Reality of inverse cascading in neutron star crusts

The braking torque that dictates the timing properties of magnetars is closely tied to the large-scale dipolar magnetic field on their surface. The formation of this field has been a topic of ongoing debate. One proposed mechanism, based on macroscopic principles, involves an inverse cascade within the neutron star's crust. However, this phenomenon has not been observed in realistic simulations. In this study, we provide compelling evidence supporting the feasibility of the inverse cascading process in the presence of an initial helical magnetic field within realistic neutron star crusts and discuss its contribution to the amplification of the large-scale magnetic field. Our findings, derived from a systematic investigation that considers various coordinate systems, peak wavenumber positions, crustal thicknesses, magnetic boundary conditions, and magnetic Lundquist numbers, reveal that the specific geometry of the crustal domain-with its extreme aspect ratio-requires an initial peak wavenumber from small-scale structures for the inverse cascade to occur. However, this same aspect ratio confines the cascade to structures on the scale of the crust, making the formation of a large-scale dipolar surface field unlikely. Despite these limitations, the inverse cascade remains a significant factor in the magnetic field evolution within the crust and may help explain highly magnetized objects with weak surface dipolar fields, such as low-field magnetars and central compact objects.