Strong Uniform Magnetic Field Research Articles

Wave turbulence in incompressible Hall magnetohydrodynamics

We investigate the steepening of the magnetic fluctuation power law spectra observed in the inner solar wind for frequencies higher than 0.5 Hz. This high frequency part of the spectrum may be attributed to dispersive nonlinear processes. In that context, the long-time behavior of weakly interacting waves is examined in the framework of 3D incompressible Hall MHD turbulence. The Hall term added to the standard MHD equations makes the Alfv\'en waves dispersive and circularly polarized. We introduce the generalized Els\"asser variables and, using a complex helicity decomposition, we derive for three-wave interaction processes the general wave kinetic equations; they describe the nonlinear dynamics of Alfv\'en, whistler and ion cyclotron wave turbulence in the presence of a strong uniform magnetic field $B_0 \ep$. Hall MHD turbulence is characterized by anisotropies of different strength. We show that electron and standard MHD turbulence can be seen as two frequency limits of the present theory but the standard MHD limit is singular; additionally, we analyze in detail the ion MHD turbulence limit. Exact power law solutions of the master wave kinetic equations are given in the small and large scale limits for which we have, respectively, the total energy spectra $E(\kpn,\kpa) \sim \kpn^{-5/2} |\kpa|^{-1/2}$ and $E(\kpn,\kpa) \sim \kpn^{-2}$. An anisotropic phenomenology is developed to describe continuously the different scaling laws of the energy spectrum; one predicts $E(\kpn,\kpa) \sim \kpn^{-2} |\kpa|^{-1/2} (1+\kpn^2d_i^2)^{-1/4}$. Nonlocal interactions between Alfv\'en, whistler and ion cyclotron waves are investigated; a non trivial dynamics exists only when a discrepancy from the equipartition between the large scale kinetic and magnetic energies happens.

RANS-Based Very Large Eddy Simulation of Thermal and Magnetic Convection at Extreme Conditions

Abstract For thermal and magnetic convection at very high Rayleigh and Hartman numbers, which are inaccessible to the conventional large eddy simulation, we propose a time-dependent Reynolds-average-Navier-Stokes (T-RANS) approach in which the large-scale deterministic motion is fully resolved by time and space solution, whereas the unresolved stochastic motion is modeled by a “subscale” model for which an one-point RANS closure is used. The resolved and modeled contributions to the turbulence moments are of the same order of magnitude and in the near-wall regions the modeled heat transport becomes dominant, emphasizing the role of the subscale model. This T-RANS approach, with an algebraic stress/flux subscale model, verified earlier in comparison with direct numerical simulation and experiments in classic Rayleigh-Bénard convection, is now expanded to simulate Rayleigh-Bénard (RB) convection at very high Ra numbers—at present up to O(1016)—and to magnetic convection in strong uniform magnetic fields. The simulations reproduce the convective cell structure and its reorganization caused by an increase in Ra number and effects of the magnetic field. The T-RANS simulations of classic RB indicate expected thinning of both the thermal and hydraulic wall boundary layer with an increase in the Ra number and an increase in the exponent of the Nu∝Ran correlation in accord with recent experimental findings and Kraichnan asymptotic theory.

Bound-state β decay of a neutron in a strong magnetic field

The \ensuremath{\beta} decay of a neutron into a bound $({\mathit{pe}}^{\ensuremath{-}})$ state and an antineutrino in the presence of a strong uniform magnetic field ($B\ensuremath{\gtrsim}{10}^{13}$ G) is considered. The \ensuremath{\beta} decay process is treated within the framework of the standard model of weak interactions. A Bethe-Salpeter formalism is employed for description of the bound $({\mathit{pe}}^{\ensuremath{-}})$ system in a strong magnetic field. For the field strengths ${10}^{13}\ensuremath{\lesssim}B\ensuremath{\lesssim}{10}^{18}$ G the estimate for the ratio of the bound-state decay rate ${w}_{b}$ and the usual (continuum-state) decay rate ${w}_{c}$ is derived. It is found that in such strong magnetic fields ${w}_{b}/{w}_{c}~0.1\text{\ensuremath{-}}0.4$. This is in contrast to the field-free case, where ${w}_{b}/{w}_{c}\ensuremath{\simeq}4.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ [J. N. Bahcall, Phys. Rev. 124, 495 (1961); L. L. Nemenov, Sov. J. Nucl. Phys. 15, 582 (1972); X. Song, J. Phys. G: Nucl. Phys. 13, 1023 (1987)]. The dependence of the ratio ${w}_{b}/{w}_{c}$ on the magnetic field strength B exhibits a logarithmiclike behavior. The obtained results can be important for applications in astrophysics and cosmology.

Fourth-order algorithms for solving local Schrödinger equations in a strong magnetic field

We describe an efficient numerical method for solving eigenvalue problems associated with the one-body Schrödinger equation or the Kohn–Sham equations in an arbitrarily strong uniform external magnetic field. The eigenvalue problem is solved in real space by using a fourth order, forward factorization of the evolution operator e − ε H , which is significantly more efficient than conventional second-order algorithms. In particular, the magnetic field is solved exactly by the decomposition process. The algorithm is applicable to any external potential, in addition to the magnetic field. We envision its primary application in the area of electronic structure calculations of quantum dots.

Fisher zeros of the Ising antiferromagnet in an arbitrary nonzero magnetic field

From the exact partition functions of the Ising model on L x L square lattices (up to L = 14) in an arbitrary nonzero external magnetic field H, the precise distributions of the Fisher zeros in the complex temperature (a = e(2betaJ)) plane are obtained. Our results indicate that in the limit L-->infinity the Fisher zeros for H not = 0 do cut the positive real axis at the antiferromagnetic critical point ac(H); these values are compared with the results of closed-form approximations for the antiferromagnetic critical line. From the Fisher zeros the thermal scaling exponent yt = 1 is also obtained along the critical line, indicating the logarithmic singularity of the specific heat for the antiferromagnetic Ising model even in a strong uniform magnetic field.

Field-induced gap in ordered Heisenberg antiferromagnets

Heisenberg antiferromagnets in a strong uniform magnetic field $H$ are expected to exhibit a gapless phase with a global O(2) symmetry. In many real magnets, a small energy gap is induced by additional interactions that can be viewed as a staggered transverse magnetic field $h=cH$, where $c$ is a small proportionality constant. We study the effects of such a perturbation, particularly for magnets with long-range order, by using several complementary approaches: numerical diagonalizations of a model with long-range interactions, classical equations of motion, and scaling arguments. In an ordered state at zero temperature, the energy gap at first grows as ${(cH)}^{1∕2}$ and then may dip to a smaller value, of order ${(cH)}^{2∕3}$, at the quantum critical point separating the ``gapless'' phase from the gapped state with saturated magnetization. In one spatial dimension, the latter exponent changes to $4∕5$.

Non-linear ring currents: effect of strong magnetic fields on π-electron circulation

Finite-field calculations of non-linear induced current density in representative [4 n + 2] and [4 n] π systems, benzene and flat cyclooctatetraene (COT), show that a strong uniform perpendicular magnetic field enhances benzene π-diatropicity and decreases COT π-paratropicity. The non-linear current is stronger by two orders of magnitude in COT, but still small: at 1 a 0 height and in a field of 25 T, third-order effects contribute −5 ppm to the first-order π ring current. Classical arguments based on radial contraction of charge density rationalise the non-linear response of benzene, but that of COT depends on a specific orbital-rotation effect, characteristic of paratropic π systems.

Effects of strong magnetic fields on the electron distribution and magnetisability of rare gas atoms

Strong uniform static magnetic fields compress the electronic distribution of rare gas atoms and cause a ‘spindle effect’, which can be illustrated by plotting charge–density functions which depend quadratically on the flux density of the applied field. The fourth rank hypermagnetisabilities of He, Ne, Ar and Kr are predicted to have small positive values. Accordingly, the diamagnetism of rare gas atoms diminishes by a very little amount in the presence of intense magnetic field.

Electric-field induced exponential enhancement of electromagnetic absorption in semiconductors at a strong magnetic field

The influence is investigated of a dc (electric) field F perpendicular to a strong uniform static magnetic field H on the absorption coefficient of a semiconductor for high-frequency electromagnetic waves polarized along the electric field. The absorption coefficient for some (e.g., phonon-assisted) cyclotron resonances is predicted to exhibit a strong, almost exponential increase by orders of magnitude with increasing F up to a relatively weak F c , the upper limit of the range in which the considered absorption mechanism holds true. The predicted effect is suggested to be observable in typical semiconductors at realistic electric and strong magnetic fields and low temperatures.

Muong — 2 measurements and non-commutative geometry of quantum beams

We discuss a completely quantum mechanical treatment of the measurement of the anomalous magnetic moment of the muon. A beam of muons move in a strong uniform magnetic field and a weak focusing electrostatic field. Errors in the classical beam analysis are exposed. In the Dirac quantum beam analysis, an important role is played by non-commutative muon beam coordinates leading to a discrepancy between the classical and quantum theories. We obtain a quantum limit to the accuracy achievable in BNL type experiments. Some implications of the quantum corrected data analysis for supersymmetry are briefly mentioned.

Effect of the Initial Laser Phase on the Interaction BetweenRelativistic Electron and Ultra-Intense Laser Field in a Strong UniformMagnetic Field

We investigate the influence of the initial laser phase on theinteraction between relativistic electron and ultra-intense linearpolarized laser field in a strong uniform magnetic field. It is foundthat the dynamic behaviour of the relativistic electron and the emissionspectrum varies dramatically with different initial laser field phases.The effect of changing initial phase is contrary in the two parameterregions divided by the resonance condition. The phase dependence of theelectron energy and velocity components are also studied. Some beatstructure is found when the initial laser phase is zero and thisstructure is absent when the initial laser phase is a quarter of a period.

New Applications of Non-Hermitian Random Matrices

We discuss recently discovered links of the statistical models of normal random matrices to some important physical problems of pattern formation and to the quantum Hall effect. Specifically, the large N limit of the normal matrix model with a general statistical weight describes dynamics of the interface between two incompressible fluids with different viscosities in a thin plane cell (the Saffman-Taylor problem). The latter appears to be mathematically equivalent to the growth of semiclassical 2D electronic droplets in a strong uniform magnetic field with localized magnetic impurities (fluxes), as the number of electrons increases. The equivalence is most easily seen by relating both problems to the matrix model.

Phase dependence of relativistic electron dynamics and emission spectra in the superposition of an ultraintense laser field and a strong uniform magnetic field.

The phase dependence of the dynamics and emission spectra of a fully relativistic electron in the superposition of an ultraintense plane wave laser field and a strong uniform magnetic field has been investigated. It is found that the effect of changing the initial laser phase is quite different for circularly and linearly polarized laser fields. For circular polarization only the axis of the helical trajectory is changed with variation of the initial laser field phase. However, for linear polarization, the effect of changing the initial phase is opposite in the two parameter regions divided by the resonance condition r=1 (r stands for the ratio between the reduced cyclotron frequency and laser frequency). When r<1, with increase in the initial laser field phase eta(0) from 0 to pi/2, both the radius of the electron's helical trajectory and the height of the peak related to the uniform magnetic field are decreased, and these two physical values are increased with an increase in the laser initial phase when r>1. The phase dependence of the electron's energy and velocity components was also studied. Some beat structure is found when eta(0)=0 and this structure is absent when eta(0)=pi/2.

Deformation of a free surface due to convective flow in a cavity in a strong uniform magnetic field

Deformation of a free surface due to convective flow in a cavity in a strong uniform magnetic field

Analytic calculation of the longitudinal dynamic susceptibility of uniaxial superparamagnetic particles in a strong uniform DC magnetic field

A simple analytic equation which allows one to obtain a qualitative understanding of the physical processes underlying the behavior of the longitudinal complex susceptibility χ ||( ω) of an assembly of noninteracting uniaxial superparamagnetic particles subjected to a strong external uniform DC magnetic field is derived in the context of Brown's model of magnetic relaxation. It is shown that a knowledge of 3 time constants characterizing the magnetization relaxation, viz. the integral relaxation time τ, the effective relaxation time τ ef, and the inverse of the smallest eigenvalue λ 1 of the Fokker–Planck operator are sufficient to accurately predict the spectrum of χ ||( ω) in all frequency ranges of interest as well as the behavior of the equilibrium correlation function of the longitudinal component of the magnetization C ||( t) in the time domain at all values of the barrier and external field parameters.

Equations for the order parameter and effective magnetic field for nonunitary phases of superfluid Fermi liquids with spin-triplet p-wave pairing

On the basis of generalized Fermi-liquid approach we have derived the systems of coupled equations for the components of the order parameter and effective magnetic field for nonunitary phases of neutral paramagnetic superfluid Fermi liquids with spin-triplet pairing in strong static uniform magnetic field at arbitrary temperatures from the interval 0⩽ T⩽ T c ( T c is the normal–superfluid transition temperature). These equations are presented here for dense superfluid neutron matter (existing inside fluid core of neutron stars) with triplet p-wave pairing of 3 He –A 2 type and using the effective Skyrme interaction between neutrons.

Magnetohydrodynamic flow in the liquid phase for a specific pool boiling scenario

In the EVOLVE concept for a nuclear fusion blanket a pool boiling scenario has been proposed where a number of permanent vertical vapour channels are formed in a horizontal layer of liquid lithium. Similar situations occur during laser beam welding where a relatively long vapour capillary is observed. The present analysis focuses on the flow of the electrically conducting liquid phase in the presence of a strong uniform horizontal magnetic field. The cross-section of vapour channels is circular if surface tension dominates magnetic forces. In the opposite case a stretching of the liquid–vapour interface along magnetic field lines is observed and contours become possible where a major part of the interface is straight and aligned with the field. For strong magnetic fields the liquid flow exhibits several distinct subregions. Most of the liquid domain is occupied by inviscid cores. These are separated from each other by parallel layers that spread along the field lines which are tangential to the vapour channel. In one core, which is located between two parallel layers, the flow direction is preferentially oriented along magnetic field lines, while in the other cores the flow is perpendicular to the field.

Nonlinear response of fine superparamagnetic particles to the sudden change of a strong uniform DC magnetic field

The nonlinear response of an assembly of superparamagnetic particles due to a sudden change both in the magnitude and in the direction of a strong external uniform DC magnetic field is evaluated. The desired system of moments (the expectation values of the spherical harmonics 〈 Y l, m 〉( t)), which governs the kinetics of the magnetization M of an individual particle, is derived by averaging the stochastic Gilbert equation augmented by a random field over its realizations. As an example, the nonlinear transient response of particles possessing cubic anisotropy is considered. Here, the solution of the moment system is obtained using the matrix continued fraction method. The spectrum of the appropriate relaxation function and the relaxation time of the magnetization are calculated for typical values of the anisotropy, dissipation, and nonlinearity parameters. In general, the relaxation time and spectrum depend strongly on the dissipation parameter due to the coupling between the transverse and longitudinal modes. This behavior is particularly pronounced in the nonlinear regime.

About nonunitary phases of superfluid helium-3 in a magnetic field

We have derived a system of coupled equations for the order parameter, effective magnetic field and unified expression for the magnetic susceptibility for nonunitary superfluid phases 3 He — A 2, 3 He — A 1 and nonunitary 2D-phase of 3 He with spin-triplet p-wave pairing in sufficiently strong static uniform magnetic field at temperatures 0 ≤ T ≤ T c ( T c is the temperature of phase transition from the normal to the superfluid state). These results are obtained within the Fermi-liquid theory generalized to superfluid systems and the Landau spin-exchange Fermi-liquid interaction is taken into account.

Eddy viscosity and laminarization of sheared flow in three dimensional reduced magnetohydrodynamic turbulence

The effect of Alfvén waves on turbulent momentum transport is studied in three-dimensional reduced magnetohydrodynamic turbulence. A strong external uniform magnetic field B0 is assumed to be present orthogonal to both background shear flow and its inhomogeneity. Energy is injected into the fluid and/or magnetic field on small scales. It is shown analytically that eddy viscosity is reduced as 1/B02 for a strong B0, due to the cancellation of the Reynolds stress by Maxwell stress. The sign of eddy viscosity is found to depend on the detailed properties of forcings. Specifically, it is positive for fluid forcing but depends on the anisotropy of the forcing in the case of magnetic forcing. Furthermore, it is indicated that a magnetic field tends to laminarize a mean shear flow. The possible implication of these results for the dynamics of the zonal flows in tokamaks is discussed in view of the cancellation of stresses.