External Conductors Research Articles

Effects of Boundary Conditions on Temperature and Density in an Extrap Z-Pinch

Using the fluid equations, we examine transport in an Extrap configuration by carrying out calculations incorporating model profiles for the density and temperature. The goal of this analysis is to examine the scaling of the pinch equilibrium plasma density, temperature and radius with parameters that are characteristic for Extrap Z-pinches. These parameters include the discharge current, the neutral hydrogen filling density, an oxygen impurity fractional concentration and the conditions at the pinch boundary. An Extrap Z-pinch is a pinch discharge where the current channel has a characteristic non-circular cross-section achieved by bounding the discharge by a magnetic separatrix produced when a vacuum octupole magnetic field, generated by currents in external conductors, combines with the self-magnetic field produced by the discharge current. The pinch boundary is changed from a plasma-vacuum boundary to an interface between a high-beta pinch plasma and a low-beta plasma contained in the vacuum magnetic field. The energy that is lost from the pinch region sustains this boundary layer. The introduction of a separatrix boundary around the pinch with four X-point nulls deteriorates the containment of the pinch somewhat. However the presence of the warm, low-beta plasma scrape-off layer, which provides a boundary condition on the pinch, tends to counteract the negative effects of the poorer confinement. Thus the equilibrium parameters that characterize the pinch may not be severely deteriorated by the introduction of the separatrix when the entire configuration, including the scrape-off layer, is considered.

Toroidal plasma equilibria in an external magnetic multipole field

The equilibrium of an axisymmetric toroidal plasma, with almost circular cross-section, situated in an external magnetic multipole field is considered. The external field is created by a number of circular current carrying conductors symmetrically arranged outside of the plasma (Extrap configuration). The equilibrium field is expanded to first orders in the inverse aspect ratio and in a small parameter describing the non-circularity of the plasma cross-section. The current density is taken on the form j= kappa 2 psi +C. With this choice, both 'peaked' ( kappa 2>0) and 'skin-type' ( kappa 2<0) profiles can be described. The results obtained indicate that, in the range of parameters where equilibria with non-elongated magnetic surfaces ('square-shaped' separatrix) can be found, in the case of four external conductors, there is a high sensitivity of the plasma location (toroidal radius) to the precise values of the currents in the external conductors.

Input mismatch of TE&amp;lt;inf&amp;gt;11&amp;lt;/inf&amp;gt;mode coaxial waveguide feeds

The reflection characteristics of the TE 11 mode in a coaxial waveguide antenna due to mismatch at the radiating aperture are described. Results are presented for conventional coaxial waveguide as well as waveguide whose inner conductor extends beyond the aperture plane. Coaxial wavegulde mismatch is often quite large, particularly for conditions of good pattern symmetry, and some matching is usually required. A broad-band matching technique using annular rings inside the waveguide is described for the case where there is no external conductor. Results presented show excellent agreement between theory and experiment.

Experimental Studies of the MHD Stability of Non-Circular Extrap Z-Pinches

Extrap Z-pinches, which can be sustained for many Alfvén times, can be characterized as non-circular Z-pinch discharges bounded by a magnetic separatrix acting somewhat like a limiter. The magnetic separatrix is produced when a vacuum magnetic field, generated by currents in external conductors, combines with the self-magnetic field produced by the discharge current. The separatrix deforms the pinch cross-section and affects the equilibrium at the pinch boundary; both effects improve stability. Experiments have been performed which indicate that both effects are necessary for the successful generation of sustained Extrap discharges. In one experiment, the importance of the non-circularity of the cross-section was investigated. The deformation provided by the vacuum field can provide regions in the discharge where field lines have good curvature, which improves the stability of the configuration against internal modes. In configurations apparently lacking good curvature, discharges could not be sustained. In a second experiment, the dependence of the amplitude of global kink instabilities on the discharge current density profile were studied. The behaviour of the modes was consistent with that which would be expected for surface current-driven modes.

MHD spectrum of a Z-pinch in an external magnetic multipole field

MHD stability properties of previously calculated equilibria for Extrap type of configurations, generalized to an arbitrary number (N) of external conductors, are investigated. A perturbation technique with a small parameter epsilon measuring the non-circularity of the plasma, is used. An important issue concerns the degeneracy of modes corresponding to various poloidal model numbers m, and some general results, due solely to the angular periodicity of the configuration, are derived. In particular, it is shown that for the mode m=1 the degeneracy prevails to all orders in epsilon if N>2 or, equivalently, if the equilibrium has no quadrupole component. This turns out to be extremely important for the possibility of stabilizing long kink modes, and probably explains why only 'square-shaped' equilibria have been found to be stable in earlier numerical computations. In the four-conductor Extrap, the mode which is most strongly affected by the external field is m=2, for which the degeneracy is removed already in first order. Leading order frequency shifts for the modes m=1 and m=2 are explicitly calculated for surface- and constant-current pinches.

The Princeton spectral equilibrium code: PSEC

A fast computer code has been developed to calculate free-boundary solutions to the plasma equilibrium equation that are consistent with the currents in external coils and conductors. The free-boundary formulation is based on the minimization of a mean-square error ε while the fixed-boundary solution is based on a variational principle and spectral representation of the coordinates x(Ψ, θ) and z(Ψ, θ). Specific calculations using the Columbia University Torus II, the Poloidal Divertor Experiment (PDX), and the Tokamak Fusion Test Reactor (TFTR) geometries are performed.

The sleeve monopole antenna in a warm plasma

AbstractA sleeve monopole antenna in a warm plasma with length almost the plasma wavelength has been analyzed in the frequency region where electron plasma waves exist. The current distribution and the input impedance have been obtained. When Landau damping is not considered, the current distribution is similar to that for a dipole and oscillates violently near the plasma frequency. It approaches a triangular shape as the frequency is increased. The input impedance varies considerably near the plasma frequency depending on the sleeve length. On the other hand, if Landau damping is taken into account, the amplitude of the oscillatory component of the current distribution becomes extremely small. For the input impedance, the effect of the sleeve beyond 25 times the Debye length can be neglected. This result agreed well with the measured input impedance values. It is found that the sleeve as the external conductor of the coaxial feeder has the effect of reducing the input impedance.

Analysis of temperature distributions in tubular specimen under high frequency induction heating.

The analysis of high frequency induction heating process was performed for the temperature distribution in tubular specimen, and a method to obtain the uniformity of the temperature distribution was investigated. The distribution of heat-producing by the external current was calculated in the case of infinite tubular conductor wound by a single induction coil. The influences of current frequency, conductivity of the tube and the distance between external current and conductor were discussed. The temperature distribution of tubular specimen was approximately obtained by solving the heat transfer equation with difference calculus. The shape of the heat coil for the uniform temperature distribution was determined on analysed results. With the heat coil thus obtained, the temperature distributions in the tubular specimen were measured. It was shown that the good uniformity in the temperature distribution was obtained.

Z-pinch equilibria in an external magnetic multipole field

An integral equation method of finding equilibria of a z-pinch situated in an external magnetic multipole field, due to a number of symmetrically placed external current-carrying conductors (Extrap configuration), is developed. A perturbation technique has been used, where the influence of the external field is treated as a small correction to a zero external field z-pinch circular equilibrium. To first order, equilibria for various current profiles are explicitly calculated. It is found that profiles of skin type give the largest perturbations of the magnetic surfaces from circular shape, whereas the plasma is much less distorted for peaked current distributions. Furthermore, except for the skin current case, the displacement of the outermost plasma edge is found to be very little affected by the details of the current profile, and is determined essentially by the total plasma current only. Second order effects are also considered.

Shell Stabilization of Tilting Mode Instability in a Moving Ring Reactor

The shell stabilization of the tilting mode in a moving ring reactor due to the arrangement of a conductor close to the plasma is studied by numerically calculating the stabilizing torque by the eddy current induced on the conductor surface. The tilting mode instability can be successfully suppressed in the slender ring plasma with the aspect ratio of four by either an internal rod conductor or an external annular conductor. The arrangement of both rodand annular-type conductors is required for stabilizing the tilting mode in a ring plasma with the aspect ratio of three. The effect of the mutual interaction among the eddy current is shown to be so small as to be safely neglected in calculating the eddy current induced by the tilted plasma, and the simplified treatment of the eddy current is suggested for the computation of the stabilizing torque due to the shell effect.

The extrap concept

The Extrap plasma confinement scheme consists of a Z pinch which is immersed in a magnetic multipole field. The latter is transverse to the pinch axis and is generated by currents in a set of external conductors. A review is given of so far performed theoretical and experimental investigations on this scheme, including considerations on the field topology, plasma start-up, equilibrium and stability. Macroscopically stable equilibria have been observed to exist in linear and toroidal sector experiments, when the ratio between the plasma pinch current and the characteristic external conductor current is chosen below a certain threshold. The observed stable behaviour can be explained by the constraints introduced by the externally imposed magnetic field, in combination with FLR effects. A cold-mantle surrounding the plasma provides further mechanisms for plasma stabilization.

On the Equilibrium of a Linear Extrap Pinch

The equilibrium is studied of a pinched linear plasma column of “Extrap” type which is confined in a purely transverse magnetic field, partly arising from currents in a set of external conductor rods being introduced for stabilizing purposes. The axial and transverse losses are separated in a simplified theoretical model for which stability is assumed as a working hypothesis and anomalous transport as well as impurity radiation are neglected. Then, the reduction of the axial heat transport by the magnetic field will have a substantial effect on the over-all heat balance, thus leading to high temperatures at large axial lengths of the plasma column. Conditions near ignition should become possible at technically realistic linear dimensions and pinch currents

Bifurcation of elliptical equilibria

It is shown that a bifurcation of the equilibrium solutions for straight elliptical plasma columns with a diffuse current profile exists for a suitable choice of the currents in the external conductors.

Composition and analysis of a new waveguide resonator filter with dielectric loading

AbstractThis paper proposes and analyzes a new waveguide resonator filter for comparatively low microwave frequency use. It describes a practical example for its application. The new waveguide structure consists of thin center conductors embedded in cylindrical dielectric rods in contact with conducting parallel plates. This structure can be viewed as a dielectric‐filled coaxial cable provided its external cylindrical conductor extends to a parallel plate. By using the relaxation method calculations are conducted under the assumption of pure TEM fields. The calculated impedance, line coupling, effective dielectric constant and circuit Q are found to be in good agreement with experiment.In order to investigate the higher‐order mode of the filter using this guided structure, the lowest higher‐order is assumed to be the TM01 mode and the effect of the conducting plate is excluded; the wave‐numbers are calculated and compared with experiment. The Q of the 1/4‐wavelength resonator using this guide is higher than that of the dielectric‐filled coaxial line resonator and, without using the interdigital arrangement, couplings between resonators can nonetheless be realized. In the example of the 850‐MHz band filter, it is clear that this waveguide can be used to realize miniaturized, light‐weight, inexpensive and high‐performance filters.

Two-dimensional plasma equilibria

Complex-variable, hodograph methods are used to solve the free-boundary problem of a plasma confined by its own skin currents and the field due to two parallel external conductors. In one extreme case the external field is a quadrupole field in the vicinity of the plasma; another extreme case describes the local perturbation of a large plasma by a single, nearby conductor.

Hamilton's principle for a hydromagnetic fluid with a free boundary

Newcomb's non-linear formulation of Hamilton's principle for an ideal hydromagnetic fluid surrounded by a wall is generalized to allow vacuum and ferromagnetic regions, and to include the effects of external conductors and circuits. The linear approximation is recovered by expanding to second order in the plasma displacement. When the accumulated charge flowing in each conductor is treated as a generalized variable, the vacuum energy appears as a kinetic energy, with the inductance matrix playing the role of a mass tensor. As an application, the generalization of the Lüst-Martenson form of δW is found for the case of passive feedback due to interconnection of the external coils. A subsidiary variational principle is used to determine the inductance matrix, thus providing an alternative to the Green's function method.

Computer model of a fast toroidal plasma compression, with application to the topolotron

The method is developed for a comuputer sequence which models a fast toroidal theta or screw pinch for a highly conducting axially symmetric plasma. The computer sequence takes into account the self-inductances of the plasma and the external conductors which drive the compression as well as the mutual inductance which electromagnetically couples the two. The computer sequence is divided into three phases: a snowplow compression phase, an adiabatic compression phase, and a crowbarred circuit phase. The computer sequence is applied to a topolotron and an example is given of a magnetohydrodynamic equilibrium geometry for which the plasma surface possesses an asymptotic magnetic field with limit cycles.

Numerical computation of axisymmetric MHD-equilibria without conducting shell

A numerical scheme for the computation of axisymmetric equilibria in the presence of external conductors, without a conducting shell, is presented. The plasma boundary is always required to pass through a given point in the equatorial plane of the plasma column. The relationship between the convergence of the iterative scheme and the position of this point is discussed. The numerical scheme is applied to two relevant problems.

A Equilibrium Magnetic Field for a Toroidal Plasma

In the toroidal coodinates, a equilibrium analysis is presented for a toroidally symmetrical, sharp boundary plasma. The plasma β and aspect ratio, Rp/rp, are assumed arbitrarily. In the equilibrium, the maximum plasma βp is evaluated as Max βp=1/4 (Rp/rp+rp/Rp) +1/2. When corrents flow on te plasmasurface and external conductors, a equilibrium magnetic iiela and the currents is analitically solved. In the case in which there exist the external conductors infinitely far from the plasma, a stagnation point and separatrix can be found near the plasma surface. Furthermore, the magnetic surfaces similar to the external conductors form can be found outside such the separatrix. The current density flowing on coils placed outside magnetic surfaces is much higer than that on inside them. The stagnation points exist inside and outside the coiles, or on the ones.

Preparation and properties of inp/cds solar cells

A fast computer code has been developed to calculate free-boundary solutions to the plasma equilibrium equation that are consistent with the currents in external coils and conductors. The free-boundary formulation is based on the minimization of a mean-square error ε while the fixed-boundary solution is based on a variational principle and spectral representation of the coordinates x(Ψ, θ) and z(Ψ, θ). Specific calculations using the Columbia University Torus II, the Poloidal Divertor Experiment (PDX), and the Tokamak Fusion Test Reactor (TFTR) geometries are performed.