论文标题
惯性电子水力动力学中的波湍流
Wave Turbulence in Inertial Electron Magnetohydrodynamics
论文作者
论文摘要
在存在相对强且均匀的外部磁场$ \ boldsymbol {b_0} = b_0 \ hat {\ boldsymbol {e}} _ \ | $的情况下，为惯性电子磁流体动力学（IEMHD）开发了波湍流理论。该制度与比电子惯性长度$ d_e $小的比例有关。我们得出了描述惯性惠斯勒或动力学alfvén波之间三波相互作用的动力学方程。我们表明，对于不变的能量和动量，转移都是各向异性（轴对称），直接级联反向沿垂直方向（$ \ perp $）到$ \ boldsymbol {b_0} $。获得了确切的固定溶液（Kolmogorov-Zakharov光谱），我们证明了该地区。我们还发现Kolmogorov常数$ C_K \ Simeq 8.474 $。在最简单的情况下，该研究揭示了$ k_ \ perp^{ - 5/2} k_ \ | |^{ - 1/2} $中的能量频谱，并在$ k_ \ perp^{ - 3/2} k_ \ |^{ - 1/2} $中固定在$ k_ \ perp^{ - 3/2} k_ perp^{ - 3/2} K_ perp^{ - 3/2} $的动量动力学上。这些解决方案对应于磁能频谱$ \ sim k_ \ perp^{ - 9/2} $，它比大于$ d_e $的量表的EMHD预测陡峭。我们最后讨论了该理论到空间等离子体的应用。
A wave turbulence theory is developed for inertial electron magnetohydrodynamics (IEMHD) in the presence of a relatively strong and uniform external magnetic field $\boldsymbol{B_0} = B_0 \hat{\boldsymbol{e}}_\|$. This regime is relevant for scales smaller than the electron inertial length $d_e$. We derive the kinetic equations that describe the three-wave interactions between inertial whistler or kinetic Alfvén waves. We show that for both invariants, energy and momentum, the transfer is anisotropic (axisymmetric) with a direct cascade mainly in the direction perpendicular ($\perp$) to $\boldsymbol{B_0}$. The exact stationary solutions (Kolmogorov-Zakharov spectra) are obtained for which we prove the locality. We also found the Kolmogorov constant $C_K \simeq 8.474$. In the simplest case, the study reveals an energy spectrum in $k_\perp^{-5/2} k_\|^{-1/2}$ and a momentum spectrum enslaved to the energy dynamics in $k_\perp^{-3/2} k_\|^{-1/2}$. These solutions correspond to a magnetic energy spectrum $\sim k_\perp^{-9/2}$, which is steeper than the EMHD prediction made for scales larger than $d_e$. We conclude with a discussion on the application of the theory to space plasmas.
