Limitations of Current Solar Magnetic Field Modeling Techniques Across Spatial and Temporal Scales

Abstract

Magneticfieldsgovernmanyofthephysicalprocessesobservedinthesolaratmosphere, includingenergytransport,wavepropagation,andtheformationofstructuredfeatures suchasfluxtubesandactiveregions. Accuratemodellingofthesemagneticconfigurations is essential for understanding their behaviour and for validating numerical magnetohy- drodynamic(MHD)simulations. Thisthesisdevelopsaunifiedanalyticalandnumericalframeworkforstudyingsolar magneticfieldsandlinearMHDwaves. Magnetohydrostatic(MHS)equilibriaarederived usingflux-functionandGrad–ShafranovformulationsinbothcylindricalandCartesian geometries. Theseequilibrianaturallysatisfythesolenoidalconditionandprovideclean, controlledmagneticstructuressuitableforbenchmarking. Numericalevaluationconfirms that divergence is preserved to machine precision, and visualisations in two and three dimensionsreproducetheexpectedexpansionandtopologyofsolar-likemagneticfields. LinearMHDwavesareanalysedwithintheseequilibriabycomputingthephasespeeds oftheAlfv´en,fast,slow,andacousticmodes. Theresultsagreecloselywiththeoretical dispersion relations, demonstrating the suitability of the equilibria as backgrounds for wavepropagationstudies. Takentogether, theanalyticalconstructionsandwavediag- nostics establish a consistent and flexible framework for understanding solar magnetic structuresandsupportongoingdevelopmentandvalidationofnumericalMHDmodels.