Resistive Scaling in the Magnetic Helicity-driven Inverse Cascade

Abstract The inverse cascade in MHD turbulence plays a crucial role in various astrophysical processes such as galaxy cluster formation, solar and stellar dynamo mechanisms, and the evolution of primordial magnetic fields in the early Universe. A standard numerical approach involves injecting magnetic helicity at intermediate length scales to generate a secondary, time-dependent spectral peak that gradually propagates toward larger scales. Previous simulations have already suggested a resistive dependence of inverse transfer rates and demonstrated the significant influence of magnetic helicity flux density ϵ H on this process. On dimensional grounds, we have for the spectral envelope E M ( k , t ) ≤ C H ϵ H 2 / 3 k − 1 , where C H represents a potentially universal dimensionless coefficient analogous to the Kolmogorov constant. We present a summary of the 25 distinct simulations conducted with the Pencil Code , systematically varying the forcing wavenumber k f , magnetic Prandtl number Pr M , grid resolution N 3 , and Lundquist number Lu. We obtained C H and corresponding error bars by calculating the compensated spectrum and investigated its dependence with Lu and k f . For the C H –Lu relationship, we observe strong correlations with a power-law exponent around unity. In contrast, we find no significant correlation between C H and k f . We also present evidence for a nonresistive scaling of the form E M ( k , t ) ≤ C 2 / 3 v A 2 k − 1 , where v A is the rms Alfvén speed and C 2/3 ≈ 0.4 for all of our runs.