A Hamiltonian two-field gyrofluid model for kinetic Alfvén waves (KAWs) in a magnetized electron–proton plasma, retaining ion finite-Larmor-radius corrections and parallel magnetic field fluctuations, is used to study the inverse cascades that develop when turbulence is randomly driven at sub-ion scales. In the directions perpendicular to the ambient field, the dynamics of the cascade turns out to be non-local and the ratio $\chi _f$ of the wave period to the characteristic nonlinear time at the driving scale affects some of its properties. For example, at small values of $\chi _f$ , parametric decay instability of the modes driven by the forcing can develop, enhancing for a while inverse transfers. The balanced state, obtained at early time when the two counter-propagating waves are equally driven, also becomes unstable at small $\chi _f$ , leading to an inverse cascade. For $\beta _e$ smaller than a few units, the cascade slows down when reaching the low-dispersion spectral range. For higher $\beta _e$ , the ratio of the KAW to the Alfvén frequencies displays a local minimum. At the corresponding transverse wavenumber, a condensate is formed, and the cascade towards larger scales is then inhibited. Depending on the parameters, a parallel inverse cascade can develop, enhancing the elongation of the ion-scale magnetic vortices that generically form.

中文翻译：

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动力学阿尔文波湍流中的反级联和磁涡旋

磁化电子-质子等离子体中动力学阿尔文波 (KAW) 的哈密顿双场旋涡流体模型，保留离子有限拉莫半径校正和平行磁场波动，用于研究随机驱动湍流时产生的逆级联在亚离子尺度。在垂直于环境场的方向上，级联的动力学结果是非局部的，并且比率 $\chi_f$ 在驱动尺度上，波周期到特征非线性时间的变化会影响其一些特性。例如，在较小的值 $\chi_f$ ，由强迫驱动的模式的参数衰减不稳定性可能会发展，从而增强一段时间的反向传输。早期获得的平衡状态，当两个反向传播的波被同等驱动时，也变得不稳定 $\chi_f$ ，导致反向级联。为了 $\beta _e$ 小于几个单位时，级联在达到低色散光谱范围时会减慢。对于更高 $\beta _e$ ，KAW 与 Alfvén 频率的比值显示一个局部最小值。在相应的横向波数处，形成凝聚物，然后抑制向更大尺度的级联。根据参数的不同，可以形成平行的反向级联，从而增强通常形成的离子级磁涡流的伸长率。