Laser wakefield and direct acceleration in the plasma bubble regime

Laser wakefield acceleration (LWFA) and direct laser acceleration (DLA) are two different kinds of laser plasma electron acceleration mechanisms. LWFA relies on the laser-driven plasma wave to accelerate electrons. The interaction of ultra-short ultra-intensive laser pulses with underdense plasma leads the LWFA into a highly nonlinear regime (“plasma bubble regime”) that attracts particular interest nowadays. DLA accelerates electrons by laser electromagnetic wave in the ion channel or the plasma bubble through the Betatron resonance. This dissertation presents a hybrid laser plasma electron acceleration mechanism. We investigate its features through particle-in-cell (PIC) simulations and the single particle model. The hybrid laser plasma electron acceleration is the merging concept between the LWFA and the DLA, so called laser wakefield and direct acceleration (LWDA). The requirements of the initial conditions of the electron to undergo the LWDA are determined. The electron must have a large initial transverse energy. Two electron injection mechanisms that are suitable for the LWDA, density bump injection and ionization induced injection, are studied in detail. The features of electron beam phase space and electron dynamics are explored. Electron beam phase space appears several unique features such as spatially separated two groups, the correlation between the transverse energy and the relativistic factor and the double-peak spectrum. Electrons are synergistically accelerated by the wakefield as well as by the laser electromagnetic field in the laser-driven plasma bubble. LWDA are also investigated in the moderate power regime (10 TW) in regarding the effects of laser color and polarization. It is found that the frequency upshift laser pulse has better performance on avoiding time-jitter of electron energy spectra, electron final energy and electron charge yield. Some basic characters that related to the LWDA such as the effects of the subluminal laser wave, the effects of the longitudinal accelerating field, the electron beam emittance, the electron charge yield and potentially applications as radiation source are discussed.Physic

Scale disparities and magnetohydrodynamics in the Earth’s core

Fluid motions driven by convection in the Earth’s fluid core sustain geomagnetic ­ fields by magnetohydrodynamic dynamo processes. The dynamics of the core is critically influenced by the combined effects of rotation and magnetic ­ fields. This paper attempts to illustrate the scale-related difficulties in modelling a convection-driven geodynamo by studying both linear and nonlinear convection in the presence of imposed toroidal and poloidal ­ fields. We show that there exist three extremely large disparities, as a direct consequence of small viscosity and rapid rotation of the Earth’s fluid core, in the spatial, temporal and amplitude scales of a convection-driven geodynamo. We also show that the structure and strength of convective motions, and, hence, the relevant dynamo action, are extremely sensitive to the intricate dynamical balance between the viscous, Coriolis and Lorentz forces; similarly, the structure and strength of the magnetic field generated by the dynamo process can depend very sensitively on the fluid flow. We suggest, therefore, that the zero Ekman number limit is strongly singular and that a stable convection-driven strong-­field geodynamo satisfying Taylor’s constraint may not exist. Instead, the geodynamo may vacillate between a strong ­field state, as at present, and a weak ­ field state, which is also unstable because it fails to convect sufficient heat

Magnetic helicity and energy spectra of a solar active region

We compute for the first time magnetic helicity and energy spectra of the solar active region NOAA 11158 during 11-15 February 2011 at 20^o southern heliographic latitude using observational photospheric vector magnetograms. We adopt the isotropic representation of the Fourier-transformed two-point correlation tensor of the magnetic field. The sign of magnetic helicity turns out to be predominantly positive at all wavenumbers. This sign is consistent with what is theoretically expected for the southern hemisphere. The magnetic helicity normalized to its theoretical maximum value, here referred to as relative helicity, is around 4% and strongest at intermediate wavenumbers of k ~ 0.4 Mm^{-1}, corresponding to a scale of 2pi/k ~ 16 Mm. The same sign and a similar value are also found for the relative current helicity evaluated in real space based on the vertical components of magnetic field and current density. The modulus of the magnetic helicity spectrum shows a k^{-11/3} power law at large wavenumbers, which implies a k^{-5/3} spectrum for the modulus of the current helicity. A k^{-5/3} spectrum is also obtained for the magnetic energy. The energy spectra evaluated separately from the horizontal and vertical fields agree for wavenumbers below 3 Mm^{-1}, corresponding to scales above 2 Mm. This gives some justification to our assumption of isotropy and places limits resulting from possible instrumental artefacts at small scales.Comment: 6 pages, 4 figures, ApJL (accepted

Optimal funding and investment strategies in defined contribution pension plans under Epstein-Zin utility

A defined contribution pension plan allows consumption to be redistributed from the plan member’s working life to retirement in a manner that is consistent with the member’s personal preferences. The plan’s optimal funding and investment strategies therefore depend on the desired pattern of consumption over the lifetime of the member. We investigate these strategies under the assumption that the member has an Epstein-Zin utility function, which allows a separation between risk aversion and the elasticity of intertemporal substitution, and we also take into account the member’s human capital. We show that a stochastic lifestyling approach, with an initial high weight in equity-type investments and a gradual switch into bond-type investments as the retirement date approaches is an optimal investment strategy. In addition, the optimal contribution rate each year is not constant over the life of the plan but reflects trade-offs between the desire for current consumption, bequest and retirement savings motives at different stages in the life cycle, changes in human capital over the life cycle, and attitude to risk

Neutrinoproduction of Photons and Pions From Nucleons in a Chiral Effective Field Theory for Nuclei

Neutrino-induced productions (neutrinoproduction) of photons and pions from nucleons and nuclei are important for the interpretation of neutrino-oscillation experiments, as they are potential backgrounds in the MiniBooNE experiment [A. A. Aquilar-Arevalo et al. (MiniBooNE Collaboration), Phys. Rev. Lett. {\bf 100}, 032301 (2008)]. These processes are studied at intermediate energies, where the \Delta (1232) resonance becomes important. The Lorentz-covariant effective field theory, which is the framework used in this series of study, contains nucleons, pions, \Delta s, isoscalar scalar (\sigma) and vector (\omega) fields, and isovector vector (\rho) fields. The lagrangian exhibits a nonlinear realization of (approximate) $SU(2)_L \otimes SU(2)_R$ chiral symmetry and incorporates vector meson dominance. In this paper, we focus on setting up the framework. Power counting for vertices and Feynman diagrams is explained. Because of the built-in symmetries, the vector current is automatically conserved (CVC), and the axial-vector current is partially conserved (PCAC). To calibrate the axial-vector transition current (N $\leftrightarrow$ \Delta), pion production from the nucleon is used as a benchmark and compared to bubble-chamber data from Argonne and Brookhaven National Laboratories. At low energies, the convergence of our power-counting scheme is investigated, and next-to-leading-order tree-level corrections are found to be small.Comment: 21 pages, 7 figures, typos corrected. arXiv admin note: substantial text overlap with arXiv:1011.591

Evolution of Magnetic Helicity and Energy Spectra of Solar Active Regions

We adopt an isotropic representation of the Fourier-transformed two-point correlation tensor of the magnetic field to estimate the magnetic energy and helicity spectra as well as current helicity spectra of two individual active regions (NOAA 11158 and NOAA 11515) and the change of the spectral indices during their development as well as during the solar cycle. The departure of the spectral indices of magnetic energy and current helicity from 5/3 are analyzed, and it is found that it is lower than the spectral index of the magnetic energy spectrum. Furthermore, the fractional magnetic helicity tends to increase when the scale of the energy-carrying magnetic structures increases. The magnetic helicity of NOAA 11515 violates the expected hemispheric sign rule, which is interpreted as an effect of enhanced field strengths at scales larger than 30-60Mm with opposite signs of helicity. This is consistent with the general cycle dependence, which shows that around the solar maximum the magnetic energy and helicity spectra are steeper, emphasizing the large-scale field.Comment: 10 pages, 15 Figures, ApJ in pres