Set of wires to simulate tokamaks with poloidal divertor

2013 ◽  
Vol 79 (5) ◽  
pp. 751-757 ◽  
Author(s):  
T. KROETZ ◽  
CAROLINE G. L. MARTINS ◽  
M. ROBERTO ◽  
I. L. CALDAS
Keyword(s):  
Differential Equation ◽  
Field Line ◽  
Electric Current ◽  
Particle Collisions ◽  
Electric Currents ◽  
Deposition Patterns ◽  
Divertor Plate ◽  
Magnetic Surfaces ◽  
Error Field ◽  
Hyperbolic Points

AbstractSimple wire models have been proposed to simulate magnetic configurations in tokamaks. Here we consider electric currents in five parallel infinite wires to obtain double-null magnetic surfaces with specific choices of magnetic axis positions, triangularity, and elongation. As an example, we choose the position and the electric current of each wire to obtain magnetic surfaces similar to those expected in the tokamak international thermonuclear experimental reactor. Moreover, we also integrate the perturbed field line differential equation to simulate chaotic layers near the hyperbolic points and deposition patterns at the divertor plate observed in tokamaks. To simulate that, we add to the model a perturbing error field, due to asymmetries in the tokamak coils, and introduce a random collisional term to the field line mapping to reproduce escape pattern alterations due to particle collisions.

scholarly journals On the Existence of Eigenmodes of Linear Quasi-Periodic Differential Equations and their Relation to the MHD Continuum

1982 ◽  
Vol 37 (8) ◽  
pp. 830-839 ◽  
Author(s):  
A. Salat
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Infinite Sequence ◽  
Periodic Coefficient ◽  
Second Order ◽  
Order Ordinary Differential Equation ◽  
Magnetic Surfaces ◽  
Toroidal Geometry

The existence of quasi-periodic eigensolutions of a linear second order ordinary differential equation with quasi-periodic coefficient f{ω1t, ω2t) is investigated numerically and graphically. For sufficiently incommensurate frequencies ω1, ω2, a doubly indexed infinite sequence of eigenvalues and eigenmodes is obtained.The equation considered is a model for the magneto-hydrodynamic “continuum” in general toroidal geometry. The result suggests that continuum modes exist at least on sufficiently ir-rational magnetic surfaces

scholarly journals Electric Currents Connected With the Proton Flares of 7 July and 2 September, 1966

1971 ◽  
Vol 43 ◽  
pp. 417-421
Author(s):  
A. B. Severny
Keyword(s):  
Active Region ◽  
Field Strength ◽  
Magnetic Flux ◽  
Electric Field ◽  
Electric Field Strength ◽  
Electric Conductivity ◽  
Electric Current ◽  
Current Density ◽  
High Energy ◽  
Electric Currents

It is observed that the change of the net magnetic flux associated with flares can exceed 1017 Mx/s, which corresponds according to Maxwell's equation to the e.m.f. ∼ 109 V which is specific for the high energy protons generated in flares. It is shown that this value of e.m.f. can hardly be compensated by e.m.f. of inductance which should appear due to the actually measured motions in a flare generating active region. The values of electric field strength thus found, together with measured values of electric current density (from rotH), leads to an electric conductivity which is 103 times smaller than usually adopted.

scholarly journals On the Nature of Electric Current in the Electrospinning Process

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Baturalp Yalcinkaya ◽  
Fatma Yener ◽  
Oldrich Jirsak ◽  
Funda Cengiz-Callioglu
Keyword(s):  
Polymer Solution ◽  
Electric Current ◽  
Electrospinning Process ◽  
Charge Carriers ◽  
Electric Currents

The electric currents between electrodes in the electrospinning process are based on the movement of charge carriers through the spinning space. The majority of the charge carriers are formed by ionization of the air close to the metallic needle and to the polymer jet. The salt contained in the polymer solution contributes to the concentration of charge carriers, depending on its amount. The conductivity of polymer jets does not significantly affect the current since the jets do not link the electrodes.

The time-dependent electric current from a flame

1984 ◽  
Vol 393 (1805) ◽  
pp. 297-308 ◽  
Keyword(s):  
Differential Equation ◽  
Electric Field ◽  
Electric Current ◽  
Diffusion Flame ◽  
Time Dependent ◽  
Two Dimensional ◽  
Ionization Detector ◽  
Flame Ionization ◽  
Dependent Potential ◽  
Ionization Detectors

An earlier static treatment of the electric current from the diffusion flame in a flame ionization detector has been extended to include time-dependent currents. The nonlinear differential equation describing the electric field in the space outside the flame has been solved analytically for a class of problems in which a time-dependent potential difference is switched on after a static current has been established. Both one- and two-dimensional geometrical configurations are considered. The results could be useful in suggesting new experiments on flame ionization detectors.

scholarly journals The influence of homodromous and heterodromous electric currents on transmission of excitation in plant and animal

1915 ◽  
Vol 88 (607) ◽  
pp. 483-507 ◽  
Keyword(s):  
Electric Current ◽  
The Other ◽  
Muscle Preparation ◽  
Mimosa Pudica ◽  
Electric Currents ◽  
Joint Effects ◽  
Conducting Tissue ◽  
The One ◽  
Conduction Of Excitation ◽  
Stimulation Of

I have in a previous paper described investigation on the conduction of excitation in Mimosa pudica . It was there shown that the various characteristics of the propagation of excitation in the conducting tissue of the plant are in every way similar to those in the animal nerve. Hence it appeared probable that any newly found phenomenon in the one case was likely to lead to the discovery of a similar phenomenon in the other. A problem of great interest which has attracted my attention my attention for several years is the question whether, in a conducting tissue, excitation travels better with or against the direction of an electric current. The experimental difficulties presented in the prosecution of this enquiry are very numerous, the results being complicated by the joint effects of the direction of current on conductivity and of the poles on excitability. As regards the latter, the changes of excitability in the animal nerve under electrotonus have been demonstrated by the well-known experiments of pflüger. In a nerve-and-muscle preparation, the presence of a pole P is shown to induce a variation of excitability of a neighbouring point S. When P is kathode, the excitability of the point S, near it, is enhanced; stimulation of S, previously ineffective, now becomes effective, and the resulting excitation is transmitted to M, causing response of the muscle. Conversely, the application of anode at P causes a depression of excitability of S. Stimulus previously effective now becomes ineffective. In this manner the transmission of excitation may be indirectly modified by the polar variation of excitability of the stimulated point (fig. 1 a ).

scholarly journals On line-integrals of the diurnal magnetic variations

1928 ◽  
Vol 119 (782) ◽  
pp. 182-196 ◽  
Keyword(s):  
Electric Current ◽  
Potential Gradient ◽  
Electromagnetic Theory ◽  
Magnetic Data ◽  
Magnetic Survey ◽  
Electric Currents ◽  
Direct Measurements ◽  
On Line ◽  
Current Densities ◽  
Current Flows

1. According to electromagnetic theory, the line-integral ∫ H . ds of the magnetic force H taken round any closed curve is equal to 4πI, where I is the electric current threading the curve, H and I being measured in c.g.s. units. Such line-integrals have been calculated by Gauss and many later investigators for various curves on the earth’s surface, in order to determine whether any electric current flows upwards or downwards across the surface. Modern computations for large areas lead in general to values of ∫ H . ds differing from zero by amounts that correspond to current-densities of the order 3·10 -2 ampere/km. 2 . The magnetic field of such currents would account for 2 or 3 per cent, of the earth’s surface field. These results are inconsistent with the direct measurements of the atmospheric electric potential gradient and the ionisation of the air, which indicate a verticalcurrent-density of the order 3·10 -6 amp./km. 2 . If the magnetic estimates are reliable, the discrepancy indicates either that atmospheric electric currents exist which escape measurement, though they are 10,000 times as great as those which are measured, or that the relation ∫ H . ds = 4πI, which is one of the foundations of electromagnetic theory, is not strictly correct. These alternatives are so remarkable that the magnetic evidence must be above suspicion if it is to gain credence. Dr. L. A. Bauer holds that the results got from independent sets of data, for different epochs, and the mutual accordance of the results from neighbouring areas, justify the acceptance of the non-zero line-integrals, and that to explain them away it is necessary to assume quite unlikely systematic errors in the magnetic data. Other investigators show less conviction: for example, Sir Frank Dyson and H. Furner conclude that “though there is some evidence for Prof. Bauer’s results, the existence of vertical electric currents is not indicated with any great certainty.” But though the magnetic evidence may not be conclusive, it cannot be lightly dismissed, and in view of the importance of the question Sir Arthur Schuster has recently urged the desirability of a detailed magnetic survey of a small area as the best means of obtaining a definite conclusion.

scholarly journals X. On the electro-chemical equivalent of silver, and on the absolute electromotive force of clark cells

1884 ◽  
Vol 37 (232-234) ◽  
pp. 142-146 ◽  
Keyword(s):  
Electric Current ◽  
Electromotive Force ◽  
Large Diameter ◽  
British Association ◽  
Electric Currents ◽  
Terrestrial Magnetism ◽  
Accurate Knowledge ◽  
Series Of Experiments ◽  
The Absolute

The paper contains a record of a long series of experiments, extending over nearly two years. The measurement of the electric currents is direct, not depending upon a knowledge of the force of terrestrial magnetism. Three horizontal coils are traversed in succession by the electric current. Of these two of large diameter are fixed, and at a distance apart equal to the radius of either. Symmetrically between them a smaller coil is suspended in the balance. When the current passes, the suspended coil is pressed down, or lifted up, according to the connexions, and the observations relate to the double force called into operation when the direction of the current in the fixed coils is reversed . In a paper read before the British Association at Southampton it was shown that this construction presents special advantages, and in particular that the calculation of the result does not require an accurate knowledge of the radii of the coils, but only of the ratio of the radii of the small and large coils. In this way one of the principal difficulties, the measurement of the small coil, is evaded.

scholarly journals Modification of conductivity due to acceleration of the ionospheric medium

2008 ◽  
Vol 26 (8) ◽  
pp. 2111-2130 ◽  
Author(s):  
V. V. Denisenko ◽  
H. K. Biernat ◽  
A. V. Mezentsev ◽  
V. A. Shaidurov ◽  
S. S. Zamay
Keyword(s):  
Magnetic Field ◽  
Field Line ◽  
Electric Current ◽  
Magnetic Field Line ◽  
Conducting Layer ◽  
Low Latitude ◽  
Ionosphere Model ◽  
Zero Current ◽  
Night Side ◽  
Low Latitude Ionosphere

Abstract. A quantitative division of the ionosphere into dynamo and motor regions is performed on the base of empirical models of space distributions of ionospheric parameters. Pedersen and Hall conductivities are modified to represent an impact of acceleration of the medium because of Ampére's force. It is shown that the currents in the F2 layer are greatly reduced for processes of a few hours duration. This reduction is in particular important for the night-side low-latitude ionosphere. The International Reference Ionosphere model is used to analyze the effect quantitatively. This model gives a second high conducting layer in the night-side low-latitude ionosphere that reduces the electric field and equatorial electrojets, but intensifies night-side currents during the short-term events. These currents occupy regions which are much wider than those of equatorial electrojets. It is demonstrated that the parameter σd=σP+σHΣH/ΣP that involves the integral Pedersen and Hall conductances ΣP, ΣH ought to be used instead of the local Cowling conductivity σC in calculations of the electric current density in the equatorial ionosphere. We may note that Gurevich et al. (1976) derived a parameter similar to σd for more general conditions as those which we discuss in this paper; a more detailed description of this point is given in Sect. 6. Both, σd and σC, appear when a magnetic field line is near a nonconducting domain which means zero current through the boundary of this domain. The main difference between σd and σC is that σd definition includes the possibility for the electric current to flow along a magnetic field line in order to close all currents which go to this line from neighboring ones. The local Cowling conductivity σC corresponds to the current closure at each point of a magnetic field line. It is adequate only for a magnetic field line with constant local conductivity at the whole line when field-aligned currents do not exist because of symmetry, but σC=σd in this case. So, there is no reason to use the local Cowling conductivity while the Cowling conductance ΣC=ΣP+ΣH2/ΣP is a useful and well defined parameter.

Almost-invariant surfaces for magnetic field-line flows

1996 ◽  
Vol 56 (2) ◽  
pp. 361-382 ◽  
Author(s):  
S. R. Hudson ◽  
R. L. Dewar
Keyword(s):  
Magnetic Field ◽  
Field Line ◽  
Magnetic Field Line ◽  
Gradient Flow ◽  
Invariant Surface ◽  
Infinite Dimensional ◽  
Invariant Surfaces ◽  
Magnetic Surfaces ◽  
Rotational Transform ◽  
The Magnetic Field

Two approaches to defining almost-invariant surfaces for magnetic fields with imperfect magnetic surfaces are compared. Both methods are based on treating magnetic field-line flow as a 1½-dimensional Hamiltonian (or Lagrangian) dynamical system. In thequadratic-flux minimizing surfaceapproach, the integral of the square of the action gradient over the toroidal and poloidal angles is minimized, while in theghost surfaceapproach a gradient flow between a minimax and an action-minimizing orbit is used. In both cases the almost-invariant surface is constructed as a family of periodic pseudo-orbits, and consequently it has a rational rotational transform. The construction of quadratic-flux minimizing surfaces is simple, and easily implemented using a new magnetic field-line tracing method. The construction of ghost surfaces requires the representation of a pseudo field line as an (in principle) infinite-dimensional vector and also is inherently slow for systems near integrability. As a test problem the magnetic field-line Hamiltonian is constructed analytically for a topologically toroidal, non-integrable ABC-flow model, and both types of almost-invariant surface are constructed numerically.

Regular Motions in the Ionosphere: Electric and Magnetic Relationships

1961 ◽  
Vol 42 (2) ◽  
pp. 85-100 ◽  
Author(s):  
Sydney Chapman
Keyword(s):  
Magnetic Field ◽  
Electric Current ◽  
Electron Density ◽  
Geomagnetic Field ◽  
Sunspot Cycle ◽  
Ionospheric Currents ◽  
Electric Currents ◽  
Dynamo Action ◽  
Ionospheric Electron Density ◽  
The Earth

Regular worldwide motions in the ionosphere produce daily varying currents there by dynamo action in association with the geomagnetic field. The changing field of these currents induces electric currents within the earth. At the earth's surface, the combined magnetic field of these currents is measured. The parts of primary and secondary origin can be determined separately. The form and intensity of the ionospheric currents can be found. Their height is inferred from the study of the ionospheric electron density and conductivity; it can also be measured by rockets. The daily varying airflow in the layer bearing the electric current, at heights from about 90 to 125 km, can to some extent be inferred. The motion is due partly to the sun's thermal and tidal action and partly to the moon's tidal action. Many aspects of the magnetic variations and the inferred ionospheric motions are considered in some detail, especially their seasonal and sunspot-cycle changes and their variations from day to day.

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