Function Of Magnetic Flux Research Articles

Interplay of Coulomb blockade and Aharonov-Bohm resonances in a Luttinger liquid

We consider a ring of strongly interacting electrons connected to two external leads by tunnel junctions. By studying the positions of conductance resonances as a function of gate voltage and magnetic flux the interaction parameter $g$ can be determined experimentally. For a finite ring the minimum conductance is strongly influenced by device geometry and electron-electron interactions. In particular, if the tunnel junctions are close to one another the interaction-related orthogonality catastrophe is suppressed and the valley current is unexpectedly large.

Nonlinear axisymmetric resistive magnetohydrodynamic equilibria with toroidal flow

The equilibrium of a resistive axisymmetric plasma with purely toroidal flow surrounded by a conductor is investigated within the framework of nonlinear magnetohydrodynamic theory. It is proved that (a) the poloidal current-density vanishes and (b) apart from an idealized case, the pressure profile should vanish on the plasma boundary. For the cases of isothermal magnetic surfaces, isentropic magnetic surfaces and magnetic surfaces with constant density, the equilibrium states obey an elliptic partial differential equation for the poloidal magnetic flux function, which is identical in form to the corresponding equation governing ideal equilibria. The conductivity, which can be neither uniform nor a surface quantity, results, however, in a restriction of the possible classes of equilibrium solutions; for example for the cases considered, the only possible equilibria with Spitzer conductivity are of cylindrical shape.

Identification of a free boundary arising in a magneto-hydrodynamics system

We study the free boundary problem to identify the plasma region in a stationary tokamak machine using the magnetic flux function. Uniqueness has been proved and the free boundary has been explicitly computed in the case where the domain is an n-dimensional ball. We also derive an energy distribution identity which is applicable to identify the location of the free boundary for more general domains in two-dimensional space.

Structure of the n = 1 mode responsible for relaxation and current drive during sustainment of the SPHEX spheromak

The structure of the n = 1 mode in the SPHEX spheromak, which plays a central role in relaxation during sustainment, is investigated by analysing the measured voltage fluctuations in the central plasma column. By combining these results with a suitably defined helical magnetic flux function, the mode is found to be due to a rotating helical distortion of the open linked flux. We propose that the distortion is due to a saturated current-driven kink mode of the open flux tube. The prolongation of this `helical column' on its return around the outside of the closed flux is found to be strongly asymmetric. Previously published measurements of the Poynting flux and -profile are re-analysed in the light of these results, and implications for the mechanism of relaxation and non-inductive current drive are discussed.

The Kondo effect in Bohm-Aharonov resonant tunneling devices

The Bohm-Aharonov effect in a mesoscopic ring containing a double-barrier structure in its upper part is investigated. The interference between electrons propagating along different sides of the ring is modified by the presence of a double barrier. A local Coulomb interaction, U, is included to describe the highly localized electrons at the well and an Abrikosov-Suhl (AS) resonance appears at low temperatures. So, in this energy range the current is flux dependent. Above the Kondo temperature T K the AS resonance disappears and the flux-independent behavior is recovered. The current is studied as a function of magnetic flux, gate potential and position of the Fermi level.

Magnetoconductance fluctuations in a strongly correlated disordered ring system at low temperatures

Using a recursive real-space Green's-function technique in the tight-binding model, we study the influence of the electron-electron Hubbard interaction on the magnetoconductance fluctuations in a disordered ring at low temperatures. Our numerical results improve the previous theoretical predictions for the magnetoconductance fluctuations as a function of magnetic flux compared with experiments. Meanwhile, we find several anomalous phenomena at low temperatures, which do not survive at high temperatures. For the Fermi level ${\mathit{E}}_{\mathit{f}}$=0.1t (t is the hopping integral) the envelope of magnetoconductance fluctuations drops to a lower value at some magnetic flux, while the Hubbard interaction causes the drop to occur at larger flux. The magnetoconductance fluctuations vary with the Hubbard interaction for magnetic flux around 20${\mathrm{\ensuremath{\Phi}}}_{0}$(${\mathrm{\ensuremath{\Phi}}}_{0}$=hc/e) mainly in the range of small U. The Hubbard interaction narrows the widths of the main peaks in the Fourier spectrum, but it does not change their positions. \textcopyright{} 1996 The American Physical Society.

Electronic thermal capacity in one-dimensional mesoscopic rings

We have investigated the Aharonov-Bohm (AB) effects of electronic thermal capacityCv in a one-dimensional normal ring using the free-electron model. The results show that the thermal capacity is an oscillation function of external magnetic flux with periods ϕ0=hc/e, ϕ0/2, ϕ0/3,... The amplitude of the capacity fluctuation decreases when temperature increases forT>3T* (T*=ħ VF/(KBπL)). We suggest an appropriate temperatureT∼3T* to observe in experiment the capacity-flux characteristic for metallic rings.

Aharonov–Bohm effect induced by light in a fiber

A weakly coupled normal-metal ring surrounding an optical fiber is considered under the condition that the frequency of light in fiber is larger than the conduction bandwidth of the metal. It is shown that in the presence of static magnetic field parallel to the fiber axis, the resistance of the ring is a nonmonotone function of the optical intensity and an oscillating function of the static magnetic flux with period equal to flux quantum hc/e. The temperature dependence of oscillations requires that inelastic mean free path of electrons is larger than the ring size, and does not relate to the energy level spacing to temperature ratio.

Magnetohydrodynamic equilibria of a cylindrical plasma with poloidal mass flow and arbitrary cross sectional shape

The equilibrium of a cylindrical plasma with purely poloidal mass flow and cross section of arbitrary shape is investigated within the framework of the ideal MHD theory. For the system under consideration it is shown that only incompressible flows are possible and, consequently, the general two-dimensional flow equilibrium equations reduce to a single second-order quasilinear partial differential equation for the poloidal magnetic flux function , in which four profile functionals of appear. Apart from a singularity occurring when the modulus of Mach number associated with the Alfvén velocity for the poloidal magnetic field is unity, this equation is always elliptic and permits the construction of several classes of analytic solutions. Specific exact equilibria for a plasma confined within a perfectly conducting circular cylindrical boundary and having (i) a flat current density and (ii) a peaked current density are obtained and studied.

A toroidal boundary-value problem in resistive magnetohydrodynamics

Under a standard set of assumptions, the magnetic flux function for a static, resistive magnetofluid is determined in axisymmetric toroidal geometry for two different scalar-conductivity profiles; in one case the conductivity is spatially uniform, and in the other it is proportional to the square of the distance from the toroidal axis. Exact analytic expressions are found in both cases for a magnetofluid that is surrounded by a perfectly conducting toroidal shell with a circular cross section.

Turbulent Two-Dimensional Magnetohydrodynamics and Conformal Field Theory

We show that an infinite number of non-unitary minimal models may describe two dimensional turbulent magnetohydrodynamics (MHD), both in the presence and absence of the Alf 'ven effect. We argue that the existence of a critical dynamical index results in the Alf 'ven effect or equivalently the equipartition of energy. We show that there are an infinite number of conserved quantities in 2D−MHDturbulent systems both in the limit of vanishing the viscocities and in force free case. In the force free case, using the non-unitary minimal modelM2, 7we derive the correlation functions for the velocity stream function and magnetic flux function. Generalising this simple model we find the exponents of the energy spectrum in the inertial range for a class of conformal field theories.

MHD Self-Similar Solutions for Collimated Jets

The MHD modelling of jets in axisymmetric geometry requires the treatment of the Bernoulli and the transfield equations, that can be treated following a self-similar approach. This technique is based on two main assumptions: i) the physical variables are factorized; ii) a suitable scaling law in one direction is prescribed. Solutions self-similar in the r direction (in a spherical frame of reference) have been studied to model collimated winds from disks (Blandford and Payne 1982). Here we present solutions self-similar in the θ direction, suitable to study the collimated wind around the polar axis of a rotating object (Tsinganos and Trussoni 1991, Sauty and Tsinganos 1994). Our basic assumptions are: –The magnetic flux function, that describes the poloidal components of velocity and magnetic field, is expressed as A(r, θ) ∝ f(r)sin2θ.–The density and the pressure of the plasma are assumed to scale linearly with A: ρ(r, θ) ∝ 1 + δA and P(r, θ) ∝ Po(r) (1 + KfA). Accordingly, the surfaces with equal poloidal Alfvén number M are spherical.

Tailward stretching of geomagnetic field lines in the presence of an enhanced ionospheric convection electric field

When the interplanetary magnetic field turns southward, dayside reconnection leads to an increase of open magnetic flux and an increase of the electric potential drop across the polar cap. The enhanced electrostatic field in the ionosphere can be mapped to the closed field region of magnetotail, contributing to a dawn‐to‐dusk electrostatic component of electric field in the plasma sheet. In the presence of this driving electric field, an adiabatic evolution of the plasma sheet is formulated in A‐space, where A is the magnetic flux function. It is found that the adiabatic evolution leads to the observed enhancement of the entropy content in the near‐earth plasma sheet and to a tailward stretching of geomagnetic field lines. As a result, the cross‐tail current in the near‐earth plasma sheet is strongly enhanced.

Three‐dimensional magnetospheric equilibrium with isotropic pressure

In the absence of the toroidal flux, two coupled quasi two‐dimensional elliptic equilibrium equations have been derived to describe self‐consistent three‐dimensional quasi‐static magnetospheric equilibria with isotropic pressure in an optimal (ψ,α,χ) flux coordinate system, where ψ is the magnetic flux function, χ is a generalized poloidal angle, α = ϕ‐δ(ψ,α,χ), ϕ is the toroidal angle, δ(ψ,α,χ) is periodic in ϕ, and the magnetic field is represented as B = ∇ψ × ∇α. A three‐dimensional magnetospheric equilibrium code, the MAG‐3D code, has been developed by employing an iterative metric method. The MAG‐3D code is the first self‐consistent three‐dimensional magnetospheric equilibrium code. The main difference between the three‐dimensional and the two‐dimensional axisymmetric solutions is that the field‐aligned current and the toroidal magnetic field are finite for the three‐dimensional case, but vanish for the two‐dimensional axisymmetric case. The toroidal magnetic field gives rise to a geodesic magnetic field curvature and thus a magnetic drift parallel to the pressure gradient direction, which gives rise to the field‐aligned current.

Conductance and persistent current in one-dimensional mesoscopic rings: Configuration-dependent effects of weak impurity scattering

The nonlinear electrical conductance and the persistent current in a one-dimensional conducting ring is calculated in the presence of an impurity potential. The impurity-induced corrections to the conductance and persistent current are shown to be sharp functions of voltage and magnetic flux. Even for weak scattering the corrections are very sensitive to the precise impurity configuration.

ECMC, a portable two-dimensional code for plasma equilibrium computation on coaxial-multiple-coil systems

A two-dimensional code ECMC for computing field-reversed configuration equilibria is described. Equilibrium states are found by solving the finite difference form of Grad-Shafranov equation by means of a successive over-relaxation method. Plasma rotation and the existence of a toroidal magnetic field component are not taken into account. Plasma trapped current is used as a constraint parameter to achieve an equilibrium state. The code computes any coaxial-multiple-coil system from the input data of coil positions in laboratory coordinates and their respective currents. It was written assuming neither a particular experimental device geometry nor a specific shape for the magnetic flux function in order to simulate the coils. Plasma pressure dependence as a function of the magnetic flux may be changed by providing a routine to replace that given by default. The code simulation includes the possibility of taking into account the infinite axial and radial coordinates. ECMC allows parameters (coil positions and currents, plasma trapped current, data to be written in output files, convergence criteria) to be changed interactively. Examples of simulated equilibria on different experimental devices are given.

Formation of thin current sheets in a quasistatic magnetotail model

Observations suggest that thin current sheets forming in the near‐Earth magnetotail late in substorm growth phases may be a crucial part of substorm evolution. In a simple theoretical model the current density was shown to become singular for suitable external perturbations. Here, we address the same problem in a more realistic model based on the adiabatic MHD ‐ theory developed by Schindler and Birn [1982]. We show that under suitable conditions the formation of a thin current sheet in the near‐Earth tail is an intrinsic aspect of flux transfer to the magnetotail. The mechanism is based on the strong variation of flux tube volume with the magnetic flux function.

An implicit FE-time solver for axisymmetric magnetic dynamo equations

Magnetic fields are an essential element in investigations for the behaviour of interstellar matter, molecular clouds, galactic disks, accretion disks for stellar and collapsed objects as well as for the collimation and propagation of galactic and extragalactic jets. The time-evolution of magnetic fields in such turbulent media follows from the mean-field electrodynamics which includes the effects of advection, shear, rotation, helicity and diffusivity of the underlying fluid. Under axisymmetry, the induction equation splits into a coupled system of diffusion-type equations for the magnetic flux function ψ ( t, R, z) and the poloidal current stream-function T ( t, R, z). For this non-linearly coupled system, a fully implicit time-solver has been developed based on the methods of finite elements. This code can easily be implemented on any modern RISC workstation. With this code, magnetic fields in galactic disks evolving on the Hubble time can be followed up. Similarly, the time-evolution of magnetic fields in accretion disks around stellar and compact objects can be simulated for a few hundred Keplerian revolution times.

Hall effect and magnetoresistance in four-probe tight-binding mesoscopic rings

The Hall effect and magnetoresistance of a mesoscopic system having a four-probe ring geometry are calculated in a tight-binding model, either ordered or disordered, as function of magnetic flux and Fermi energy. The changes induced in the spectrum by the magnetic field affect differently the Aharonov-Bohm (AB) oscillating pattern of the two resistances: after the gap reaches the Fermi energy, the Hall effect remains bounded while the magnetoresistance increases exponentially with the sample size. The results are shown to depend significantly on the number and geometry of the probes.

2D tomography with bolometry in DIII-Da)

A 48-channel platinum-foil bolometer system on DIII-D was installed to achieve better spatial and temporal resolution of the radiated power in diverted discharges. Two 24-channel arrays provide complete plasma coverage with optimized views of the divertor. The divertor radiation profile was measured for a series of radiative divertor and power balance experiments. A significant change in the magnitude and distribution of divertor radiation with heavy gas puffing was observed. Unfolding the radiation profile with only two views requires one to treat the core and divertor radiation separately. The core radiation is fitted to a function of magnetic flux and is then subtracted from the divertor viewing chords. The divertor profile is then fit to a 2D spline as a function of magnetic flux and distance from divertor floor.