Ion heat and parallel momentum transport by stochastic magnetic fields and turbulence

The theory of turbulent transport of parallel momentum and ion heat by the interaction of stochastic magnetic fields and turbulence is presented. Attention is focused on determining the kinetic stress and the compressive energy flux. A critical parameter is identified as the ratio of the turbulent scattering rate to the rate of parallel acoustic dispersion. For the parameter large, the kinetic stress takes the form of a viscous stress. For the parameter small, the quasilinear residual stress is recovered. In practice, the viscous stress is the relevant form, and the quasilinear limit is not observable. This is the principal prediction of this paper. A simple physical picture is developed and shown to recover the results of the detailed analysis.

Effects of magnetic perturbations and radiation on the runaway avalanche

The electron runaway phenomenon in plasmas depends sensitively on the momentum- space dynamics. However, efficient simulation of the global evolution of systems involving runaway electrons typically requires a reduced fluid description. This is needed, for example, in the design of essential runaway mitigation methods for tokamaks. In this paper, we present a method to include the effect of momentum-dependent spatial transport in the runaway avalanche growth rate. We quantify the reduction of the growth rate in the presence of electron diffusion in stochastic magnetic fields and show that the spatial transport can raise the effective critical electric field. Using a perturbative approach, we derive a set of equations that allows treatment of the effect of spatial transport on runaway dynamics in the presence of radial variation in plasma parameters. This is then used to demonstrate the effect of spatial transport in current quench simulations for ITER-like plasmas with massive material injection. We find that in scenarios with sufficiently slow current quench, owing to moderate impurity and deuterium injection, the presence of magnetic perturbations reduces the final runaway current considerably. Perturbations localised at the edge are not effective in suppressing the runaways, unless the runaway generation is off-axis, in which case they may lead to formation of strong current sheets at the interface of the confined and perturbed regions.

Inflation of universe by nonlinear electrodynamics

Nonlinear electrodynamics with two-dimensional parameters is studied. The range of electromagnetic fields, when principles of causality, unitarity and the classical stability hold, are obtained. A singularity of the electric field at the center of charges is absent within our model and there are corrections to the Coulomb law as [Formula: see text]. The universe inflation takes place in the background of stochastic magnetic fields. The second stage of the universe evolution is the radiation era so that the graceful exit exists. We estimated the spectral index, the tensor-to-scalar ratio, and the running of the spectral index that are in a rough accordance with the PLANCK and WMAP data.

Rational nonlinear electrodynamics causes the inflation of the universe

The source of the universe inflation is electromagnetic fields obeying rational nonlinear electrodynamics proposed earlier. Within this model the singularities of the electric field at the center of charges, the Ricci scalar, the Ricci tensor squared and the Kretschmann scalar are absent. We consider the universe which is filled by stochastic magnetic fields. It is demonstrated that the inflation lasts approximately [Formula: see text] s with the reasonable [Formula: see text]-folding number [Formula: see text]. The inflation starts from de Sitter space–time and after the universe inflation end it decelerates approaching the radiation era.

Inflation of Universe by Nonlinear Electrodynamics

Nonlinear electrodynamics with two dimensional parameters is studied. The range of electromagnetic fields when principles of causality, unitarity and the classical stability hold are obtained. A singularity of the electric field at the center of charges is absent within our model and there are corrections to the Coulomb law as $r\rightarrow\infty$. The universe inflation takes place in the background of stochastic magnetic fields. The second stage of the universe evolution is the radiation era so that the graceful exit exists. We estimated the spectral index, the tensor-to-scalar ratio, and the running of the spectral index that are in an approximate agreement with the PLANK and WMAP data.

Proton imaging of stochastic magnetic fields

Recent laser-plasma experiments (Foxet al.,Phys. Rev. Lett., vol. 111, 2013, 225002; Huntingtonet al.,Nat. Phys., vol. 11(2), 2015, 173–176; Tzeferacoset al.,Phys. Plasmas, vol. 24(4), 2017a, 041404; Tzeferacoset al., 2017b,arXiv:1702.03016[physics.plasm-ph]) report the existence of dynamically significant magnetic fields, whose statistical characterisation is essential for a complete understanding of the physical processes these experiments are attempting to investigate. In this paper, we show how a proton-imaging diagnostic can be used to determine a range of relevant magnetic-field statistics, including the magnetic-energy spectrum. To achieve this goal, we explore the properties of an analytic relation between a stochastic magnetic field and the image-flux distribution created upon imaging that field. This ‘Kugland image-flux relation’ was previously derived (Kuglandet al., Rev. Sci. Instrum.vol. 83(10), 2012, 101301) under simplifying assumptions typically valid in actual proton-imaging set-ups. We conclude that, as with regular electromagnetic fields, features of the beam’s final image-flux distribution often display a universal character determined by a single, field-scale dependent parameter – the contrast parameter$\unicode[STIX]{x1D707}\equiv d_{s}/{\mathcal{M}}l_{B}$– which quantifies the relative size of the correlation length$l_{B}$of the stochastic field, proton displacements$d_{s}$due to magnetic deflections and the image magnification${\mathcal{M}}$. For stochastic magnetic fields, we establish the existence of four contrast regimes, under which proton-flux images relate to their parent fields in a qualitatively distinct manner. These are linear, nonlinear injective, caustic and diffusive. The diffusive regime is newly identified and characterised. The nonlinear injective regime is distinguished from the caustic regime in manifesting nonlinear behaviour, but as in the linear regime, the path-integrated magnetic field experienced by the beam can be extracted uniquely. Thus, in the linear and nonlinear injective regimes we show that the magnetic-energy spectrum can be obtained under a further statistical assumption of isotropy. This is not the case in the caustic or diffusive regimes. We discuss complications to the contrast-regime characterisation arising for inhomogeneous, multi-scale stochastic fields, which can encompass many contrast regimes, as well as limitations currently placed by experimental capabilities on one’s ability to extract magnetic-field statistics. The results presented in this paper are of consequence in providing a comprehensive description of proton images of stochastic magnetic fields, with applications for improved analysis of proton-flux images.

Inflation of universe due to nonlinear electrodynamics

A model of nonlinear electrodynamics with a dimensional parameter [Formula: see text] is considered. Electromagnetic fields are the source of the gravitation field and inflation of the universe. We imply that the universe is filled by stochastic magnetic fields. It is demonstrated that after the universe inflation the universe decelerates approaching the Minkowski space–time. We evaluate the spectral index, the tensor-to-scalar ratio, and the running of the spectral index which approximately agree with the Planck and WMAP data.