A fast high-order method to calculate wakefield forces in an electron beam

In this paper we report on a high-order fast method to numerically calculate wakefield forces in an electron beam given a wake function model. This method is based on a Newton-Cotes quadrature rule for integral approximation and an FFT method for discrete summation that results in an $O(Nlog(N))$ computational cost, where $N$ is the number of grid points. Using the Simpson quadrature rule with an accuracy of $O(h^4)$, where $h$ is the grid size, we present numerical calculation of the wakefields from a resonator wake function model and from a one-dimensional coherent synchrotron radiation (CSR) wake model. Besides the fast speed and high numerical accuracy, the calculation using the direct line density instead of the first derivative of the line density avoids numerical filtering of the electron density function for computing the CSR wakefield force

Large-Scale Simulation of Beam Dynamics in High Intensity Ion Linacs Using Parallel Supercomputers

In this paper we present results of using parallel supercomputers to simulate beam dynamics in next-generation high intensity ion linacs. Our approach uses a three-dimensional space charge calculation with six types of boundary conditions. The simulations use a hybrid approach involving transfer maps to treat externally applied fields (including rf cavities) and parallel particle-in-cell techniques to treat the space-charge fields. The large-scale simulation results presented here represent a three order of magnitude improvement in simulation capability, in terms of problem size and speed of execution, compared with typical two-dimensional serial simulations. Specific examples will be presented, including simulation of the spallation neutron source (SNS) linac and the Low Energy Demonstrator Accelerator (LEDA) beam halo experiment

Vortex State in Na_xCoO_2.yH_2O: p_x\pm ip_y-wave versus d_{x^2-y^2}\pm id_{xy}-wave Pairing

Based on an effective Hamiltonian specified in the triangular lattice with possible $p_x\pm ip_y$- or $d_{x^2-y^2}\pm id_{xy}$-wave pairing, which has close relevance to the newly discovered Na$_{0.35}$CoO$_2$$\cdot y$H$_2$O, the electronic structure of the vortex state is studied by solving the Bogoliubov-de Gennes equations. It is found that $p_x\pm ip_y$-wave is favored for the electron doping as the hopping integral $t<0$. The lowest-lying vortex bound states are found to have respectively zero and positive energies for $p_x\pm ip_y$- and $d_{x^2-y^2}\pm id_{xy}$-wave superconductors, whose vortex structures exhibit the intriguing six-fold symmetry. In the presence of strong on-site repulsion, the antiferromagnetic and ferromagnetic orders are induced around the vortex cores for the former and the latter, respectively, both of which cause the splitting of the LDOS peaks due to the lifting of spin degeneracy. STM and NMR measurements are able to probe the new features of vortex states uncovered in this work.Comment: 4 pages, 4 figures, The slightly shorter version was submitted to PR

Nuclear Spin Relaxation Rate of Disordered px+ipyp_x+ip_y-wave Superconductors

Based on an effective Hamiltonian with the binary alloy disorder model defined in the triangular lattice, the impurity scattering effects on the density of states and especially on the spin-lattice relaxation rate $1/T_1$ of $p_x+ip_y$-wave superconductors are studied by solving numerically the Bogoliubov-de Gennes equations. In the clean limit, the coherence peak of $1/T_1$ is observed as expected. More intriguingly, for strong scattering potential, the temperature dependence of $1/T_1$ exhibits the two different power law behaviors near $T_{\text{c}}$ and at low temperatures, respectively, which is in good agreement with the nuclear quadrupolar resonance measurement.Comment: 4 pages, 3 figure

Crossing of Phantom Divide in F(R)F(R) Gravity

An explicit model of $F(R)$ gravity with realizing a crossing of the phantom divide is reconstructed. In particular, it is shown that the Big Rip singularity may appear in the reconstructed model of $F(R)$ gravity. Such a Big Rip singularity could be avoided by adding $R^2$ term or non-singular viable $F(R)$ theory to the model because phantom behavior becomes transient.Comment: 9 pages, 1 figure, to be published in the proceedings of the International Workshop on Dark Matter, Dark Energy and Matter-antimatter Asymmetry in Special Issue of Modern Physics Letters A, Department of Physics, National Tsing Hua University, Hsinchu, Taiwan, 20th - 21st November, 200