External Conductors Research Articles

Electrostatic modeling and ESD damage of magnetoresistive sensors

The response of a thin-film sensor to the excessive current and/or voltage during an electrostatic discharge (ESD) event is studied. An unshielded magnetoresistive (MR)-like recording head structure is analyzed and modeled from the viewpoint of electrostatic theory. An electrical model for the MR head structure is proposed and used in circuit simulations to study the current flow through the thin-film resistor during a Human Body Model ESD transient. A thermal model for the thin-film resistor burnout is compared with experiment and 2D modeling of the fields and voltages are presented. Finally, Maxwell's method is used to calculate the induced charge on the MR structure when a charged external conductor is present.

Ion sheath formation in radiofrequency inductive discharges

The electron drift caused by fields arising from radiofrequency currents in external conductors is shown to be directed away from the conductors.

Towards magnetic centering of the discharge in a krypton flashlamp

The filamentary surface discharge, which occurs in a 2 bar krypton flashlamp before complete breakdown of the whole gas volume, has been guided along a rectilinear path using an earthed, external strip conductor. It has then been pushed away from the tube wall with an impulsionally applied magnetic field of order 0.2 T, reaching the axis of the 5-mm internal diameter lamp in a time of less than 1 ms.

Surface current equilibria from a geometric point of view

In this paper the inverse problem of the existence of surface current magnetohydrodynamic (MHD) equilibria in toroidal geometry with vanishing magnetic field inside is addressed. Inverse means that the plasma–vacuum interface rather than the external wall or conductors is given, and the latter remain to be determined. This makes a reformulation of the problem possible in geometric terms: what toroidal surfaces with analytic parametrization allow a simple analytic covering by geodesics? If such a covering by geodesics (field lines) exists, their orthogonal trajectories (current lines) also form a simple covering, and are described by a function satisfying a nonlinear partial differential equation of the Hamilton–Jacobi type, whose coefficients are combinations of the metric elements of the surface. All known equilibria—equilibria with zero and infinite rotational transform and the symmetric ones in the case of finite rotational transform—turn out to be solutions of separable cases of that equation, and allow a unified description if the toroidal surface is parametrized in the moving trihedral associated with a closed curve. Analogously to volume current equilibria, the only continuous symmetries compatible with separability are plane, helical, and axial symmetry. In the nonseparable case numerical evidence is presented for cases with chaotic behavior of geodesics, thus restricting possible equilibria for these surfaces. For weak deviation from axisymmetry, Kolmogorov–Arnold–Moser (KAM)-type behavior is observed, i.e., destruction of geodesic coverings with a low rational rotational transform and preservation of those with irrational rotational transform. A previous attempt to establish three-dimensional surface current equilibria on the basis of the KAM theorem is rejected as incomplete, and a complete proof of the existence of equilibria in the weakly nonaxisymmetric case, based on the twist theorem for mappings, is given. Finally, for a certain class of strong deviations from axisymmetry, an analytic criterion is formulated that rules out equilibria for these surfaces.

The propagation of the guided discharge front in a krypton flashlamp

The trajectory of the luminous ionization front in a high-pressure krypton flashlamp has been studied using an external grounded conductor placed longitudinally against the tube wall to guide the discharge. The propagation velocity of the discharge front has been measured as a function of distance, applied voltage and width of the guiding band. A semi-empirical model which fits the results is presented. The longitudinal variation of the current in the discharge channel is also presented.

Numerical study of the axisymmetric ideal MHD stability of EXTRAP

A numerical study of the free-boundary axisymmetric (n = 0) ideal magnetohydrodynamical (MHD) motions of the EXTRAP device is presented. The dependence of stability on current profiles in the plasma and currents in the external conductors is investigated. Results are shown for linear growth-rates and nonlinear saturation amplitudes and their dependence on plasma radius as well as on the conducting shell radius.The interior region of the plasma is simulated by means of a Lagrangian Finite Element Method (FEM) for ideal magnetohydrodynamics. The method is based on a nonlinear variational principle for the Lagrangian description of ideal MHD. The Boundary Element Method (BEM) is used together with the Lagrangian FEM to simulate nonlinear motion of an ideal MHD plasma behaviour in a vacuum region under the influence of external magnetic fields.

Comments on the extended energy principle

The present analysis concerns a plasma confined in a magnetic field, which consists of one part due to the plasma current density and one part due to steady currents in fixed external conductors. Unrestricted free-boundary displacements are studied that lead to an unbalanced pressure force at the plasma boundary and to a corresponding change in potential energy. Thus the total change in energy is due to two factors: (i) the work done against the plasma volume forces, and (ii) the work done against the unbalanced pressure forces at the plasma boundary. As a consequence, the conventional extended energy principle has to be reconsidered. This reconsideration applies in particular to its final formulation, where unrestricted displacements are made to replace restricted ones in an expression for the potential energy change deduced from the work of the plasma volume force only. The conventional MHD analysis on perturbed plasmas thus has to be revised, by taking induced surface currents properly into account. This applies to all plasmas in inhomogeneous externally applied magnetic fields.

Method of fabrication of matrix carbon fiber field emission cathode structures for flat-panel indicators

A matrix carbon fiber field-emission cathode structure with isolated emitters has been developed for use in flat-panel fluorescent indicators and displays. The array is composed of singular carbon polyacrilonitril fibers, 7 μA in diameter, united into a matrix by a silicoorganic dielectric. A method of fabrication of the matrix cathode structure is discussed. Cathode matrices with the number of emitters from 10 to 32×32 and isolated connections for power supply were made. Control of the emission currents is possible both independently and by coupling the emitters as a common cathode circuit with external conductors. The distance between the emitters in the array is 1.5 or 1 mm; the matrix external sizes are 18×20 or 32×32 mm. Nominal potential for the designed cathode in a diode configuration was ∼1.5 kV. The current could be controlled in the range from 0.01 to 100 mA/emitter. Models of flat digital indicators based on the designed cathode arrays were tested.

Analysis and application of NRD-guide excitors

In this paper, the NRD-guide excitors using a length of coaxial line which consists of a rectangle external conductor and a thin round inner conductor are presented, and the characteristics of the input impedances of LSE 11 o mode and LSM 11 o mode at the insertion points are analysed and calculated by using the method of the rector Green's function respectively. The computation results show that the mode excitors are able to improve the operating modes matching between NRD-guide and the quasi-TEM transmission line. The structures are suitable for fabrication LSE 11 o mode oscillator and LSM 11 o mode oscillator to compose millimeter wave NRD-guide integrated front ends. An example of an LSE 11 o mode oscillator in Ka-band is given. Its oscillation frequency and output power could be easily adjusted by changing the parameters of the excitor.

Energy principle with induced surface currents

An extended analysis is presented of the earlier investigated induced surface current effects which arise in a magnetized plasma when the confining field has an imposed inhomogeneous part generated by currents in external conductors. The electromagnetic induction law requires a corresponding contribution from these effects to be added to the formulation of the energy principle for plasma MHD stability. For a plasma with a free boundary, conventional theory therefore holds in a strict sense only when there is a homogeneous external magnetic field. An illustration is given by two-dimensional straight Extrap geometry with a peaked current distribution, subject to a combined translational and ballooning-like displacement. In this case there are strong restoring forces, leading to stable oscillations around the plasma equilibrium position.

Energy principle with induced surface currents

An extended analysis is presented of the earlier investigated induced surface current effects which arise in a magnetized plasma when the confining field has an imposed inhomogeneous part generated by currents in external conductors. The electromagnetic induction law requires a corresponding contribution from these effects to be added to the formulation of the energy principle for plasma MHD stability. For a plasma with a free boundary, conventional theory therefore holds in a strict sense only when there is a homogeneous external magnetic field. An illustration is given by two-dimensional straight Extrap geometry with a peaked current distribution, subject to a combined translational and ballooning-like displacement. In this case there are strong restoring forces, leading to stable oscillations around the plasma equilibrium position.

Induced surface current effects of a magnetized plasma

The linearized MHD perturbation theory of a magnetically confined plasma is reconsidered, with special emphasis on systems where there is a spatially inhomogeneous magnetic field part generated by constant currents in fixed external conductors. Electromagnetic induction then leads to induced surface current effects at the plasma boundary, due to the inhomogeneity of the externally imposed magnetic field. The corresponding surface currents are physically different from those which arise from the pressure balance condition at the plasma boundary. The apparent contradiction between the electromagnetically induced surface current effect and the pressure balance condition at the boundary is resolved by a transfer of the force due to the surface current into a volume force acting on the entire plasma body. The integrated effect of the surface current is thus included in the form of an additional volume contribution to the change in potential energy, whereas all other parts of conventional theory and its boundary conditions are preserved in the present approach.

On the effect of passive feedback in the toroidal Extrap configuration

The ideal MHD stability properties of the axisymmetric free-boundary m = 1 mode of toroidal Extrap equilibria with large aspect ratio and weakly non-circular cross-section are investigated. The effect of passive feedback due to induced currents in the external conductors, represented as ideal current loops, and in a surrounding conducting wall, is taken into account in an approximate fashion by using the inductances of the circuits. The dependence of the effect of the feedback on different parameters such as the plasma radius, the radius of the wall and the horizontal position of the equilibrium plasma is studied. It is found that the effect of feedback becomes significant in the Extrap configuration when the plasma radius is not too small. The axisymmetric mode is thereby stabilized over a parameter regime which is roughly corresponding to the experimental situation of the Extrap T1 device.

In vitro model of far-field stationary potentials: boundary effects on propagated potentials

Far-field stationary potentials have been said to result from several factors such as changes in the anatomical orientation of the direction of a propagating nerve action potential (AP) or local modifications of the impedance in the external volume conductor by changes in its geometry or resistivity. In the case of an impedance variation due to the presence of boundaries in the geometry of the medium, the findings reported in this paper showed that it is possible to record simultaneously AP and stationary potentials which we have called boundary potentials (BPs). The BP amplitude depended on the number of active axons at the boundary, on the distance between the boundary and one of the recording electrodes, and on the local impedance variation. Its polarity depended only on the direction of the AP propagation relative to the sign of the local inpedance modification, the recording electrodes being in the same relative positions with respect to the direction of the propagating impulse. Finally, the recording of a BP remained possible whatever the relative position of the boundary and of the recording electrodes. These findings are in accordance with some clinical observations not yet explained.

Improved photomultiplier tube for positron emission tomography

The paper describes an investigation in which it is shown that small positive voltage pulses applied to an external conductor placed against the photocathode of a photomultiplier tube can be used to switch the photocathode completely off for the duration of the pulses. This suggests that a photomultiplier tube with a multisegment photocathode can be constructed, the individual cathode segments of which can be switched off independently by means of such pulses. A theoretical explanation for the effect is provided with the aid of a simple circuit model for the photocathode. Analysis of the model also shows that it is possible to identify the particular cathode segment in which a photon is detected when a pulse is recorded at the phototube's anode. A phototube with these characteristics can have important implications for positron emission tomography, as it can provide improved spatial resolution, simultaneous multislice capability and the ability to eliminate distortion due to dead-time effects at high count rates.

Computational study of three-dimensional magnetohydrodynamic equilibria in toroidal helical systems

Computational methods based on the time-dependent relaxation technique for obtaining finite beta stellarator equilibria with no net current are described. The computation grid is Eulerian corresponding to space-fixed non-orthogonal helical coordinates. The poloidal cross section, which is composed of rectangular grids, rotates with the same pitch as that of external helical conductors along the toroidal direction. By this choice, it is possible to handle complicated field topologies and to economize the computer memory. Also, numerical convergence is greatly improved compared with that in cylindrical coordinates. The developed code is applied to a typical low shear l=2 stellarator (Wendelstein VII-A). Furthermore, breaking up of magnetic surfaces due to finite β effect in a low aspect ratio l=2 torsatron is shown.

Non-linear motion of a rigid conductor in a magnetic multipole field

The non-linear motion of an ideally conducting current-carrying rigid cylinder in a magnetic multipole field is analyzed. It is found that non-linear stability is achieved provided the current in the external conductor rods is sufficiently large. Since the results agree qualitatively with experimental observations of the Extrap z-pinch, it is suggested that the so far unexplained stability of this configuration is due to non-linear effects.

Feedback control of rotating resistive modes

To gain information for the design of practical feedback schemes, the response of nonlinear resistive modes to boundary conditions imposed by external conductors and resistive vessels is analyzed in the time domain. Newly derived explicit dynamical equations describe the nonlinear evolution of the tearing mode island width and frequency of rotation. These equations are appropriate to explain previous experimental and theoretical results quantitatively.

Tokamak Fusion Reactor Start-Up Simulation

A simulation code TSEC (Time-dependent Spectral Equilibrium Code) has been developed to model the axisymmetric evolution of a tokamak on the resistive (L/R) time scale of the external coils, conductors, or shell. The electromagnetic interaction between the plasma and the external circuit is taken into account in a self-consistent manner. TSEC is Lagrangian and utilizes magnetic flux coordinates with spectral decomposition in the angle variable theta. The plasma is modeled as a finite-size, zero-inertia, finite-pressure fluid which adjusts its position and shape to remain in free-boundary equilibrium consistent with the currents in the external circuits. At the heart of TSEC is a fast method of calculating the self-consistent free-boundary plasma equilibrium at each time step which is based on the minimization of a certain mean-square error. 3 refs., 6 figs., 3 tabs.

Viscous damping of Free Boundary Models in a Non-Circular z-Pinch

The MHD stability properties of a slightly non-circular z-pinch are studied, taking classical viscosity into account. A surface current model is used, and the perturbations are assumed to be incompressible with infinite axial wavelength.It is found that the only unstable mode is that with m = 1, m being the poloidal mode number. This mode is unstable for all values of the viscosity coefficient μ. Although the growth rate can be made arbitrarily small, even a moderate reduction requires a very large of μ.Clearly, the observed stability of Extrap, where the non-circularity is due to currents in a number of external conductors, can not be explained by viscosity alone. The required viscosity is about six orders of magnitude larger than the observed classical one.