Dynamic Phase Alignment in Inertial Alfven Turbulence

In weakly-collisional plasma environments with sufficiently low electron beta, Alfvenic turbulence transforms into inertial Alfvenic turbulence at scales below the electron skin-depth. We argue that, in inertial Alfvenic turbulence, both energy and generalized kinetic helicity exhibit direct cascades. We demonstrate that the two cascades are compatible due to the existence of a strong scale-dependence of the phase alignment angle between velocity and magnetic field fluctuations, with the phase alignment angle scaling as proportional to the perpendicular wavenumber to the power of -1. The kinetic and magnetic energy spectra scale as the perpendicular wavenumber to the power of -5/3 and -11/3, respectively. As a result of the dual direct cascade, the generalized-helicity spectrum scales as the perpendicular wavenumber to the power of -5/3, implying progressive balancing of the turbulence as the cascade proceeds to smaller scales in the sub-electron-skin-depth range. Turbulent eddies exhibit a phase-space anisotropy, with the parallel wavenumber scaling as the perpendicular wavenumber to the power of 5/3, consistent with critically-balanced inertial Alfven fluctuations. Our results may be applicable to a variety of geophysical, space, and astrophysical environments, including the Earth's magnetosheath and ionosphere, solar corona, non-relativistic pair plasmas, as well as to strongly rotating non-ionized fluids.

在电子β参数（electron beta）足够低的弱碰撞等离子体（weakly-collisional plasma）环境中，阿尔文湍流（Alfvenic turbulence）会在小于电子趋肤深度（electron skin-depth）的尺度下转变为惯性阿尔文湍流（inertial Alfvenic turbulence）。本文论证，在惯性阿尔文湍流中，能量与广义动理学螺旋度（generalized kinetic helicity）均呈现直接级联现象。本文证明，由于速度与磁场涨落间的相位对准角（phase alignment angle）存在显著的尺度依赖性，且该相位对准角与垂直波数（perpendicular wavenumber）的-1次方正比，因此两种级联可兼容共存。动理学能谱与磁能谱分别随垂直波数以-5/3和-11/3的幂次标度。得益于这一双重直接级联，广义螺旋度能谱（generalized-helicity spectrum）随垂直波数以-5/3次幂标度，这意味着在亚电子趋肤深度区间内，随着级联向更小尺度推进，湍流将逐渐趋于平衡状态。湍流涡旋（turbulent eddies）表现出相空间各向异性（phase-space anisotropy），其平行波数（parallel wavenumber）与垂直波数的5/3次幂成正比，这与临界平衡惯性阿尔文涨落（critically-balanced inertial Alfven fluctuations）的结论一致。本研究结果可应用于多种地球物理、空间与天体物理环境，包括地球磁鞘与电离层（Earth's magnetosheath and ionosphere）、日冕（solar corona）、非相对论性正负电子对等离子体（non-relativistic pair plasmas），以及强旋转非电离流体（strongly rotating non-ionized fluids）。