Rotating matter in general relativity -- stationary state I

Stationary rotating matter configurations in general relativity are considered. A formalism for general stationary space times is developed. Axisymmetric systems are discussed by the use of a nonholonomic and nonrigid frame in the three-space of the time-like Killing trajectories. Two symmetric and trace-free tensors are constructed. They characterize a class of matter states in which both the interior Schwarzschild and the Kerr solution are contained. Consistency relations for this class of perfect fluids are derived. Incompressible fluids characterized by these tensors are investigated, and one differentially rotating solution is found.Comment: 25 pages, REVTe

Particle-in-Cell simulations of electron spin effects in plasmas

We have here developed a particle-in-cell code accounting for the magnetic dipole force and for the magnetization currents associated with the electron spin. The electrons is divided into spin-up and spin-down populations relative to the magnetic field, where the magnetic dipole force acts in opposite directions for the two species. To validate the code, we have studied the wakefield generation by an electromagnetic pulse propagating parallel to an external magnetic field. The properties of the generated wakefield is shown to be in good quantitative agreement with previous theoretical results. Generalizations of the code to account for more quantum effects is discussedComment: 5 pages, 6 figure

Circularly polarized modes in magnetized spin plasmas

The influence of the intrinsic spin of electrons on the propagation of circularly polarized waves in a magnetized plasma is considered. New eigenmodes are identified, one of which propagates below the electron cyclotron frequency, one above the spin-precession frequency, and another close to the spin-precession frequency.\ The latter corresponds to the spin modes in ferromagnets under certain conditions. In the nonrelativistic motion of electrons, the spin effects become noticeable even when the external magnetic field $B_{0}$ is below the quantum critical\ magnetic field strength, i.e., $B_{0}<$ $B_{Q} =4.4138\times10^{9}\, \mathrm{T}$ and the electron density satisfies $n_{0} \gg n_{c}\simeq10^{32}$m$^{-3}$. The importance of electron spin (paramagnetic) resonance (ESR) for plasma diagnostics is discussed.Comment: 10 page

Focussing effects in laser-electron Thomson scattering

We study the effects of laser pulse focussing on the spectral properties of Thomson scattered radiation. Modelling the laser as a paraxial beam we find that, in all but the most extreme cases of focussing, the temporal envelope has a much bigger effect on the spectrum than the focussing itself. For the case of ultra-short pulses, where the paraxial model is no longer valid, we adopt a sub-cycle vector beam description of the field. It is found that the emission harmonics are blue shifted and broaden out in frequency space as the pulse becomes shorter. Additionally the carrier envelope phase becomes important, resulting in an angular asymmetry in the spectrum. We then use the same model to study the effects of focussing beyond the limit where the paraxial expansion is valid. It is found that fields focussed to sub-wavelength spot sizes produce spectra that are qualitatively similar to those from sub-cycle pulses due to the shortening of the pulse with focussing. Finally, we study high-intensity fields and find that, in general, the focussing makes negligible difference to the spectra in the regime of radiation reaction.Comment: 14 pages, 17 figure

Graviton mediated photon-photon scattering in general relativity

In this paper we consider photon-photon scattering due to self-induced gravitational perturbations on a Minkowski background. We focus on four-wave interaction between plane waves with weakly space and time dependent amplitudes, since interaction involving a fewer number of waves is excluded by energy-momentum conservation. The Einstein-Maxwell system is solved perturbatively to third order in the field amplitudes and the coupling coefficients are found for arbitrary polarizations in the center of mass system. Comparisons with calculations based on quantum field theoretical methods are made, and the small discrepances are explained.Comment: 5 pages, 3 figure

Prospects and limitations of wakefield acceleration in solids

Advances in the generation of relativistic intensity pulses with wavelengths in the X-ray regime, through high harmonic generation from near-critical plasmas, opens up the possibility of X-ray driven wakefield acceleration. The similarity scaling laws for laser plasma interaction suggest that X-rays can drive wakefields in solid materials providing TeV/cm gradients, resulting in electron and photon beams of extremely short duration. However, the wavelength reduction enhances the quantum parameter $\chi$, hence opening the question of the role of non-scalable physics, e.g., the effects of radiation reaction. Using three dimensional Particle-In-Cell simulations incorporating QED effects, we show that for the wavelength $\lambda=5\,$nm and relativistic amplitudes $a_0=10$-100, similarity scaling holds to a high degree, combined with $\chi\sim 1$ operation already at moderate $a_0\sim 50$, leading to photon emissions with energies comparable to the electron energies. Contrasting to the generation of photons with high energies, the reduced frequency of photon emission at X-ray wavelengths (compared to at optical wavelengths) leads to a reduction of the amount of energy that is removed from the electron population through radiation reaction. Furthermore, as the emission frequency approaches the laser frequency, the importance of radiation reaction trapping as a depletion mechanism is reduced, compared to at optical wavelengths for $a_0$ leading to similar $\chi$.Comment: 9 pages, 7 figure

Turbulence in Binary Bose-Einstein Condensates Generated by Highly Non-Linear Rayleigh-Taylor and Kelvin-Helmholtz Instabilities

Quantum turbulence (QT) generated by the Rayleigh-Taylor instability in binary immiscible ultracold 87Rb atoms at zero temperature is studied theoretically. We show that the quantum vortex tangle is qualitatively different from previously considered superfluids, which reveals deep relations between QT and classical turbulence. The present QT may be generated at arbitrarily small Mach numbers, which is a unique property not found in previously studied superfluids. By numerical solution of the coupled Gross-Pitaevskii equations we find that the Kolmogorov scaling law holds for the incompressible kinetic energy. We demonstrate that the phenomenon may be observed in the laboratory.Comment: Revised version. 7 pages, 8 figure

Generation of wakefields by whistlers in spin quantum magnetoplasmas

The excitation of electrostatic wakefields in a magnetized spin quantum plasma by the classical as well as the spin-induced ponderomotive force (CPF and SPF, respectively) due to whistler waves is reported. The nonlinear dynamics of the whistlers and the wakefields is shown to be governed by a coupled set of nonlinear Schr\"{o}dinger (NLS) and driven Boussinesq-like equations. It is found that the quantum force associated with the Bohm potential introduces two characteristic length scales, which lead to the excitation of multiple wakefields in a strongly magnetized dense plasma (with a typical magnetic field strength $B_{0}\gtrsim10^{9}$ T and particle density $n_{0}\gtrsim10^{36}$ m$^{-3}$), where the SPF strongly dominates over the CPF. In other regimes, namely $B_{0}\lesssim10^{8}$ T and $\ n_{0}\lesssim10^{35}$ m$^{-3}$, where the SPF is comparable to the CPF, a plasma wakefield can also be excited self-consistently with one characteristic length scale. Numerical results reveal that the wakefield amplitude is enhanced by the quantum tunneling effect, however it is lowered by the external magnetic field. Under appropriate conditions, the wakefields can maintain high coherence over multiple plasma wavelengths and thereby accelerate electrons to extremely high energies. The results could be useful for particle acceleration at short scales, i.e. at nano- and micrometer scales, in magnetized dense plasmas where the driver is the whistler wave instead of a laser or a particle beam.Comment: 8 pages, 2 figures; Revised version to appear in Physics of Plasmas (Dec. 2010 issue

Ultrarelativistic nanoplasmonics as a new route towards extreme intensity attosecond pulses

The generation of ultra-strong attosecond pulses through laser-plasma interactions offers the opportunity to surpass the intensity of any known laboratory radiation source, giving rise to new experimental possibilities, such as quantum electrodynamical tests and matter probing at extremely short scales. Here we demonstrate that a laser irradiated plasma surface can act as an efficient converter from the femto- to the attosecond range, giving a dramatic rise in pulse intensity. Although seemingly similar schemes have been presented in the literature, the present setup deviates significantly from previous attempts. We present a new model describing the nonlinear process of relativistic laser-plasma interaction. This model, which is applicable to a multitude of phenomena, is shown to be in excellent agreement with particle-in-cell simulations. We provide, through our model, the necessary details for an experiment to be performed. The possibility to reach intensities above 10^26 W/cm^2, using upcoming 10 petawatt laser sources, is demonstrated.Comment: 15 pages, 5 figure

Effects of the gg-factor in semi-classical kinetic plasma theory

A kinetic theory for spin plasmas is put forward, generalizing those of previous authors. In the model, the ordinary phase space is extended to include the spin degrees of freedom. Together with Maxwell's equations, the system is shown to be energy conserving. Analysing the linear properties, it is found that new types of wave-particle resonances are possible, that depend directly on the anomalous magnetic moment of the electron. As a result new wave modes, not present in the absence of spin, appear. The implications of our results are discussed.Comment: 4 pages, two figures, version to appear in Physical Review Letter