Incorporating Ambipolar and Ohmic Diffusion in the AMR MHD code RAMSES

We have implemented non-ideal Magneto-Hydrodynamics (MHD) effects in the Adaptive Mesh Refinement (AMR) code RAMSES, namely ambipolar diffusion and Ohmic dissipation, as additional source terms in the ideal MHD equations. We describe in details how we have discretized these terms using the adaptive Cartesian mesh, and how the time step is diminished with respect to the ideal case, in order to perform a stable time integration. We have performed a large suite of test runs, featuring the Barenblatt diffusion test, the Ohmic diffusion test, the C-shock test and the Alfven wave test. For the latter, we have performed a careful truncation error analysis to estimate the magnitude of the numerical diffusion induced by our Godunov scheme, allowing us to estimate the spatial resolution that is required to address non-ideal MHD effects reliably. We show that our scheme is second-order accurate, and is therefore ideally suited to study non-ideal MHD effects in the context of star formation and molecular cloud dynamics

Effect of thermal fluctuations on spin degrees of freedom in spinor Bose-Einstein condensates

We consider the effect of thermal fluctuations on rotating spinor F=1 condensates in axially-symmetric vortex phases, when all the three hyperfine states are populated. We show that the relative phase among different components of the order parameter can fluctuate strongly due to the weakness of the interaction in the spin channel. These fluctuations can be significant even at low temperatures. Fluctuations of relative phase lead to significant fluctuations of the local transverse magnetization of the condensate. We demonstrate that these fluctuations are much more pronounced for the antiferromagnetic state than for the ferromagnetic one.Comment: 5 pages, 2 figures; final version, accepted for publication in Phys. Rev.

Bernoulli potential in type-I and weak type-II superconductors: III. Electrostatic potential above the vortex lattice

The electrostatic potential above the Abrikosov vortex lattice, discussed earlier by Blatter {\em et al.} {[}PRL {\bf 77}, 566 (1996){]}, is evaluated within the Ginzburg-Landau theory. Unlike previous studies we include the surface dipole. Close to the critical temperature, the surface dipole reduces the electrostatic potential to values below a sensitivity of recent sensors. At low temperatures the surface dipole is less effective and the electrostatic potential remains observable as predicted earlier.Comment: 8 pages 5 figure

Vortex structures and zero energy states in the BCS-to-BEC evolution of p-wave resonant Fermi gases

Multiply quantized vortices in the BCS-to-BEC evolution of p-wave resonant Fermi gases are investigated theoretically. The vortex structure and the low-energy quasiparticle states are discussed, based on the self-consistent calculations of the Bogoliubov-de Gennes and gap equations. We reveal the direct relation between the macroscopic structure of vortices, such as particle densities, and the low-lying quasiparticle state. In addition, the net angular momentum for multiply quantized vortices with a vorticity $\kappa$ is found to be expressed by a simple equation, which reflects the chirality of the Cooper pairing. Hence, the observation of the particle density depletion and the measurement of the angular momentum will provide the information on the core-bound state and $p$-wave superfluidity. Moreover, the details on the zero energy Majorana state are discussed in the vicinity of the BCS-to-BEC evolution. It is demonstrated numerically that the zero energy Majorana state appears in the weak coupling BCS limit only when the vortex winding number is odd. There exist the $\kappa$ branches of the core bound states for a vortex state with vorticity $\kappa$, whereas only one of them can be the zero energy. This zero energy state vanishes at the BCS-BEC topological phase transition, because of interference between the core-bound and edge-bound states.Comment: 15 pages, 9 figures, published versio

Coreless and singular vortex lattices in rotating spinor Bose-Einstein condensates

We theoretically investigate vortex-lattice phases of rotating spinor Bose-Einstein condensates (BEC) with the ferromagnetic spin-interaction by numerically solving the Gross-Pitaevskii equation. The spinor BEC under slow rotation can sustain a rich variety of exotic vortices due to the multi-component order parameters, such as the Mermin-Ho and Anderson-Toulouse coreless vortices (the 2-dimensional skyrmion and meron) and the non-axisymmetric vortices with the sifting vortex cores. Here, we present the spin texture of various vortex-lattice states at higher rotation rates and in the presence of the external magnetic field. In addition, the vortex phase diagram is constructed in the plane by the total magnetization $M$ and the external rotation frequency $\Omega$ by comparing the free energies of possible vortices. It is shown that the vortex phase diagram in a $M$-$\Omega$ plane may be divided into two categories; (i) the coreless vortex lattice formed by the several types of Mermin-Ho vortices and (ii) the vortex lattice filling in the cores with the pure polar (antiferromagnetic) state. In particular, it is found that the type-(ii) state forms the composite lattices of coreless and polar-core vortices. The difference between the type-(i) and type-(ii) results from the existence of the singularity of the spin textures, which may be experimentally confirmed by the spin imaging within polarized light recently proposed by Carusotto and Mueller. We also discussed on the stability of triangular and square lattice states for rapidly rotating condensates.Comment: to be published in Phys. Rev.

Comparison of Zgoubi and S-Code regarding the FFAG muon acceleration

The high flux accelerator based neutrino source is foreseen as one the next generation facilities of particle physics. Called Neutrino Factory (NuFact), it will be based on a muon storage ring where muons will decay, creating high flux neutrino beams. Muons are supposed to be accelerated from 5 to 20 GeV before being injected into the storage ring. In that purpose, Fixed Field Alternating Gradient accelerators (FFAG) are one of the possibilities. Cell designs have been done and tracking studies are on their way using codes such as MAD, S-Code or Zgoubi. In order to cross-check results so obtained, we have performed comparisons between S-Code and Zgoubi at Rutherford Appleton Laboratory. The present report will explain the different simulations done and the results

Modeling the magnetic field in the protostellar source NGC 1333 IRAS 4A

Magnetic fields are believed to play a crucial role in the process of star formation. We compare high-angular resolution observations of the submillimeter polarized emission of NGC 1333 IRAS 4A, tracing the magnetic field around a low-mass protostar, with models of the collapse of magnetized molecular cloud cores. Assuming a uniform dust alignment efficiency, we computed the Stokes parameters and synthetic polarization maps from the model density and magnetic field distribution by integrations along the line-of-sight and convolution with the interferometric response. The synthetic maps are in good agreement with the data. The best-fitting models were obtained for a protostellar mass of 0.8 solar masses, of age 9e4 yr, formed in a cloud with an initial mass-to-flux ratio ~2 times the critical value. The magnetic field morphology in NGC 1333 IRAS 4A is consistent with the standard theoretical scenario for the formation of solar-type stars, where well-ordered, large-scale, rather than turbulent, magnetic fields control the evolution and collapse of the molecular cloud cores from which stars form.Comment: 4 pages, 5 figures. Accepted by Astronomy and Astrophysic