Can a simplified theory capture the complex dynamics of plasma turbulence? This paper presents a weak turbulence formalism for incompressible magnetohydrodynamics (MHD), offering new insights into energy spectra. Three-wave interactions lead to kinetic equations for the spectral densities of energy and helicity, conserving energy in wavevector planes normal to the applied magnetic field. Through numerical and analytical methods, the study identifies energy spectra with a specific relationship between spectral indices. In the two-dimensional case, the constants of the spectra depend on the correlation between velocity and the magnetic field. The research provides an exact computation of these constants. This theoretical framework is compared with numerical simulations and models, offering a valuable tool for understanding MHD turbulence. The findings contribute to a deeper comprehension of energy transfer and spectral properties in plasma physics, with implications for various astrophysical and laboratory plasmas.
This theoretical work aligns with the Journal of Plasma Physics's focus on original research in plasma physics. By deriving a weak turbulence formalism for incompressible magnetohydrodynamics, the paper contributes to the journal's goal of advancing the understanding of plasma behavior. The findings on energy spectra and correlations between velocity and magnetic fields are relevant to the journal's readership.