisotropic whistler wave turbulence for electron MHD in the presence of a strong and uniform external magnetic field. Using helicity decomposition, the wave kinetic equations for energy and magnetic helicity are derived at the level of three-wave interactions between whistler waves. It is shown that nonlinear interactions of whistler waves transfer energy and magnetic helicity mainly in the direction perpendicular to the external magnetic field. The anisotropic turbulence thus generated has exact stationary power law solutions which scale as k(perpendicular to)(-5/2)k(parallel to)(-1/2) for the energy spectrum and k(perpendicular to)(-7/2)k(parallel to)(-1/2) for the magnetic helicity spectrum. A strong analogy is found with the problem of rotating turbulence for incompressible neutral flows which share almost all the same properties.
机译：众所周知，太阳风中的磁场和速度场涨落具有完全发展的磁流体动力学（MHD）湍流所期望的许多特征。但是，对于高于0.1 Hz的频率，情况就不同了，最近已经观察到明显的差异，例如，磁波动功率定律频谱变陡。为了给出令人满意的高频太阳风描述，有必要采用新的描述，例如电子MHD近似，其中动力学完全由电子控制。在这种情况下，我们回顾并讨论了在强且均匀的外部磁场存在下，电子MHD在各向异性哨声波湍流中获得的最新理论结果。使用螺旋分解，在惠斯勒波之间的三波相互作用的水平上导出了能量和磁性螺旋的波动力学方程。结果表明，哨声波的非线性相互作用主要在垂直于外部磁场的方向上传递能量和磁螺旋。由此产生的各向异性湍流具有精确的固定幂定律解，其能谱的缩放比例为k（垂直）（-5/2）k（平行）（-1/2），k（垂直于）（-7 / 2）k（平行于）（-1/2）用于磁螺旋光谱。对于具有几乎所有相同特性的不可压缩的中性流，存在旋转湍流问题的强烈类比。

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