Magnetization dynamics of two interacting spins in an external magnetic field

The longitudinal relaxation time of the magnetization of a system of two exchange coupled spins subjected to a strong magnetic field is calculated exactly by averaging the stochastic Gilbert-Landau-Lifshitz equation for the magnetization, i.e., the Langevin equation of the process, over its realizations so reducing the problem to a system of linear differential-recurrence relations for the statistical moments (averaged spherical harmonics). The system is solved in the frequency domain by matrix continued fractions yielding the complete solution of the two-spin problem in external fields for all values of the damping and barrier height parameters. The magnetization relaxation time extracted from the exact solution is compared with the inverse relaxation rate from Langer's theory of the decay of metastable states, which yields in the high barrier and intermediate-to-high damping limits the asymptotic behaviour of the greatest relaxation time.Comment: 32 pages, 5 figures. The paper has been revised and new results added (e.g., Fig. 5

Signatures of the transition from galactic to extragalactic cosmic rays

We discuss the signatures of the transition from galactic to extragalactic cosmic rays in different scenarios, giving most attention to the dip scenario. The dip is a feature in the diffuse spectrum of ultra-high energy (UHE) protons in the energy range $1\times 10^{18} - 4\times 10^{19}$ eV, which is caused by electron-positron pair production on the cosmic microwave background (CMB) radiation. The dip scenario provides a simple physical description of the transition from galactic to extragalactic cosmic rays. Here we summarize the signatures of the pair production dip model for the transition, most notably the spectrum, the anisotropy and the chemical composition. The main focus of our work is however on the description of the features that arise in the elongation rate and in the distribution of the depths of shower maximum $X_{\rm max}$ in the dip scenario. We find that the curve for $X_{\max}(E)$ shows a sharp increase with energy, which reflects a sharp transition from an iron dominated flux at low energies to a proton dominated flux at $E\sim 10^{18}$ eV. We also discuss in detail the shape of the $X_{\max}$ distributions for cosmic rays of given energy and demonstrate that this represents a powerful tool to discriminate between the dip scenario and other possible models of the transition.Comment: Version accepted for publication in Physical Review

The influence of the geomagnetic field and of the uncertainties in the primary spectrum on the development of the muon flux in the atmosphere

In this paper we study the sensitivity of the flux of atmospheric muons to uncertainties in the primary cosmic ray spectrum and to the treatment of the geomagnetic field in a calculation. We use the air shower simulation program AIRES to make the calculation for two different primary spectra and under several approximations to the propagation of charged particles in the geomagnetic field. The results illustrate the importance of accurate modelling of the geomagnetic field effects. We propose a high and a low fit of the proton and helium fluxes, and calculate the muon fluxes with these different inputs. Comparison with measurements of the muon flux by the CAPRICE experiment shows a slight preference for the higher primary cosmic ray flux parametrization.Comment: 24 pages, 13 figures, submitted to Phys.Rev.

Flux of atmospheric muons: Comparison between AIRES simulations and CAPRICE98 data

We report on a comparison between the flux of muons in the atmosphere measured by the CAPRICE98 experiment and simulations performed with the air shower simulation program AIRES. To reduce systematic uncertainties we have used as input the primary fluxes of protons and helium nuclei also measured by the CAPRICE98 experiment. Heavy nuclei are also taken into account in the primary flux, and their contribution to the muon flux is discussed. The results of the simulations show a very good agreement with the experimental data, at all altitudes and for all muon momenta. With the exception of a few isolated points, the relative differences between measured data and simulations are smaller than 20 %; and in all cases compatible with zero within two standard deviations. The influence of the input cosmic ray flux on the results of the simulations is also discussed. This report includes also an extensive analysis of the characteristics of the simulated fluxes.Comment: Accepted for publication in Physical Review

Fluctuations of Xmax and Primary Particle Mass Composition in the Range of Energy 5 10^{17} - 3 10^{19} ev by Yakutsk Data

The experimental distributions of \Xmax obtained with the Yakutsk EAS array at fixed energies of $5 \times10^{17}$, $1\times10^{18}$ and $5\times10^{18}$ eV are analysed. A recent version of the QGSJET model is used as a tool of our analysis. In the framework of this model, the most adequate mass composition of primary particles satisfying the experimental data on \Xmax is selected.Comment: 19th European Cosmic Ray Symposium, Aug 30 - Sep 3 2004, Florence, Italy. 3 pages, 1 figure. Submitted for publication in International Journal of Modern Physics

Computationally efficient methods for modelling laser wakefield acceleration in the blowout regime

Electron self-injection and acceleration until dephasing in the blowout regime is studied for a set of initial conditions typical of recent experiments with 100 terawatt-class lasers. Two different approaches to computationally efficient, fully explicit, three-dimensional particle-in-cell modelling are examined. First, the Cartesian code VORPAL using a perfect-dispersion electromagnetic solver precisely describes the laser pulse and bubble dynamics, taking advantage of coarser resolution in the propagation direction, with a proportionally larger time step. Using third-order splines for macroparticles helps suppress the sampling noise while keeping the usage of computational resources modest. The second way to reduce the simulation load is using reduced-geometry codes. In our case, the quasi-cylindrical code CALDER-CIRC uses decomposition of fields and currents into a set of poloidal modes, while the macroparticles move in the Cartesian 3D space. Cylindrical symmetry of the interaction allows using just two modes, reducing the computational load to roughly that of a planar Cartesian simulation while preserving the 3D nature of the interaction. This significant economy of resources allows using fine resolution in the direction of propagation and a small time step, making numerical dispersion vanishingly small, together with a large number of particles per cell, enabling good particle statistics. Quantitative agreement of the two simulations indicates that they are free of numerical artefacts. Both approaches thus retrieve physically correct evolution of the plasma bubble, recovering the intrinsic connection of electron self-injection to the nonlinear optical evolution of the driver