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Two recent papers, P. H. Yoon and G. Choe, Phys. Plasmas 28, 082306 (2021) and Yoon et al., Phys. Plasmas 29, 112303 (2022), utilized in the derivation of the kinetic equation for the intensity of turbulent fluctuations the assumption that the wave spectra are isotropic, that is, the ensemble-averaged magnetic field tensorial fluctuation intensity is given by the isotropic diagonal form, ⟨ δ B i δ B j ⟩ k = ⟨ δ B 2 ⟩ k δ i j . However, it is more appropriate to describe the incompressible magnetohydrodynamic turbulence involving shear Alfvénic waves by modeling the turbulence spectrum as being anisotropic. That is, the tensorial fluctuation intensity should be different in diagonal elements across and along the direction of the wave vector, ⟨ δ B i δ B j ⟩ k = 1 2 ⟨ δ B ⊥ 2 ⟩ k (δ i j − k i k j / k 2) + ⟨ δ B ∥ 2 ⟩ k (k i k j / k 2). In the present paper, we thus reformulate the weak magnetohydrodynamic turbulence theory under the assumption of anisotropy and work out the form of nonlinear wave kinetic equation. [ABSTRACT FROM AUTHOR]

In a recent paper [P. H. Yoon and G. Choe, Phys. Plasmas 28, 082306 (2021)], the weak turbulence theory for incompressible magnetohydrodynamics is formulated by employing the method customarily applied in the context of kinetic weak plasma turbulence theory. Such an approach simplified certain mathematical procedures including achieving the closure relationship. The formulation in the above-cited paper starts from the equations of incompressible magnetohydrodynamic (MHD) theory expressed via Elsasser variables. The derivation of nonlinear wave kinetic equation therein is obtained via a truncated solution at the second-order of iteration following the standard practice. In the present paper, the weak MHD turbulence theory is alternatively formulated by employing the pristine form of incompressible MHD equation rather than that expressed in terms of Elsasser fields. The perturbative expansion of the nonlinear momentum equation is carried out up to the third-order iteration rather than imposing the truncation at the second order. It is found that while the resulting wave kinetic equation is identical to that obtained in the previous paper cited above, the third-order nonlinear correction plays an essential role for properly calculating derived quantities such as the total and residual energies. [ABSTRACT FROM AUTHOR]

Electrostatic weak turbulence theory for plasmas immersed in an ambient magnetic field is developed by employing a hybrid two-fluid and kinetic theories. The nonlinear susceptibility response function is calculated with the use of warm two-fluid equations. The linear dispersion relations for longitudinal electrostatic waves in magnetized plasmas are also obtained within the warm two-fluid theoretical scheme. However, dissipations that arise from linear and nonlinear wave–particle interactions cannot be discussed with the macroscopic two-fluid theory. To compute such collisionless dissipation effects, linearized kinetic theory is utilized. Moreover, a particle kinetic equation, which is necessary for a self-consistent description of the problem, is derived from the quasilinear kinetic theory. The final set of equations directly generalizes the electrostatic weak turbulence theory in unmagnetized plasmas, which could be applied for a variety of problems including the electron beam–plasma interactions in magnetized plasma environments. [ABSTRACT FROM AUTHOR]