Weak Magnetic Field Region Research Articles

Waves in magnetic flux concentrations: The critical role of mode mixing and interference

Time-dependent numerical simulations of nonlinear wave propagation in a two-dimensional (slab) magnetic field geometry show wave mixing and interference to be important aspects of oscillatory phenomena in starspots and sunspots. Discrete sources located within the umbra generate both fast and slow MHD waves. The latter are compressive acoustic waves which are guided along the magnetic field lines and steepen into N-waves with increasing height in the spot atmosphere. The former are less compressive, and accelerate rapidly upward through the overlying lowportion of the umbral photosphere and chromosphere ( ). As the fast wave fronts impinge upon the penumbral “magnetic canopy” from above, they interfere with the outward-propagating field-guided slow waves, and they also mode convert to (non-magnetic) acoustic-gravity waves as they penetrate into the weak magnetic field region which lies between the penumbral canopy and the base of the surrounding photosphere. In a three-dimensional situation, one expects additional generation, mixing and interference with the remaining torsional Alfven waves.

Longitudinal spin transport in diluted magnetic semiconductor superlattices: The effect of the giant Zeeman splitting

Longitudinal spin transport in diluted magnetic semiconductor superlattices is investigated theoretically. The longitudinal magnetoconductivity (MC) in such systems exhibits an oscillating behavior as function of an external magnetic field. In the weak magnetic field region the giant Zeeman splitting plays a dominant role which leads to a large negative magnetoconductivity. In the strong magnetic field region the MC exhibits deep dips with increasing magnetic field. The oscillating behavior is attributed to the interplay between the discrete Landau levels and the Fermi surface. The decrease of the MC at low magnetic field is caused by the $s-d$ exchange interaction between the electron in the conduction band and the magnetic ions.

Bound state of the quantum dot formed at intersection of L- or T-shaped quantum wire in inhomogeneous magnetic field

A quantum dot (QD) can be formed at the intersection of the symmetric or asymmetric L-shaped (LQW) or T-shaped quantum wire (TQW). The bound state energies in such QD systems surrounded by inhomogeneous magnetic fields are found to depend strongly on the asymmetric parameter α=W2/W1, i.e., the ratio of the arm widths and magnetic field applied on the wire arms. Two effects of the magnetic field on the bound state energy of the electron can be obtained. One is the depletion effect which purges the electron out of the QD system. The other is to create an effective potential due to the quantized Landau levels of the magnetic field. Depletion effect is found to be more prominent in weak field region. Our results show the bound state energy of the electron in such QD system depends quadratically (linearly) on the magnetic field in the weak (strong) field region. It is also found that the bound state energy of the electron depends on the magnetic field strength only and not on its direction. A simple model is proposed to explain the behavior of the magnetic dependence of the bound state energy of the electron both in weak and strong magnetic field regions. The contour plots of the relative probability of the bound state in LQW or TQW in magnetic field are also presented.

Bound states of L- or T-shaped quantum wires in inhomogeneous magnetic fields

The bound state energies of L-shaped or T-shaped quantum wires in inhomogeous magnetic fields are found to depend strongly on the asymmetric parameter $\alpha =W_{2}/W_{1}$, i.e. the ratio of the arm widths. Two effects of magnetic field on bound state energies of the electron are obtained. One is the depletion effect which purges the electron out of the OQD system. The other is to create an effective potential due to quantized Landau levels of the magnetic field. The bound state energies of the electron in L-shaped or T-shaped quantum wires are found to depend quadratically (linearly) on the magnetic field in the weak (strong) field region and are independent of the direction of the magnetic field. A simple model is proposed to explain the behavior of the magnetic dependence of the bound state energy both in weak and strong magnetic field regions.

Electronic and Transport Properties of Boronated Graphite — 3D-Weak Localization Effect —

Boronated graphite sample with B4C contents of few wt% exhibit characteristic of 3D-weak localization at low temperatures and in weak magnetic field region. A boron atom supplies one hole and the Fermi surface with E F = −0.4 eV (1 wt% sample) is composed of the two hole bands E 1- and E 2- and the electron Fermi surface disappears. E 1- band (majority hole) plays a dominant role in the 3D-weak localization. Kawabata theory is extended to the SWMcC-band and the present theory well explains the resistivity, magnetoresistance and Hall effect behaviors.

Dayside isotropic precipitation of energetic protons

Abstract. Recently it has been shown that isotropic precipitation of energetic protons on the nightside is caused by a non-adiabatic effect, namely pitch-angle scattering of protons in curved magnetic field lines of the tail current sheet. Here we address the origin of isotropic proton precipitation on the dayside. Computations of proton scattering regions in the magnetopheric models T87, T89 and T95 reveal two regions which contribute to the isotropic precipitation. The first is the region of weak magnetic field in the outer cusp which provides the 1–2° wide isotropic precipitation on closed field lines in a ~2–3 hour wide MLT sector centered on noon. A second zone is formed by the scattering on the closed field lines which cross the nightside equatorial region near the magnetopause which provides isotropic precipitation starting ≈ 1.5–2 h MLT from noon and which joins smoothly the precipitation coming from the tail current sheet. We also analyzed the isotropic proton precipitation using observations of NOAA low altitude polar spacecraft. We find that isotropic precipitation of >30 to >80 keV protons continues around noon forming the continuous oval-shaped region of isotropic precipitation. Part of this region lies on open field lines in the region of cusp-like or mantle precipitation, its equatorward part is observed on closed field lines. Near noon it extends ~1–2° below the sharp boundary of solar electron fluxes (proxy of the open/closed field line boundary) and equatorward of the cusp-like auroral precipitation. The observed energy dispersion of its equatorward boundary (isotropic boundary) agrees with model predictions of expected particle scattering in the regions of weak and highly curved magnetic field. We also found some disagreement with model computations. We did not observe the predicted split of the isotropic precipitation region into separate nightside and dayside isotropic zones. Also, the oval-like shape of the isotropic boundary has a symmetry line in 10–12 MLT sector, which with increasing activity rotates toward dawn while the latitude of isotropic boundary is decreasing. Our conclusion is that for both dayside and nightside the isotropic boundary location is basically controlled by the magnetospheric magnetic field, and therefore the isotropic boundaries can be used as a tool to probe the magnetospheric configuration in different external conditions and at different activity levels.

Magnetotransport Through Antidot Lattices: How Does It Depend on Antidot Diameter?

Electron transport through square arrays of antidots in a magnetic field is numerically studied for various antidot diameters. Using the linear response theory, we find two features: (1) At the magnetic field of the main peak in the resistivity, there is an optimum antidot diameter at which the conductivity is maximized. (2) In the region of weak magnetic field, negative Hall conductivity is observed. The range of the magnetic field in which the conductivity is negative becomes large when the antidot diameter is increased. Further the origins of the above features are clarified in connection with the classical trajectories of the electron.

3-D magnetic field and current system in the heliosphere

In this paper a global system of the magnetic field and current from the interaction of the solar wind plasma and the interstellar medium is modeled using a 3-D MHD simulation. The terminal shock, the heliopause and the outer shock are clearly determined in our simulation. In the heliosheath the toroidal magnetic field is found to increase with the distance from the sun. The magnetic field increases rapidly in the upstream region of the heliosheath and becomes maximum between the terminal shock and the heliopause. Hence a shell-type magnetic wall is found to be formed in the heliosheath. Because of this magnetic wall the radially expanding solar wind plasma changes its direction tailward in all latitudes except the equatorial region. Only the equatorial disk-like plasma flow is found to extend to the heliopause through the weak magnetic-field region around the equator. Two kinds of global current loops which sustain the toroidal magnetic field in the heliosphere are found in our simulation.

Magnetohydrodynamic stability of an axisymmetric mirror device with ‘‘massive’’ end-sections

Magnetohydrodynamic (MHD) stability of an axisymmetric mirror device with long end-sections filled with a collisional plasma is studied. It is shown that unstable perturbations in such a system, if they exist, are localized at a distance ∼vA/Γ near the central cell (vA is the Alfvén velocity and Γ is the growth rate). Perturbations of the magnetic field do not penetrate into regions where plasma beta is greater than unity. Therefore, regions of weak magnetic field has a stabilizing effect on MHD-perturbations.

Magnetopolaron in a Rectangular Harmonic Quantum Wire

Cyclotron resonance of a magnetopolaron in a rectangular harmonic quantum wire with magnetic field normal to the quantum wire is investigated theoretically. The results we obtained show that, the Landau levels in the quantum wire are raised relative to those in two-dimensional quantum well due to the addition of a parabolic potential. The results also show that, the cyclotron frequency and cyclotron mass of 1D polaron are very different from those of 2D polaron, especially for weak magnetic field region

Self-energy of a magnetopolaron at the interface of polar crystals

The self-energy of an interface electron interacting with bulk longitudinal-optical phonons as well as interface optical (IO) phonons in a magnetic field of arbitrary strength is studied using the Green function method. Our results show that the absolute value mod Ee-ph(0) mod of the ground-state self-energy of the electron is a rapidly increasing function of the magnetic field in the weak magnetic-field region, but mod Ee-ph(0) mod is a slowly decreasing function of the magnetic field beyond a critical magnetic field Bc. For the excited states, mod Ee-ph(n) mod (n>or=1) is an increasing function of the magnetic field in the pre-resonant region, while Ee-ph(n) is a positive and decreasing function of the magnetic field beyond the resonant region. Numerical results show that the electron-IO phonon interaction contributes only when the mean distance of the polaron from the interface is small and in the extremely-weak-magnetic-field region.

Hopping conduction in disordered systems in the presence of a magnetic field: Linearized rate equation and magnetoresistance

Rate equations are derived, in the linear approximation with respect to the electric field, for hopping transport in disordered systems in the presence of a magnetic field H. The resulting system of linear equations is in general not equivalent to a random resistor network. By means of an effective-medium approximation, an analytical expression for the magnetoresistance \ensuremath{\Delta}\ensuremath{\sigma}(H) has been obtained for R hopping. In the case of strong coupling with phonons, \ensuremath{\Delta}\ensuremath{\sigma}(H) is independent of the temperature T and it is proportional to ${\mathit{H}}^{2}$ in the region of weak magnetic fields. For weak coupling with phonons, we find that \ensuremath{\Delta}\ensuremath{\sigma}(H)\ensuremath{\sim}${\mathit{H}}^{2}$/T. $DELTA sigma (H)--- shows a monotonic behavior in a wide range of magnitude of the magnetic field. It does not exhibit an oscillating contribution. The sign of \ensuremath{\Delta}\ensuremath{\sigma}(H) depends on the character of the conductivity (electronlike or holelike). \ensuremath{\Delta}\ensuremath{\sigma}(H) approaches zero at some point if one varies the chemical potential.

Hall electron density and mobility in HgCdTe alloys with anomalous behavior of the Hall coefficient in weak magnetic field

It is difficult to extract unique values of the Hall electron density, nH, and Hall mobility, μH, in indium-doped Hg1−xCdxTe alloys usually in a region of weak magnetic fields where the Hall coefficient RH behaves anomalously. Since this is also the field region where the weak magnetic field condition of semiclassical transport equations is valid, derivatives of Hall resistivity ρxy(B) and the ratio (Hall angle) of ρxy(B) and transverse resistivity ρxx(B) with respect to the field are used to determine unique values of the weak magnetic field nH and μH. This analysis reduces to calculating the slopes of ρxy(B) and ρxy(B)/ρxx(B) in the region of weak magnetic fields where linearity is observed. The conductivity, σ0, determined from the ratio of the slopes is compared to the zero magnetic-field experimental value. The conductivities agree to within 10%, indicating that nH is constant in contrast to the RH result. The values of nH determined from the slopes are in very good agreement with the values of nH determined from a high magnetic field RH and from the period of Shubnikov–de Haas oscillations in heavily doped alloys.

Effects of permanent magnet arrangements and antenna locations on the generation of multicusp electron cyclotron resonance plasma

A comparative study on the generation of 2.45-GHz multicusp electron cyclotron resonance (ECR) plasma is performed. Looped cusp structures such as the ring-cusp give a low-power and low-pressure ignition, and vice versa, indicating an importance to keep the electron trajetory of gradient-B drift motion inside the chamber even in the case of ECR plasmas. The importance of the antenna location in such multicusp fields is elucidated by comparison in two cases of the axial antenna located in the weak magnetic field region, generating a hydrogen plasma of limited density (ne<7.4×1010 cm−3), and a radial antenna located in the strong magnetic field region, generating an overdense plasma (ne∼2×1011 cm−3).

Influence of twinning planes on upper critical fields

Within the framework of a Ginzburg-Landau theory for a scalar order parameter, we discuss the effect of the presence of twinning planes on the behavior of the upper critical field as function of the temperature. In particular we study the case of a finite array of planes in the region of weak magnetic field, both from the analytical and the numerical point of view.

Some hydrodynamic investigations of a magnetically stabilized air-fluidized bed of ferromagnetic particles

To gain fundamental understanding about the structure of a magnetically stabilized bed, an experimental facility has been designed, fabricated and tested. In particular, experimental data on spherical steel shots of three different sizes are reported as a function of increasing and decreasing fluidization velocities. Experimental data of bed pressure drop, bed voidage and mass minimum bubbling velocity reveal that bed behavior and its structure can be understood in terms of three broad categories of the applied uniform magnetic field intensity. The bed properties and its distinguishing features in the weak, moderate and strong magnetic field regions are reported. Earlier in the literature, somewhat similar classifications have been proposed on the basis of heat transfer and theological measurements.

Asymmetric time‐dependent and stationary magnetic reconnection at the dayside magnetopause

Using a two‐dimensional compressible MHD code we have numerically studied the reconnection process at an interface where (1) the magnetic field is higher on one side than on the other and total pressure is in balance by a higher density on the weak field side, and where (2) the magnetic field is identical on both sides, but the temperature is higher on one side than on the other. Reconnection is caused by applying a localized resistivity in the center of the current sheet. The plasma is allowed to enter and exit freely at the boundaries. By using a system size with a large extension parallel to the current sheet, we are able to study time‐dependent as well as steady state effects. Denoting the weak magnetic field or low temperature region as magnetosheath and the high magnetic field or high temperature region as magnetosphere we find the following. Sudden onset of reconnection causes the development of a bulge in the current layer. The bulge moves with about 70% of the magnetosheath Alfvén speed along the magnetopause away from the reconnection region. The growth of the bulge normal to the magnetopause is proportional to the reconnection rate. For a ratio of magnetospheric to magnetosheath magnetic field larger than about 1.5 the bulge is almost exclusively on the magnetosheath side of the magnetopause current layer. The motion of the bulge along the magnetopause leads to signatures in the normal magnetic field component similar to the ones observed in flux transfer events. When the bulge has moved far enough from the reconnection site, stationary reconnection proceeds at the X line. If there exists initially a magnetic field difference across the magnetopause current layer, a slow mode shock is formed in the magnetosphere and possibly a strong intermediate shock is formed in the magnetosheath. The magnetosheath plasma is accelerated to about twice the magnetosheath Alfvén speed and constitutes a boundary layer on the magnetospheric side of the magnetopause current layer.

Dynamics of decaying two-dimensional magnetohydrodynamic turbulence

High-resolution numerical studies of decaying two-dimensional magnetohydrodynamic turbulence were performed with up to 10242 collocation points in general periodic systems using various initial states, but restricting consideration to weak velocity-magnetic field correlation ρ. The global evolution is self-similar with constant kinetic to magnetic energy ratio EV/EM, macro- and microscale Reynolds numbers, and correlation ρ, while the total energy decays as E(t)∝(t+t0)−1. As in three dimensions, dissipative small-scale turbulence adjusts in such a way as to make the energy dissipation rate ε independent of the collisional dissipation coefficients. Normalized energy spectra are also invariant. The spectral index in the inertial range is, in general, close to 3/2 in agreement with Kraichnan’s Alfvén wave argument Ek =DB1/2ε1/2k−3/2, B=(EM)1/2, D≂1.8±0.2, but may be close to 5/3 in transient states, in which turbulence is concentrated in regions of weak magnetic field. In the dissipation range, intermittency gives rise to a modified dissipation scale leff =(l2λ)1/3, with l=Kolmogorov scale and λ=Taylor microscale. This reflects the intermittency of the dissipation process, which is consistent with the picture of current microsheets of thickness l and width and spacing λ.

Motion of trapped electrons in gyro-resonant electromagnetic field

It is shown that the phase space of magnetically trapped electrons in plasmas interacting with gyro-resonant electromagnetic waves is divided into two parts. In one, as a particle gains energy its turning point moves towards the region of weaker magnetic field; in the other, energy gain results in the turning point moving towards the region of stronger magnetic field, with possible detrapping.

On the generation of field‐aligned plasma flow at the boundary of the plasma sheet

This paper deals with a possible cause of the large plasma flow velocities parallel to the magnetic field observed near the boundary of the plasma sheet in the earth's magnetotail. For a large class of steady state configurations with typical cases involving magnetic reconnection we first show qualitatively that high parallel flow velocities can be expected to exist on field lines connecting to a region of weak magnetic field. For reconnection configurations this weak field region contains the diffusion region. The maximum value of the parallel flow velocity is sensitive to the lowest magnetic field magnitude just outside the diffusion region. The physical mechanism causing large values of the parallel velocity component υ∥ can be visualized as a strong imbalance of perpendicular mass flux into and out of magnetic flux tubes passing through regions where the magnetic field is weak and inhomogeneous. In a steady state the unbalanced perpendicular flow requires large parallel flow to establish mass conservation. The presence of a parallel velocity is not unusual in MHD systems. The new (generic) aspect is that near the separatrix, parallel flow is the dominant form of plasma transport. For a quantitative evaluation we consider an MHD model specialized for the domains where the inertia force can be neglected. By a self‐consistent treatment we evaluate υ∥ and find that |υ∥| can substantially exceed the perpendicular velocity υ⊥ = E/B; in a typical example with stretched magnetic field lines we obtain |υ∥| ≈ 40υ⊥. We apply our results to the earth's magnetotail and conclude that this mechanism is able to explain the parallel flow velocities near the boundary of the plasma sheet in the range of several hundreds of kilometers per second.