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Effect of Magnetised Discontinuity on Diffusive Shock Acceleration

We investigate the impact of magnetic fields and diffusion mechanisms on the energy spectra of particles accelerated via diffusive shock acceleration. We analyse magnetised shock jump conditions and demonstrate how magnetisation and angular dependence modify upstream and downstream velocities, which enter the transport equation within a Monte Carlo simulation framework. We consider constant, momentum-dependent, and pitch-angle-dependent diffusion coefficients to assess their influence on particle acceleration. Our results show that magnetic fields enhance particle confinement and facilitate more efficient energy gain. In the absence of magnetisation, particle spectra tend to be steeper due to rapid escape and weaker scattering effects, whereas magnetised shocks systematically produce flatter spectra across all diffusion models. Among them, pitch-angle-dependent diffusion leads to the strongest spectral flattening, underscoring its role in sustaining extended acceleration. It is also seen that an increased upstream pressure, associated with enhanced magnetic turbulence, broadens the spectral range by improving particle scattering efficiency and enabling multiple shock crossings. As the shock inclination angle increases, the velocity contrast between upstream and downstream regions diminishes, modulating the spatial extent of the acceleration zone. Notably, pitch-angle-dependent diffusion remains robust under varying shock conditions, ensuring sustained acceleration.