Perpendicular Conductivity Research Articles

Nonlinear magnetohydrodynamics simulation using high-order finite elements

A conforming representation composed of 2D finite elements and finite Fourier series is applied to 3D nonlinear non-ideal magnetohydrodynamics using a semi-implicit time-advance. The self-adjoint semi-implicit operator and variational approach to spatial discretization are synergistic and enable simulation in the extremely stiff conditions found in high temperature plasmas without sacrificing the geometric flexibility needed for modeling laboratory experiments. Growth rates for resistive tearing modes with experimentally relevant Lundquist number are computed accurately with time-steps that are large with respect to the global Alfvén time and moderate spatial resolution when the finite elements have basis functions of polynomial degree (p) two or larger. An error diffusion method controls the generation of magnetic divergence error. Convergence studies show that this approach is effective for continuous basis functions with p⩾2, where the number of test functions for the divergence control terms is less than the number of degrees of freedom in the expansion for vector fields. Anisotropic thermal conduction at realistic ratios of parallel to perpendicular conductivity ( χ ∥/ χ ⊥) is computed accurately with p⩾3 without mesh alignment. A simulation of tearing-mode evolution for a shaped toroidal tokamak equilibrium demonstrates the effectiveness of the algorithm in nonlinear conditions, and its results are used to verify the accuracy of the numerical anisotropic thermal conduction in 3D magnetic topologies.

Potentials and currents in the edge tokamak plasma: simplified approach and comparison with two-dimensional modelling

A method of reduction of the two-dimensional equation for the potential to a one-dimensional ordinary equation is suggested and implemented in the B2SOLPS5.0 transport code to simulate a divertor tokamak. The one-dimensional version, which gives similar results as the full two-dimensional version, provides better understanding of the role of various mechanisms of perpendicular conductivity and reduces computational time. The scheme of poloidal (parallel) current calculation is presented and compared to the two-dimensional code results both for the core region and for the scrape-off layer.

Discotic liquid crystals as quasi–one–dimensional electrical conductors

We have studied the electrical conductivity of well–aligned samples of hexahexylthiotriphenylene (HHTT) and hexapentyloxyanthraquinone (HPA) in the pure, as well as doped, states. The former compound was doped with 0.62 mol % by weight of the electron acceptor, trinitrofluorenone (TNF), the latter with 0.60 mol % by weight of the electron donor, anthracene. In the columnar phases, doping causes the AC (1 kHz) conductivity along the columnar axis (σ∥) to increase by a factor of 10 7 or more relative to that in undoped samples; σ∥ attains a value of 10 −2 S m −1 , which was the maximum measurable limit of our experimental set–up. On the other hand, in the isotropic phase, doping makes hardly any difference to the conductivity. The DC conductivity of doped HHTT exhibits an enormous anisotropy, σ ∥ /σ ⊥ ≥10 10 , which is seven orders of magnitude higher than that reported for any liquid crystalline system, and, to our knowledge, the largest observed in an organic conductor. Further, the perpendicular conductivity, σ ⊥ , reaches the insulating regime. Thus the columnar phases behave nearly as one–dimensional conductors and may be described as ‘molecular wires’. Thermoelectric power studies have also been carried out on the molecular wires that show a reversal of the sign on going from the p–type to the n–type system (positive for p–type and negative for n–type). This is in conformity with the expected nature of the charge carriers, namely, holes in HHTT + TNF (p–type) and electrons in HPA+anthracene (n–type). It is pointed out that since the doped systems behave nearly as one–dimensional conductors unusual physical properties might be anticipated. Finally, we discuss very briefly some further studies that are under way.We propose to adopt the four–probe method to increase the highest measurable conductivity to the metallic range (after eliminating the lead and contact resistances) with a view to finding metallic conductivity in discotic liquid crystals. We also intend to carry out Hall–effect studies and to explore the possibility of observing superconductivity by looking for the Meissner effect in magnetic susceptibility measurements.

Radial electric field in the biasing experiments and effective conductivity in a tokamak

The biasing experiments and the problem of the effective perpendicular conductivity in a tokamak are studied both analytically and numerically. The simulations were performed by means of the B2SOLPS5.0 transport code [V. A. Rozhansky et al., Nucl. Fusion 41, 387 (2001)] where the fluid set of equations is solved for the real divertor geometry. It is demonstrated that there exist three regimes, which correspond to the different values of the effective perpendicular conductivity and to different profiles of the radial electric field and toroidal and poloidal rotations. Simulation results are compared with existing and developed analytical models.

Effect of ion-neutral charge exchange on radial electric fields in the edge plasma

A fluid treatment of the perpendicular plasma conductivity is extended to include the effects of arbitrary ion-neutral collision frequency ν and large perpendicular drifts. It is shown that ion-neutral friction (charge-exchange) can give a nonmonotonic relationship between the nonambipolar radial current and the radial electric field, leading to a bifurcated plasma equilibrium. This bifurcation may influence the properties of the low-to-high-confinement (L-H) transition in the presence of neutrals. The physical origin of this effect is an interplay between the surface-averaged equilibrium drifts and the small poloidal variations in the pressure and parallel flow around the flux surface generated by the geodesic curvature.

Exponentially growing tearing modes in Rijnhuizen Tokamak Project plasmas.

The local measurement of the island width w, around the resonant surface, allowed a direct test of the extended Rutherford model [P. H. Rutherford, PPPL Report-2277 (1985)], describing the evolution of radiation-induced tearing modes prior to disruptions of tokamak plasmas. It is found that this model accounts very well for the observed exponential growth and supports radiation losses as being the main driving mechanism. The model implies that the effective perpendicular electron heat conductivity in the island is smaller than the global one. Comparison of the local measurements of w with the magnetic perturbed field B showed that w proportional to B1/2 was valid for widths up to 18% of the minor radius.

Phonon propagation in nonpolar semiconductor heterostructures

A recently developed long-wavelength continuum phenomenological model is employed to study phonon tunneling for an arbitrary incidence angle, and to estimate the contribution of optical phonons to the perpendicular thermal conductivity in simple and multisuperlattice nonpolar semiconductor heterostructures. Phonon tunneling is a multicomponent problem with different tunneling channels. We rigorously define the transmission and reflection coefficients from the energy density balance equation. Simple general rules are presented for the relationship between (a) the key features of the transmission and reflection rates, and (b) the vibrational properties. The range of applicability of the model is increased by simultaneously considering both acoustic and optical phonons. The defined coefficients are employed to test the interrelationship between the coupled modes. Interesting oscillation effects in the relative contribution of different coefficients as a function of the incidence angle are found. We report numerical results for isotopic Ge superlattices to illustrate the model considered. Approximate analytical expressions for the dispersion relation are derived for this system. The contribution of optical phonons to the thermal conductivity is elucidated with the help of these expressions.

Simulation of tokamak edge plasma including self-consistent electric fields

A complete system of transport equations with all the important perpendicular currents is derived for the simulation of tokamak edge plasma. These transport equations are implemented in the B2.5 code and solved for the parameters of the ASDEX Upgrade tokamak. The relative roles of different mechanisms of transverse conductivity in the formation of the potential profile are studied. It is demonstrated that a reasonable potential distribution in the tokamak edge plasma can be obtained without an ad hoc assumption of the existence of the anomalous perpendicular conductivity. The role of E × B drifts in the redistribution of edge plasma and closing of the currents in the plasma is analysed.

Optical, electrochemical and conductive properties of polythiophene multilayers on ITO/glass electrodes

Polythiophene-based polyelectrolyte multilayers have been layer-by-layer deposited on ITO/glass and characterized by UV-vis spectroscopy, cyclic voltammetry and conductivity. Multilayers in which both polycation and polyanion are based on the same polythiophene backbone are reported for the first time. Uv-vis spectroscopy and cyclic voltammetry indicate a linear dependence of the amount of deposited polymer on the number of deposition cycles. The amount of deposition depends on the oxidation state of the polythiophene. The sheet and perpendicular conductivities of the multilayers and their photoluminescence properties are reported.

Nonlinear thermal instability in two dimensions

Nonlinear thermal disturbances are analyzed for a two-dimensional structure taking into account thermal conduction parallel to and perpendicular to the magnetic field, as well as heating and cooling effects. In general, small structures are linearly stable while larger ones are unstable. Heat conduction perpendicular to the field has a stabilizing effect and increases the maximum stable size of a structure. In many cases, the second-order growth rate is positive (enhancing heating but preventing cooling) for very large structures and is negative (opposite effect) otherwise. The perpendicular conduction causes a negative correction other than for the largest structures. This perpendicular conduction is particularly important for structures in the marginal linear state; strong cooling occurs in the absence of perpendicular conduction but if such conduction is included and is strong enough, catastrophic heating may occur. Perpendicular heat conduction is found to be most significant in long, thin, cool structures.

The generation of poloidal pressure gradients in the SOL of TdeV by plate biasing

In the TdeV tokamak, the convection of the plasma towards the divertors can be studied by changing the radial electric field in the scrape-off-layer (SOL) through biasing the divertor plates relative to the vacuum vessel wall. Electrostatic probes were used to determine the plasma parameters on both the outboard midplane and the bottom of the discharge. From these measurements, poloidal differences in the electron kinetic pressure were seen to arise due to the application of the biasing voltage on the neutralizer plates and that these pressure differences were correlated to the changing radial electric field. By using a linear relation between the poloidal kinetic pressure drop and the radial electric field averaged between the two observation points, an experimental value of 8.8 × 10 −3 (Ω m) −1 is obtained for the perpendicular conductivity. A comparison with current models would tend to favor inertia and viscosity over friction with neutrals to counterbalance the j × B force during biasing although the scaling of the conductivity with the toroidal magnetic field, plasma density and plasma current should be verified to confirm this conclusion.

Effective conductivities of rectangular arrays of aligned spheroids

The effective conductivities (σeff) of rectangular arrays of aligned spheroids are accurately determined. The array structure is governed by the array aspect ratio (ra), inclusion aspect ratio (ri), and inclusion volume fraction ( f ). By varying these three parameters, a wide range of array structure can be generated and the effects of the three parameters on the effective conductivities of the array are investigated. The present array is found to be a more efficient structure in utilizing the enhancing or reducing effect of the inclusion, as compared to the simple cubic array of spheres. For cases of equal ra and ri, the effective parallel conductivity (σeff=) increases, while the effective perpendicular conductivity (σeff+) decreases with increasing aspect ratio, but both are only a weak function of the aspect ratio if the reduced conductivity of the inclusion (σ) is within the range of 0.1–10. At a fixed ri, σeff= decreases while σeff+ increases with increasing ra. If ra is fixed, σeff= increases while σeff+ decreases with increasing ri. For prolate systems (ri>1), σeff= is greater than σeff+ for all permissible f if ri⩾ra, but the magnitude order switches at higher f when ri<ra. As to oblate systems (ri<1), σeff= is less than σeff+ for all permissible f if ri⩽ra, but the magnitude order switches at higher f when ri>ra.

Solitary radial electric field structure in tokamak plasmas

The solitary structure solution of the radial electric field Er in the tokamak plasmas is obtained. It is shown to be stable under an external power supply, like a biased electrode at the edge. The radial gradient is governed by the ion viscosity and the nonlinearlity of the perpendicular conductivity. The radial structure of Er and reduction of turbulent transport, which belong to key issues of the high confinement mode (H-Mode) [F. Wagner et al., Phys. Rev. Lett. 49, 1408 (1982)], are self-consistently determined. A bifurcation from a radially-uniform one to a solitary one occurs at a certain applied voltage, and a hysteresis is associated.

Radiation fronts in tokamak divertor plasmas

The impurity radiation from a tokamak divertor can be significantly enhanced due to the formation of a V-shaped impurity radiation front and the effects of perpendicular plasma heat conduction. For some conditions, the transition to a V-shaped radiation front can have a bifurcation character, such that the impurity radiation region jumps from the divertor targets to the entrance into the divertor. The divertor geometry can play a significant role in the formation of a V-shaped impurity radiation front. The analysis of the energy transport and impurity radiation suggest that divertor geometries with “vertical” target, neutral gas recirculation where sidewalls, or their combination are the most attractive from the point of view of the formation of a V-shaped radiation front and the plasma energy loss.

Conduction of electrons on liquid helium along channels produced by multi-layer microfabrication

We demonstrate the conduction of free electrons along an array of microchannels of liquid helium, 30 μm wide, 1 μm deep and 1.5 mm long, held by surface tension between conducting ribs. No perpendicular conduction occurs until the bulk helium level rises above the channels.

Photothermal approach to magnetoresistance monitoring in magnetic multilayers

Photothermal methods were used to monitor thermal effects related to magnetoresistance of epitaxial magnetic metallic multilayers, in a direction perpendicular to the layers, as a function of the applied magnetic field. Photothermal signal changes induced by thermal conductivity variations were modeled in order to determine the suitable experimental conditions according to the technique used. Both photothermal microscopy and mirage detection were successfully applied to such measurements. For the sample studied here, a magneto induced perpendicular conductivity variation of ∼6% was determined.

Physical Characterization and Electrical Transport in End-Group Functionalized Self-Assembled Monolayers

AbstractWe have previously demonstrated that a self-assembled monolayer (SAM) of alkyltrichlorosilane molecules, covalently bonded to the native oxide of a silicon substrate, allows the fabrication of MIS (Metal-Insulator-Semiconductor) devices with excellent electrical properties [1]. Here we demonstrate that we can functionalize, with π-electron moieties, the end-groups of the molecules, once grafted to the substrate, without disturbing the low conductivity through the SAM (σ⊥), while strongly increasing the in-plane conductivity (σ//). The functionalization of the monolayer is monitored by FTIR, ellipsometry and X ray reflectivity. Conductivity, photoconductivity and capacitance measurements are carried out to study the effect of these chemical functionalizations on the electrical properties of the monolayers. We demonstrate that the low perpendicular conductivity (σ⊥≈10−15 S/cm) is not altered by the end-group functionalities while high anisotropic conductivities (σ///σ⊥ ≈ 107-108) are obtained at a monolayer level. Interfacial (Si/SAM and SAM/metal) energy barriers are investigated as a function of the end-group functionalities. We also show that conducting monomers substituted by alkyl chains (3,6- dibromocarbazole-N-octyltrimethoxysilane), directly grafted to the substrate, exhibit similar behavior.

Resonant tunneling and perpendicular conduction in cuprate conductors with varying O-content

Anisotropy is inherent to layered cuprates with conduction mainly confined to the CuO2-planes, claimed to be the source of superconductivity. Resonant tunnel exchange for conduction parallel and perpendicular to the CuO2-planes shows different normal and superconducting properties by charging energies and localizations at the in-plane perturbations being atomic-like and between the CuO2-planes, being extended. By overdoping the wave function overlap in perpendicular direction via the extended states grows, especially in the superconducting state. The counteraction of overlap and charging energies yield activated resonant tunneling, i.e. the pseudo gap, in the normal state and Josephson tunneling in the superconducting state.

Photothermal measurement of thermal anisotropy in pyrolytic graphite

We investigated the anisotropic thermal conductivity in pyrolytic graphite by thermoreflectance. A laser-heated circular spot on a surface perpendicular to the planes developed into an elliptical temperature distribution which was recorded by a raster scanning technique at modulation frequencies ranging from 600 Hz to 100 kHz. The ratio of in-plane and perpendicular thermal conductivity was determined by fitting the phase of the temperature data with an analytical model, and was found to decrease with increasing modulation frequency. Highest conductivity values were considerably smaller than previously published data based on steady-state measurements. The frequency dependence and additional features in the phase profiles at high frequencies are discussed in view of sample surface preparation and the local nature of the thermoreflectance measurement.

Analytic solutions of the two-dimensional transport equation in scrape-off-layer plasmas

Exact analytic solutions of the two-dimensional (2D) heat transport equation in scrape-off-layer (SOL) plasmas are obtained for the plausible heat conductivity models. The temperature and the temperature-gradient dependences of parallel and perpendicular heat conductivities are taken into account as and , respectively. For arbitrary values of , and , the analytic solutions are found when separation of variables is allowed. The poloidal profile of the heat flow from the core across the separatrix is consistently parametrized. A weak dependence of the global scaling law on this profile is found, which gives a basis on which to use a point model.