On Rapidly Rotating Magnetic Core-Collapse Supernovae

We have analyzed the magnetic effects that may occur in rapidly rotating core collapse supernovae. We consider effects from both magnetic turbulence and the formation of magnetic bubbles. For magnetic turbulence we have made a perturbative analysis for our spherically symmetric core-collapse supernova model that incorporates the build up of magnetic field energy in the matter accreting onto the proto-neutron star shortly after collapse and bounce. This significantly modifies the pressure profile and increases the heating of the material above the proto-neutron star resulting in an explosion even in rotating stars that would not explode otherwise. Regarding magnetic bubbles we show that a model with a modest initial uniform magnetic field and uniform angular velocity of ~0.1 rad/s can form magnetic bubbles due to the very non homologous nature of the collapse. It is estimated that the buoyancy of the bubbles causes matter in the proto-neutron star to rise, carrying neutrino-rich material to the neutron-star surface. This increases the neutrino luminosity sufficiently at early times to achieve a successful neutrino-driven explosion. Both magnetic mechanisms thus provide new means for initiating a Type II core-collapse supernova.Comment: 12 pages, 9 figure

Future Detection of Supernova Neutrino Burst and Explosion Mechanism

Future detection of a supernova neutrino burst by large underground detectors would give important information for the explosion mechanism of collapse-driven supernovae. We studied the statistical analysis for the future detection of a nearby supernova by using a numerical supernova model and realistic Monte-Carlo simulations of detection by the Super-Kamiokande detector. We mainly discuss the detectability of the signatures of the delayed explosion mechanism in the time evolution of the \anue luminosity and spectrum. For a supernova at 10 kpc away from the Earth, we find that not only the signature is clearly discernible, but also the deviation of energy spectrum from the Fermi-Dirac (FD) distribution can be observed. The deviation from the FD distribution would, if observed, provide a test for the standard picture of neutrino emission from collapse-driven supernovae. For the $D$ = 50 kpc case, the signature of the delayed explosion is still observable, but statistical fluctuation is too large to detect the deviation from the FD distribution. We also propose a method for statistical reconstruction of the time evolution of \anue luminosity and spectrum from data, by which we can get a smoother time evolution and smaller statistical errors than a simple, time-binning analysis. This method is useful especially when the available number of events is relatively small, e.g., a supernova in the LMC or SMC. Neutronization burst of $\nu_e$'s produces about 5 scattering events when $D$ = 10 kpc and this signal is difficult to distinguish from \anue p events.Comment: 28 pages including all figures. Accepted by Astrophys.

MHD equilibrium properties of tokamak fusion reactor designs

The equilibrium properties of several Tokamak Reactor Designs are analyzed and compared for varying pressure and current profiles using the Princeton Equilibrium Code. It is found that the UWMAK configuration has a broader range of equilibria than the Princeton Reference Design configuration, but that the safety factor on axis is less than unity for peaked current distributions. The Argonne Experimental Power Reactor has a satisfactory range of equilibria, but a means of limiting or diverting the plasma has not yet been proposed, and this may substantially change the results obtained. (auth

Numerical determination of axisymmetric toroidal magnetohydrodynamic equilibria

Numerical schemes for the determination of stationary axisymmetric toroidal equilibria appropriate for modeling real experimental devices are given. Iterative schemes are used to solve the elliptic nonlinear partial differential equation for the poloidal flux function psi. The principal emphasis is on solving the free boundary (plasma-vacuum interface) equilibrium problem where external current-carrying toroidal coils support the plasma column, but fixed boundary (e.g., conducting shell) cases are also included. The toroidal current distribution is given by specifying the pressure and either the poloidal current or the safety factor profiles as functions of psi. Examples of the application of the codes to tokamak design at PPPL are given

MHD stability of vertically asymmetric tokamak equilibria

The ideal MHD stability properties of a special class of vertically asymmetric tokamak equilibria are examined. The calculations confirm that no major new physical effects are introduced and the modifications can be understood by conventional arguments. The results indicate that significant departures from up-down symmetry can be tolerated before the reduction in ..beta.. becomes important for reactor operation

Ideal MHD beta-limits of poloidally asymmetric equilibria

The ideal MHD stability of poloidally asymmetric equilibria, which are typical of a tokamak reactor design with a single-null poloidal divertor is examined. As with symmetric equilibria, stability to non-axisymmetric modes improves with increasing triangularity and ellipticity, and with lower edge safety factor. Pressure profiles optimized with respect to ballooning stability are obtained for an asymmetric shape, resulting in ..beta../sub critical/ approx. = 5.7%. The corresponding value for an equivalent symmetric shape is ..beta../sub critical/ approx. = 6.5%