Core collapse supernovae: magnetorotational explosion
  Core-collapse supernovae are connected with formation of neutron stars. Part of the gravitation energy is transformed into the energy of the explosion, observed in SN II, SN Ib,c type supernovae. The mechanism of transformation is not simple, because the overwhelming majority of the energy is going into weakly interacting neutrino. The attempts to use this energy for the explosion were not successful during about 40 years of investigation. We consider the explosion mechanism in which the source of energy is the rotation, and magnetic field serves for the transformation of the rotation energy into the energy of explosion. 2-D MHD simulations of this mechanism were performed. After the collapse the core consists of a rapidly rotating proto-neutron star with a differentially rotating envelope. The toroidal part of the magnetic energy generated by the differential rotation grows as quadratic function with time at the initial stage of the evolution of the magnetic field. The linear growth of the toroidal magnetic field is terminated by the development of magnetohydrodynamic instability, when the twisted toroidal component strongly exceeds the poloidal field, leading to a drastic acceleration in the growth of magnetic energy. At the moment when the magnetic pressure becomes comparable to the gas pressure at the periphery of the proto-neutron star the MHD compression wave appears and goes through the envelope of the collapsed core. It transforms into the fast MHD shock and produces a supernova explosion. Our simulations give the energy of the explosion $0.6\cdot 10^{51}$ ergs. The amount of the mass ejected by the explosion is $\sim 0.14M_\odot$. The implicit numerical method, based on the Lagrangian triangular grid of variable structure, was used for the simulations. 
G.S.Bisnovatyi-Kogan, S.G.Moiseenko and N.V.Ardeljan