Equilibrium Field Research Articles

The effect of water seepage forces on the face stability of an experimental microtunnel

The face heading stability of underground constructions remains quite difficult to assess, especially when groundwater is present. To investigate this, an experimental microtunnel was excavated at shallow depth in soft ground, below the water table. In agreement with field measurements of the piezometric level changes, a three-dimensional finite element analysis of groundwater flow shows that the head losses are concentrated in the close vicinity of the tunnel face. Both numerical equilibrium analysis and field measurements were used to show that the resulting seepage forces substantially increase the supporting pressure required to ensure face stability. Key words : microtunnel, shallow depth, soft ground, seepage forces, face stability, supporting pressure.

Evaluation of stress intensity factors in circular arc-shaped interfacial crack using [formula omitted] integral

A numerical method is proposed to obtain the individual stress intensity factor in a circular arc-shaped interfacial crack. The method is based on the path-independency of L integral and M L integral which involves two independent equilibrium fields, from which each stress intensity factor at the crack tip may be evaluated from the displacements and stresses remote from the crack tip. Some numerical examples are presented to compare the accuracy of this method to the well-known “method of extrapolation”. It is found that the accurate values of each individual stress intensity factor k 1 and k 2 are obtained based on the present method without using the very fine meshes or singular elements at the crack tip.

Peripheral Stochasticity in Tokamaks.The Martin-Taylor Revisited

Abstract We analyse the effect of an Ergodic Magnetic Limiter on the magnetic field line dynamics in the edge of a large aspect-ratio Tokamak. We model the limiter action as an impulsive perturbation and use a peaked-current model for the Tokamak equilibrium field. The theoretical analysis is made through the use of invariant flux functions describing magnetic surfaces. Results are compared with a numerical mapping of the field lines

Fast dynamic reconnection at X-type neutral points

view Abstract Citations (57) References (15) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Fast Dynamic Reconnection at X-Type Neutral Points Craig, I. J. ; Watson, P. G. Abstract The time evolution of disturbed X-type neutral points is considered. An analytic treatment is given for the case of small disturbances of the equilibrium field in the absence of gas pressure. This problem admits well-defined azimuthal modes which allow a formally exact determination of the magnetic annihilation rate. Reconnection can only occur in the case of purely radial (m = 0) disturbances. The linear theory supports the notion of an initial implosive stage which rapidly releases the bulk of the energy associated with reconnective field disturbances. In the nonlinear problem, although fast reconnection is maintained for low-amplitude disturbances in noncylindrical geometries, finite gas pressure can stall the reconnection if sufficiently large. This effect may not be critical in more complex X-point geometries. More seriously, for finite-amplitude disturbances the cylindrical current structure close to the neutral point is distorted into a quasi-one-dimensional current sheet whose thickness is limited by resistive diffusion. In this case fast reconnection is consistent with a flux pileup solution in which the bulk of the energy is released as heat rather than as the kinetic energy of mass motion. Publication: The Astrophysical Journal Pub Date: July 1992 DOI: 10.1086/171512 Bibcode: 1992ApJ...393..385C Keywords: Magnetic Field Reconnection; Magnetohydrodynamics; Solar Corona; Solar Flares; Linear Equations; Scaling Laws; Solar Physics; MAGNETOHYDRODYNAMICS: MHD full text sources ADS |

Microwave absorption by single and polycrystals of Bi 2Sr 2CaCu 2O 8+δ

X-band (∼ 9.4 GHz) microwave-absorption measurements have been performed on single and polycrystals of the high- T c superconducting material Bi 2Sr 2CaCu 2O 8+δ in the temperature range 4.2–100 K. The microwave absorption indicated the onset of the transition to the superconducting phase at 89 K, the transition to the superconducting phase being complete at 84 K. Low-field microwave absorptions were recorded at temperatures below 89 K. These absorptions exhibited large anisotropies with respect to the relative orientations of the microwave and external magnetic fields; as well, they exhibited dependence on the orientation of the c-axis of the crystals relative to the external and microwave fields. The magnetic hysteresis, as well as the effect of field cooling on microwave absorption were also investigated and the equilibrium fields, B eq, were determined. In addition, the value of the lower critical field B ⊥ c1 has been estimated. Itis concluded that, although some features of microwave absorptions are common to the various samples investigated, there exist some significant differences in the natures of the microwave absorption by the samples; an explanation based on the existence of isolated superconducting grains and defects has been provided.

Taylor relaxation of a Gold-Hoyle flux tube

Force-free magnetic field equilibria satisfy the condition ⊇ × B = αB. The relaxation of a nonconstant-α force-free equilibrium, the Gold-Hoyle field, to linear force-free equilibria where α is a constant is considered. The relaxation proceeds assuming the global magnetic helicity to be an invariant, the basis of the so-called Taylor hypothesis. This approach circumvents the need for sophisticated time-dependent nonlinear simulations, but clearly relies heavily on the applicability of the Taylor hypothesis to the solar corona

Study on the Phase equilibrium in the Systems Sodium Selenate — Cadmium Selenate — Water and Sodium Selenate — Manganese Selenate — Water at 25 °C

AbstractThe phase equilibrium in the systems Na2SeO4CdSeO4H2O and Na2SeO4MnSeO4H2O were studied and it was established that new phases were obtained — double salts with a composition: Na2Cd(SeO4)2 · 2 H2O and Na2Mn(SeO4)2 · 2 H2O. The fields of phase equilibrium of the double salts in the triple systems were determined. The composition of the new phases and the number of the water molecules of crystallization were investigated, respectively by the Schreinemackers' method of physico‐chemical analysis and thermogravimetrical analysis. An X‐ray diffraction analysis of the new phases obtained was done.

Contact potentials of solution interfaces: phase equilibrium and interfacial electric fields

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTContact potentials of solution interfaces: phase equilibrium and interfacial electric fieldsLawrence R. PrattCite this: J. Phys. Chem. 1992, 96, 1, 25–33Publication Date (Print):January 1, 1992Publication History Published online1 May 2002Published inissue 1 January 1992https://doi.org/10.1021/j100180a010RIGHTS & PERMISSIONSArticle Views359Altmetric-Citations94LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (1 MB) Get e-Alerts

The nonequilibrium behavior of electron swarms in nonuniform fields in SF/sub 6/

The behavior of electron swarms in nonuniform electric fields in SF/sub 6/ has been analyzed by Monte Carlo simulation. Decreasing and increasing electric field configurations have been studied. The spatial variations of the electron mean energy, drift velocity, and ionization and attachment coefficients are calculated for different field slopes and compared with the values calculated assuming equilibrium field conditions. It is found that the nonequilibrium behavior depends on the ratio of the field slope to pressure, and not on the field slope alone. The mean energy and drift velocity are almost the same as the equilibrium values, while the ionization and attachment coefficients show significant nonequilibrium features. The electron and ion distributions along the uniformly decreasing and increasing fields have also been studied. >

Thermodynamic properties of iron silicides and phase equilibria in {(1 − x)Si + xFe}

A Knudsen-effusion technique with mass-spectrometric analysis of evaporation products has been employed to determine thermodynamic properties of {(1 − x)Si + xFe} alloys. The temperature and mole-fraction ranges investigated were T = 1351 K to 1664 K and x = 0.349 to 0.646. Alloys with compositions belonging to each of the two equilibrium fields of two solid phases and to the regions of equilibrium between FeSi and liquid phase were studied. Activities and partial molar thermodynamic functions of Fe and Si were calculated from the values of pFe and pSi found. The minimal values of ΔfGm and ΔfHm with respect to their dependence on mole fraction were found at T = 1423 K to correspond to iron monosilicide. Computations of a number of phase equilibria in {(1 − x)Si + xFe} have been carried out to prove the reliability of the thermodynamic information acquired. Temperature dependences of the molar Gibbs energies of formation of the intermediate phases established in the present work as well as thermodynamic characteristics of formation of the associative complexes reported previously were used for the purpose. The coordinates of melting temperatures of iron silicides were found to coincide with those recommended in the literature.

Theory of formation of the stable ferromagnetic phase in a metamagnet

The formation of a new ferromagnetic phase (F) within the antiferromagnetic phase (AF) environment in an external magnetic field is considered. The surface energy of a ferromagnetic phase (F) nucleus and the probability of its formation are calculated. It is shown that the magnetoelastic interactions lead to the two different fields of equilibrium, both the antiferromagnetic nucleus in the ferromagnetic environment and the ferromagnetic nucleus in the antiferromagnetic environment.

Impact of the Design Point on the Poloidal Field Coil System for the CIT (Compact ignition Tokamak)

The poloidal field (PF) coil system in a tokamak must provide the flux swing and the equilibrium and shaping field distributions required to create, maintain, and control the plasma during the discharge. The present design for CIT calls for an 11.8 MA plasma in a double null configuration with a major radius of 2.59 m, a minor radius of 0.795 m, and an elongation (at the 95% flux surface) of 2.0. The toroidal field at the major radius is 9 T. The central solenoid is self-supporting and the TF coils wedge under the Lorentz load.The previous design point called for the TF and PF to buck against each other in order to lower the stresses in both. That design called for an 11 MA, 10 T plasma with a major radius of 2.14 m and a minor radius of 0.66 m. The impact on the PF system of this change in the design point is assessed.

Unbounded Perturbations of Boson Equilibrium States in Fock Space

Abstract Based on the linear coupling term in the non-relativistic quantum theory of matter-photon interactions, the coupling of a finite dimensional quantum system (finitely many finite-level atoms) with the boson gas (radiation field) in thermal equilibrium by means of perturbation theoretical methods is calculated. For the perturbation term of the Dyson expansion the unbounded interaction operator is taken. By a detailed analysis of the perturbation integrals and series, it is possible to derive the trace-class property of e-ßH , where H is the corresponding hamiltonian of the interacting systems and ß the inverse temperature

Phase Interaction in the Systems Sodium Selenate – Copper Selenate – Water and Sodium Selenate – Zinc Selenate – Water at 25 °C

AbstractThe phase equilibrium in the systems Na2SeO4–CuSeO4–H2O and Na2SeO4–ZnSeO4–H2O were studied and it was established that new phases were obtained – double salts with a composition: Na2Cu(SeO4)2 · 2 H2O and Na2Zn(SeO4)2 · 2 H2O. The fields of phase equilibrium of the double salts in the triple systems were determined. The composition of the new phases was investigated by the Schreinemackers' method of physico‐chemical analysis, and the number of the water molecules of crystallization – by thermogravimetrical analysis. An X‐ray diffraction analysis of the new phases obtained was done.

The Evolution of Disturbed Neutral Point Equilibria

AbstractWe consider the linear and non-linear evolution of a perturbed X-type neutral point. A semi-analytic treatment is given for the case of small disturbances of the equilibrium field. This problem admits well defined azimuthal modes which allow a formally exact determination of the magnetic annihilation rate. It is shown that the longest lived modes are purely radial and decay of the timescale τ ≈ |ln η| where η defines the resistivity of the coronal plasma. Higher azimuthal modes decay much faster, generally on a fraction (O(m−1)) of the Alfvén timescale for the outer field.We go on to perform finite amplitude calculations that demonstrate the implosive current build-up that precedes the reconnective phase of the relaxation. In general both linear and non-linear studies support the idea of an initial implosive stage which rapidly releases the bulk of the energy associated with arbitrary field disturbances.

Experimental study of the vertical stability of high decay index plasmas in the DIII-D tokamak

Experiments on the stabilization of highly elongated, vertically unstable plasmas were carried out on the DIII-D tokamak. Identification of the closed-loop transfer function showed that vertical stability could be usefully modelled as a second order dynamical system. The effect of varying the controller gains and the vertical field decay index was studied and found to be qualitatively as predicted by a low order model proposed previously. The implementation of a new hybrid inboard/outboard coil positional control with differing controller dynamics allowed operation of DIII-D up to 92% of the limiting equilibrium field decay index of the vacuum vessel for the plasmas used. This improved control allowed operation at a plasma elongation κ of up to 2.5.

Nonlinear stability for stratified magnetohydrodynamics

Abstract By extending Arnol'd's Hamiltonian stability techniques to the situation of magnetohydrodynamics, we determine sufficient conditions for nonlinear Lyapunov stability with respect to three dimensional perturbations of axisymmetric steady flows of an electrically conducting, density stratified, Boussinesq, nondissipative fluid. The steady flow is prescribed by an equilibrium condition given by a nonlinear elliptic partial differential equation for the magnetic flux function Y. It is shown that nonlinear stability follows from the positivity of a quadratic form, whose coefficients are given in terms of explicit functions of Y together with certain technical conditions concerning convexity and regularity that are necessary for the application of Arnol'd's techniques. Some specific examples are discussed. The stability criterium for axisymmetric perturbations is exhibited for a simple spherical model for the Earth's fluid core. Explicit Rayleigh type criteria for nonlinear stability are obtained in the special case where the equilibrium fields depend only on the distance from the axis of symmetry. In this example the regularity conditions hold under the assumption that there are no “resonant magnetic tori” and the convexity inequality is explicitly exhibited.

Particle orbits in two‐dimensional equilibrium models for the magnetotail

Particle orbits in two‐dimensional (2‐D) kinetic equilibrium solutions for the magnetotail are considered. A comparison is made between the orbits in the equilibrium fields and those found in previous studies of the orbits where the main component of the magnetic field (Bx) was approximated as either a hyperbolic tangent or a linear function of z with the normal field (Bz) taken to be a constant (one‐dimensional models). Here, the plane z = 0 defines the neutral plane. The orbits in the 2‐D fields are found to be significantly different from those in the one‐dimensional models. The particles are generally reflected in much shorter distances and the loss region is much smaller than in the one‐dimensional fields. This holds true independent of ρ/L, where L is the current sheet thickness and ρ is the Larmor radius in the asymptotic field. For ρ/L ≳ 0.1, the fraction of integrable orbits in the equilibrium fields also becomes different from that in the one‐dimensional fields. As ρ/L becomes larger than 0.3 (with the exact value depending on the equilibrium model and particle position in the tail), the phase space becomes dominated by integrable orbits, whereas in the one‐dimensional fields the phase space remains divided into integrable and chaotic regions. Another major difference between the orbits in the 1‐D and 2‐D fields lies in the fact that the equilibrium orbits have a net drift in the y direction whereas the orbits in the 1‐D models have zero net drift. In the presence of an electric field Ey, the equilibrium orbits can be accelerated to much larger energies and behave quite differently from the orbits in the 1‐D fields. The differences between the orbits in the equilibrium and one‐dimensional fields are mainly due to the neglect of the variation of Bx with x in the one‐dimensional fields. In fact, it is found that even a weak variation of Bx with x can alter the orbits significantly. The effect of a constant‐shear field on the orbits is also examined. Finally, it is shown that the border between the integrable and chaotic orbits is in general “sticky”; i.e. if a stochastic orbit comes close to an integrable region, it can get trapped. Since the orbit is stochastic, it will escape eventually, but the detrapping time can be very long. The stickiness occurs where there are islands embedded in phase space. Thus, care must be taken in applying the diffusion formalism to such regions. The relevance of the above findings to the problem of magnetic reconnection in the tail is discussed.

MHD Stability of Free Boundary Toroidal Z Pinch

The Magnetohydrodynamic (MHD) stability of a free boundary toroidal Z pinch plasma is investigated. Equilibrium field profiles are chosen so that µ is nearly uniform in the central region, µ and dµ/d r vanish on the boundary and Suydam's criterion is satisfied throughout the plasma. The stability of the equilibrium is examined for the ratio b of the conducting wall radius to the plasma radius and plasma pressure. The stability of non-resonant ideal modes is determined mainly from the safty factor on the axis. Non-resonant modes are dominant for low plasma pressure, whereas resonant modes are dominant for high plasma pressure. Tearing modes are stable only for b below 1.04. The width of the magnetic islands produced from the tearing modes is evaluated. As b increases, overlap of the magnetic islands occurs over a wide area in the plasma.

A review of results from the HBTX reversed field pinch

The series of experiments carried out in recent years on the HBTX reversed field pinch [Plasma Phys. Controlled Fusion 30, 843 (1988)] have highlighted the importance of minimizing the flux that penetrates the plasma–wall boundary. This flux penetration, whether from equilibrium field errors, the presence of limiters, or plasma magnetic activity from the growth of thin shell modes, leads to an increase in the loop voltage. The magnitude of this increase can be understood in terms of magnetic helicity balance. Feedback stabilization of the (m,n)=(1,2) thin shell mode has been successfully demonstrated, though with little effect on global plasma properties. A new design is being developed for HBTX aimed at minimizing the flux that can penetrate the first wall.