Strong Uniform Magnetic Field Research Articles

Classification of Aggregate Structure of Ferrofluids under Condition of Strong Magnetic Fields and Simple Shear Flow Fields.

Ferrofluids make aggregations under a strong magnetic field. Therefore, the rheological property becomes complex and nonlinear. In this research, the numerical analysis of the aggregation of ferrofluids under the strong uniform magnetic field and simple shear flow field was made by the Stokesian dynamics method. Results obtained are as follows. (1) The aggregate structure can be classified into four types : the cylindrical structure type, the layered structure type, the diagonal structure type and the corrupt structure type. (2) The apparent shear viscosity by magnetic force shows a characteristic peculiar to each aggregate type. (3) The apparent shear viscosity by magnetic force decreases as the shear rate increases. (4) The apparent shear viscosity by magnetic force increases as the saturation magnetization of magnetic particles increases.

The Anisotropy of Magnetohydrodynamic Alfvenic Turbulence

We perform direct three-dimensional numerical simulations for magnetohydrodynamic (MHD) turbulence in a periodic box of size 2π threaded by strong uniform magnetic fields. We use a pseudospectral code with hyperviscosity and hyperdiffusivity to solve the incompressible MHD equations. We analyze the structure of the eddies as a function of scale. A straightforward calculation of anisotropy in wavevector space shows that the anisotropy is scale independent. We discuss why this is not the true scaling law and how the curvature of large-scale magnetic fields affects the power spectrum and leads to the wrong conclusion. When we correct for this effect, we find that the anisotropy of eddies depends on their size: smaller eddies are more elongated than larger ones along local magnetic field lines. The results are consistent with the scaling law ∥ ~ recently proposed by Goldreich & Sridhar. Here ∥ (and ⊥) are wavenumbers measured relative to the local magnetic field direction. However, we see some systematic deviations that may be a sign of limitations to the model or our inability to fully resolve the inertial range of turbulence in our simulations.

Longitudinal dynamic susceptibility and relaxation time of superparamagnetic particles with cubic anisotropy: Effect of a biasing magnetic field

The magnetic relaxation of single domain ferromagnetic particles with cubic magnetic anisotropy subjected to a strong uniform magnetic field is treated by averaging the Gilbert-Langevin equation for an individual particle, so that the system of linear differential-recurrence equations for the appropriate equilibrium correlation functions is derived. The solution of this system (in terms of matrix continued fractions) is obtained and the longitudinal relaxation time ${\ensuremath{\tau}}_{\ensuremath{\parallel}}$ of the magnetization and spectrum of the complex magnetic susceptibility ${\ensuremath{\chi}}_{\ensuremath{\parallel}}(\ensuremath{\omega})$ are evaluated. It is shown that the depletion effect discovered for uniaxial particles by Coffey et al. [Phys. Rev. B 51, 15 947 (1995)] and interpreted by Garanin [Phys. Rev. E 54, 3250 (1996)] also exists for particles having a cubic anisotropy. This effect consists of the drastic deviation of ${\ensuremath{\tau}}_{\ensuremath{\parallel}}$ from the inverse of the smallest nonvanishing eigenvalue $({\ensuremath{\lambda}}_{1}^{\ensuremath{-}1})$ of the Fokker-Planck equation in the low temperature limit starting from some critical values ${h}_{c}$ of the ratio bias field parameter/anisotropy barrier height parameter and is due to depletion of the upper (shallow) potential well involved into the relaxation process. For uniaxial particles the critical value is known to be ${h}_{c}\ensuremath{\approx}0.17.$ For cubic crystals it is shown that ${h}_{c}\ensuremath{\approx}0.3$ (for positive anisotropy constant, Fe-type) and ${h}_{c}\ensuremath{\approx}0.1$ (for negative anisotropy constant, Ni-type). However, it is also demonstrated, in contrast to uniaxial particles, that for cubic crystals there is an inherent geometric dependence of the complex susceptibility and the relaxation time on the damping parameter arising from the coupling of longitudinal and transverse relaxation modes.

Coupling between nonlinear Alfvén waves and reduced magnetohydrodynamics for compressible fluids

A reduced description of magnetohydrodynamic (MHD) turbulence in a plasma permeated by a strong uniform magnetic field is derived using a reductive perturbative expansion method. This leads to a coupled system of equations for the velocity and magnetic fields in the planes perpendicular to the ambient field, described by the usual reduced MHD equations [Zank and W. H. Matthaeus, J. Plasma Phys. 48, 85–100 (1992)] and for parallel propagating Alfvén waves, which on the characteristic time and length scale of the transverse flow, undergo cumulative nonlinear effects described by a generalized Derivative Nonlinear Schrödinger equation (DNLS). The cases β far from unity and β≈1 are addressed separately. In the latter case, the nonlinear Alfvén waves drive a mean longitudinal velocity whose magnitude is comparable to that of the transverse components. A modulational analysis for a quasi-monochromatic plane Alfvén wave at β far from unity illustrates the effect of the transverse MHD flow on the Alfvén wave filamentation.

Strong-field magnetotransport of conducting composites with a columnar microstructure

The transport properties of composite conductors with a columnar microstructure, and subject to a strong uniform magnetic field perpendicular to the columnar axis, are discussed with special emphasis on the strong-field limit. Asymptotic considerations provide detailed insight into the factors that govern the local current distribution, and hence the bulk effective Ohmic resistivity components. Particularly explicit asymptotic results are found in the case of periodic arrays of long, parallel inclusions that are either perfect insulators or perfect conductors, and are embedded in a conducting host that is a simple, free-electron-like conductor. In some configurations, simple closed form expressions are derived for the current distribution as well as for the bulk effective resistivities. Numerical calculations of those distributions and resistivities are also performed and compared to the asymptotic expressions. We thus achieve a detailed understanding of the rich phenomenology of strong-field magnetotransport in such systems, some of which was predicted earlier from numerical calculations and subsequently found in a recent experiment.

Relativistic free-electron dynamics and light-emission spectra in the simultaneous presence of a superintense laser field and a strong uniform magnetic field

We present exact analytic trajectories for a relativistic electron in the presence of an elliptically polarized superintense laser field and a strong uniform magnetic field. Also derived are expressions for the velocity components of the electron and for its energy as functions of the phase of the laser field as a parameter. The analytic trajectory solutions are illustrated by numerical calculations employing laser-field parameters and magnetic-field strengths currently available for laboratory experiments. The trajectory solutions are useful for (among other things) the study of the related problem of emission of radiation in the combined laser and magnetic fields. An exact expression for the cross section of light scattered by an electron initially moving along the laser propagation direction and in a magnetic field is given. It is found that, for observation along the common direction of laser propagation and the magnetic field, light at two frequencies $\ensuremath{\omega}={\ensuremath{\omega}}_{0}$ and ${\ensuremath{\Omega}}_{0}$ is scattered, where ${\ensuremath{\Omega}}_{0}={\ensuremath{\gamma}}_{0}(1+{\ensuremath{\beta}}_{0}){\ensuremath{\omega}}_{c},$ ${\ensuremath{\omega}}_{c}$ is the cyclotron frequency of the electron motion in the magnetic field, ${\ensuremath{\beta}}_{0}$ is the initial speed of the electron normalized by the speed of light, ${\ensuremath{\gamma}}_{0}=(1\ensuremath{-}{\ensuremath{\beta}}_{0}^{2}{)}^{\ensuremath{-}1/2}$, and ${\ensuremath{\omega}}_{0}$ is the laser frequency. Using the analytic solutions, we also study numerically the spectrum of radiation emitted along observation directions parallel to the electric and parallel to the magnetic components of the laser field. In each case, we present and discuss the dependence of the spectra on (a) the increase of the electron initial velocity, (b) the intensity and the frequency of the laser, and (c) the strength of the magnetic field.

Laminar buoyant magnetohydrodynamic flow in vertical rectangular ducts

The buoyancy-driven laminar magnetohydrodynamic flow in long vertical channels is investigated. It is assumed that the channels have a rectangular cross section with one pair of walls aligned with the strong uniform magnetic field. The walls may have arbitrary electrical conductance. Using asymptotic methods, solutions are derived for general temperature distributions inside the ducts. Results are shown for different values of the control parameters. One finds the typical subregions for the flow inside the duct, namely the inviscid core, surrounded by viscous Hartmann layers and side layers. The character of the solution inside these regions may deviate from what is expected by a comparison with the classical solutions for pressure-driven duct flows. The main difference is that the flow in the core not necessarily exhibits a two-dimensional behavior. Most surprising, however, is the fact, that high-velocity jets are observed for the first time along perfectly conducting sidewalls. These jets are able to carry a major part of the flow rate.

Screening in Two-Dimensional Electron Gas Quantized by Strong Magnetic Field

Within the Thomas-Fermi approximation a rigorous solution of the problem on screening is obtained in zero-temperature limit for a concrete configuration of a two-dimensional electron system in strong uniform magnetic field.

Heat-transfer intensification promoted by vortical structures in closed channel under magnetic field

The effect of large two-dimensional vortical structures on heat transfer in liquid metal flow in an annular channel under an axial uniform strong magnetic field has been experimentally investigated. Hot and cold channel walls were parallel to the field. Structures commensurable with the channel's cross-sectional dimension and stretched along the field were generated owing to flow around the stagnant zones in flow above and below the conducting cylindrical obstacles placed on the hot wall. It is shown that transversal heat transfer increases six times compared with free channel flow. Here, the hot-wall temperature decreased more than three times. In the presence of cylindrical obstacles in the channel, the increase in the power spent for fluid motion is not required to achieve the large Nusselt numbers. The mean and fluctuating velocities in the flow cross section were measured by using a potential probe. The Reynolds stresses and turbulent energy production for the flow were also obtained experimentally. The temperature distributions were measured by thermocouples. Local characteristics measured in the channel are used to provide analysis of flow structure and redistribution of velocity and temperature fields.

Landau Level Mixing and Levitation of Extended States in Two Dimensions

We study the effects of mixing of different Landau levels on the energies of one-body states, in the presence of a strong uniform magnetic field and a random potential in two dimensions. We use a perturbative approach and develop a systematic expansion in both the strength and smoothness of the random potential. We find the energies of the extended states shift upward, and the amount of levitation is proportional to $(n+1/2)/{B}^{3}$ for strong magnetic field, where $B$ is the magnetic field strength and $n$ is the Landau level index.

Effective mass of a polaron in a quantum wire under a strong magnetic field

AbstractUsing the Lee‐Low‐Pines variational method the effective mass of a polaron in a rectangular quantum wire subject to a strong uniform external magnetic field along the wire length is studied. Taking the GaAs quantum wire as an example numerical results are given. The results show that the effective mass of the polaron is dominated mainly by the smaller dimension of the quantum wire cross section and the external magnetic field has an interesting influence on it.

Liquid-metal flow in a system of electrically coupled U-bends in a strong uniform magnetic field

Liquid-metal magnetohydrodynamic flow in a system of electrically coupled U-bends in a strong uniform magnetic field is studied. The ducts composing the bends are electrically conducting and have rectangular cross-sections. It has been anticipated that very strong global electric currents are induced in the system, which modify the flow pattern and produce a very high pressure drop compared to the flow in a single U-bend. A detailed asymptotic analysis of flow for high values of the Harmann number (in fusion blanket applications of the order of 103−104) shows that circulation of global currents results in several types of peculiar flow patterns. In ducts parallel to the magnetic field a combination of helical and recirculatory flow types may be present and vary from one bend to another. The magnitude of the recirculatory motion may become very high depending on the flow-rate distribution between the bends in the system. The recirculatory flow may account for about 50% of the flow in all bends. In addition there are equal and opposite jets at the walls parallel to the magnetic field, which are common to any two bends. The pressure drop due to three-dimensional effects linearly increases with the number of bends in a system and may significantly affect the total pressure drop. To suppress this and some other unwelcome tendencies either the ducts perpendicular to the magnetic field should be electrically separated, or the flow direction in the neighbouring ducts should be made opposite, so that leakage currents cancel each other.

Derivative expansion of the effective action and vacuum instability for QED in 2+1 dimensions.

We investigate the effective action of (2+1)-dimensional charged spin-1/2 fermions and spin-0 bosons in the presence of a U(1) gauge field. We evaluate terms in an expansion up to second order in derivatives of the field strength, but exactly in the mass parameter and in the magnitude of the nonvanishing constant field strength. We find that in a strong uniform magnetic field background, space-derivative terms lower the energy, and there arises an instability toward inhomogeneous magnetic fields.

Kinetic model of the electron plasma component in plasma accelerators with closed drift

The dynamics of the electron plasma component in plasma accelerators with closed drift and a long acceleration zone are considered under certain simplifying assumptions (strong uniform magnetic field, elastic diffuse electron scattering by the channel walls, etc.). Exact solutions of the kinetic equation for electrons in different limiting cases are found. The results are generalized to include the case of a weakly nonuniform magnetic field.

Liquid metal flow in a U-bend in a strong uniform magnetic field

Magnetohydrodynamic flows in a U-bend and in a right-angle bend are considered with reference to the toroidal concepts of self-cooled liquid-metal blankets. The ducts composing the bends have rectangular cross-sections. The applied magnetic field is aligned with the toroidal duct and perpendicular to ducts supplying liquid metal. For high Hartmann numbers the flow region is divided into cores and boundary layers of different types. The magnetohydrodynamic equations are reduced to a system of partial differential equations governing wall electric potentials and the core pressure. The system is solved numerically. The results show that the flow is very sensitive to variations of certain parameters, such as the wall conductance ratio and the aspect ratio of the toroidal duct cross-section. Depending on these parameters, the flow exhibits a variety of qualitatively different flow patterns. In particular, structures of helical and vortex type are obtained. A high-velocity jet occurs at the plasma-facing first wall and there is mixing of the fluid in the toroidal duct. These factors lead to desirable heat-transfer conditions.

The effect of strong longitudinal magnetic fields on dose deposition from electron and photon beams.

The use of strong, uniform, longitudinal magnetic fields for external electron and photon beam irradiation is considered. Using the EGS4 Monte Carlo code modified to account for the presence of magnetic fields, dramatic narrowing of penumbra for photon and electron irradiations is demonstrated. In the vicinity of heterogeneities, "hot" and "cold" spots due to multiple scattering in electron beams are reduced substantially. However, in the presence of strong magnetic fields, the effect of inhomogeneities can be observed far from the location of the inhomogeneity due to reduced "washout" caused by lateral multiple scattering. The enhanced "Bragg peak," proposed or calculated by other authors, is not observed on the central axis of broad beams, owing to lateral equilibrium. It is proven that for broad parallel beams, the central axis depth-dose curve is independent of the strength of the external longitudinal magnetic field, as long as it is uniform. However, strong longitudinal magnetic fields can induce enhancements by redirection of the electron fields coming from point sources. Strong uniform longitudinal magnetic fields provide a way of controlling the spreading of electron beams due to multiple scattering, making the electron beams more "geometrical" in character, simplifying dose-deposition patterns, possibly allowing electron beams to be used in new ways for radiotherapy. Photon therapy also benefits from strong uniform longitudinal magnetic fields since the penumbra or other lateral disequilibrium effects associated with lateral electron transport can be eliminated.

Wave generation in a sunspot

In this paper we analyze the generation of waves in a sunspot by extending Stein's hydrodynamic approach to the turbulent medium permeated by a strong uniform magnetic field oriented parallel to the gravity. For wave sources appropriate to the sunspot, we consider magnetic perturbations and entropy changes as well as turbulent convection. To describe the anisotropy imposed by the sunspot, we use a one-dimensional correlation function relating the turbulent eddies separated along the symmetry axis of the spot. This treatment yields several interesting possibilities for wave generation in a sunspot. First, it is demonstrated that the entropy change and magnetic perturbation can lead to a relative enhancement of acoustic wave emission. Second, the energy flux of Alfven waves may be comparable to that of acoustic waves in sunspots. Third, the anisotropy of the sunspot dynamics can lead to wave energy spectrum in a form which may explain the origin of umbral atmospheric oscillations.

Stability of ion-acoustic cnoidal and solitary waves in a magnetized plasma

The Zakharov-Kuznetsov equation describes nonlinear ion-acoustic waves in a strongly magnetized plasma and is used here to investigate the stability of nonlinear periodic and solitary ion-acoustic waves in a strong uniform magnetic field with respect to long wavelength plane wave perturbations in an arbitrary direction. A dispersion relation is obtained in the form of a quadratic equation. From this it is found that there is instability when the angle between the direction of propagation and the external magnetic field exceeds a critical value. The growth rate is computed and attains a maximum when the said angle is π/2. A solitary wave is always found to be unstable unless the perturbation is along the direction of propagation.

On the theory of the Heiser and Shercliff experiment. I. MHD flow in an open channel in a strong uniform magnetic field

The wall-driven MHD flow of a viscous incompressible fluid in an open channel is investigated. A strong magnetic field is applied parallel to the free surface. The problem is treated by means of matched asymptotic expansions. The flow region is divided into various subregions and the leading terms of the different asymptotic expansions are obtained for M to infinity , where M is the Hartmann number. An exact analytical solution of the equations governing the free-surface layer is obtained. The thickness is of order M-12/, but it is appreciably different from the bottom layer which has the same thickness.

Constraint equation for the lowest Landau level in the fractional quantum Hall system.

We apply the singular gauge transformation to the constraint equation for the lowest Landau level to investigate the generic properties of the quasiparticles of the fractional quantum Hall system by using the collective-field-theory approach. It shows a transparent connection with Laughlin s wave functions. If we take an average over the wave functional for the constraint equation, the resulting equation can be interpreted as the vortex equation for the fractionally charged quasiparticles. By introducing a generalized duality transformation, p(density)-8(phase) transformation, we can obtain the fractional statistics as well as the hierarchy scheme from the constraint equation. At present we have a fairly good understanding of the fractional quantum Hall effect' (FQHE) based on Laughlin's wave-function approach. Stimulated by an investigation of the off-diagonal long-range order for the FQHE, Girvin, and Girvin and MacDonald and others proposed a Ginzburg-Landau-like effective-field theory of the FQHE. This is in fact an eff'ective-field theory of a (2+1)-dimensional Schrodinger-Bose wave field coupled with a Chem-Simons gauge field that exhibits vortex solutions with finite energy and fractional charge. Although these are appealing, their connection to Laughlin's wave-function approach is not entirely clear. In particular, it is still not very clear to what extent the lowest Landau level (LLL) constraint has been properly accounted for. At the lowest Landau level the kinetic-energy part of the electron Hamiltonian, which usually bears the gauge properties of the system, should be projected away with only the Coulomb interaction term left. Therefore it is reasonable to expect that a rich variety of interesting properties for the FQHE systems, which are independent of the concrete form of the interactions, can be explored via the application of the Chem-Simons gauge-fieldtheory approach to the constraint for the electrons in the LLL. In this paper, we express the condition that all the electrons are in the LLL as a constraint equation for the state functional and apply the collective-field-theory technique ' which in fact is a field-theoretic approach, to this equation. The general solution of this constraint equation shows a transparent connection to Laughlin's wave function. If we take a quantum average of the constraint equation, the resulting equation can be interpreted as a vortex equation for the fractionally charged quasiparticles that is derived directly from the microscopic theory. The Coulomb interaction does not appear explicitly in the equation. The vortex solutions in turn require singularities of the phase of the wave functional. In the particle coordinate representation these singularities are pre cisely the ones that appear in the singular exponent of the prefactor of Laughlin's quasiparticles wave function. Next we introduce a generalized duality transformation as a generalized Fourier transformation — p(electron density)-8(phase variable conjugate to the electron density) transformation — of the state functional. Then the transformed constraint equation not only makes the fractional charge and statistics of quasiparticles (vortices) explicit, but also provides a natural derivation for the hierarchy scheme. We introduce the Hamiltonian for the interacting Xelectron system in a strong uniform magnetic field B by subtracting the zero-point energy for the lowest Landau level NAeB/2moc as