We study properties of magnetohydrodynamic (MHD) eigenmodes by decomposing the data of MHD simulations into linear MHD modes - namely the Alfv{'e}n, slow magnetosonic, and fast magnetosonic modes. We drive turbulence with a mixture of solenoidal and compressive driving, while varying the Alfv{'e}n Mach number ($M_A$), plasma $\beta$, and the sonic Mach number from sub-sonic to trans-sonic. We find that the proportion of fast and slow modes in the mode mixture increases with increasing compressive forcing. This proportion of the magnetosonic modes can also become the dominant fraction in the mode mixture. The anisotropy of the modes is analyzed by means of their structure functions. The Alfv{'e}n mode anisotropy is consistent with the Goldreich-Sridhar theory. We find a transition from weak to strong Alfv{'e}nic turbulence as we go from low to high $M_A$. The slow mode properties are similar to the Alfv{'e}n mode. On the other hand the isotropic nature of fast modes is verified in the cases where the fast mode is a significant fraction of the mode mixture. The fast mode behavior does not show any transition in going from low to high $M_A$. We find indications that there is some interaction between the different modes and the properties of the dominant mode can affect the properties of the weaker modes. This work identifies the conditions under which magnetosonic modes can be a major fraction of turbulent astrophysical plasmas, including the regime of weak turbulence. Important astrophysical implications for cosmic ray transport and magnetic reconnection are discussed.

中文翻译：

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压缩驱动等离子体湍流中的磁流体动力学模式的性质

我们通过将MHD模拟数据分解为线性MHD模式（即Alfv {'e} n，慢磁声和快磁声模式）来研究磁流体动力学（MHD）本征模式的特性。我们通过混合螺线管驱动和压缩驱动来驱动湍流，同时改变Alfv {'e} n马赫数（${\mathrm{中号}}_{\mathrm{一种}}$），等离子 $\beta$，以及从亚音速到反音速的音速马赫数。我们发现，快速和慢速模式在混合模式中的比例随着压缩力的增加而增加。磁声模式的这一比例也可以成为模式混合物中的主要部分。通过其结构函数来分析模式的各向异性。Alfv {'e} n模各向异性与Goldreich-Sridhar理论是一致的。从低到高，我们发现了从弱Alfv {'e} nic湍流的过渡${\mathrm{中号}}_{\mathrm{一种}}$。慢速模式属性类似于Alfv {'e} n模式。另一方面，在快速模式是模式混合的重要部分的情况下，可以验证快速模式的各向同性性质。快速模式行为不会显示从低到高的任何过渡${\mathrm{中号}}_{\mathrm{一种}}$。我们发现有迹象表明，不同的模式之间存在一些相互作用，主导模式的属性会影响较弱模式的属性。这项工作确定了条件，在这些条件下，磁声模式可以是湍流天体等离子体的主要部分，包括弱湍流状态。讨论了宇宙射线传输和磁重连的重要天体物理意义。