We study the effects of the magnetic field on the dynamics of non-rotating stellar cores by performing two-dimensional (2D), magnetohydrodynamics (MHD) simulations. To this end, we have updated our neutrino-radiation-hydrodynamics supernova code to include MHD employing a divergence cleaning method with both careful treatments of finite volume and area reconstructions. By changing the initial strength of the magnetic field, the evolution of $15.0$, $18.4$ and $27.0$ $M_odot$ presupernova progenitors is investigated. An intriguing finding in our study is that the neutrino-driven explosion occurs regardless of the strength of the initial magnetic field. For the 2D models presented in this work, the neutrino heating is the main driver for the explosion, whereas the magnetic field secondary contributes to the pre-explosion dynamics. Our results show that the strong magnetic field weakens the growth of the neutrino-driven turbulence in the small scale compared to the weak magnetic field. This results in the slower increase of the turbulent kinetic energy in the postshock region, leading to the slightly delayed onset of the shock revival for models with the stronger initial magnetic field.
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