A Two-Dimensional Mathematical Model of a Short Vacuum Arc in External Magnetic Field

Londer, Ya. I.; Ul’yanov, K. N.

doi:10.1007/s10740-005-0131-3

Cited by 9 publications

(16 citation statements)

References 8 publications

(18 reference statements)

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“…Note further that the model suggested in [1] differs significantly from models [5][6][7][8] based on the solution of the Poisson equation. In the case of our model, there is no need to find the distribution of physical parameters in a region exceeding significantly the region of current passage.…”

Section: Discussion Of the Resultsmentioning

confidence: 94%

“…Therefore, if we take the origin of cylindrical coordinates to be zero potential, the radial distribution of potential on the cathode boundary may be found by integrating the intensity of radial electric field (Eq. (31) in [1]) at z = 0. We derive, in the dimensionless variables introduced in [1], .…”

Section: Results Of Numerical Simulation For the Case Of Nonequipotenmentioning

confidence: 98%

“…6, a curve is plotted which relates the critical values of magnetic field B z and arc current I 0 , i.e., each point on the curve in Fig. 6 decreases insignificantly and is still far from the ionsound velocity which amounts to ~0.3 in the dimensionless variables of [1]. Figure 7 gives the radial distribution on the anode boundary of plasma of the dimensionless axial velocity of ions for two values of magnetic field B z at which varies most strongly.…”

Section: Results Of Numerical Simulation For the Case Of Nonequipotenmentioning

confidence: 99%

“…In [1], we have developed a mathematical model for the calculation of the parameters of a high-current vacuum arc. The motion of electrons and fast cathode ions is described by hydrodynamic and electrodynamic equations which may be used to calculate the distributions of electron and ion current densities, the distribution of electric and magnetic fields, and the distribution of plasma density in the channel of a vacuum arc (VA).…”

Section: Introductionmentioning

confidence: 99%

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A two-dimensional mathematical model of a short vacuum arc in external magnetic field: results of numerical calculations

Londer

Ul’yanov

2006

High Temp

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The paper deals with the investigation of the impact made by two-dimensional effects on the process of passage of current in a short vacuum arc in an axial magnetic field. A two-fluid mathematical model is used, which is based on hydrodynamic and electrodynamic equations. The axial magnetic field B z affects significantly the magnitude of two-dimensional effects: the two-dimensional effects increase with decreasing B z . The simulation results demonstrate that the contraction of plasma density exceeds that of current density. The distribution of anode drop of potential on the anode surface is nonuniform; in the case of certain (critical) values of current, the anode drop goes to zero on the external boundary of plasma. The dependence of the critical current on B z is determined. The distribution of current density on the starting plane is nonuniform with a maximum on the axis, and the ion trajectories are inclined to the discharge axis. The possibility is discussed of matching the solution in the plasma region of vacuum arc with that for cathode flames.

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Section: Discussion Of the Resultsmentioning

confidence: 94%

Section: Results Of Numerical Simulation For the Case Of Nonequipotenmentioning

confidence: 98%

Section: Results Of Numerical Simulation For the Case Of Nonequipotenmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A two-dimensional mathematical model of a short vacuum arc in external magnetic field: results of numerical calculations

Londer

Ul’yanov

2006

High Temp

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“…For this purpose, it is necessary that the density of VAD current would decrease from the center to periphery by quite a definite law. In so doing, no strong contraction of current is observed [3,4].…”

Section: Introductionmentioning

confidence: 89%

A theoretical study of the impact of magnetic field of Hall current on the parameters of a high-current vacuum-arc discharge

Londer

Ul’yanov

2008

High Temp

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It is demonstrated that the magnetic field of Hall current in a short high-current vacuum-arc discharge significantly distorts the external axial magnetic field and affects the distribution of current density in the discharge gap. This effect decreases with increasing external magnetic field, with decreasing arc current, and with decreasing ratio of the length of discharge gap to its transverse dimension. A 2D magnetohydrodynamic mathematical model is used to calculate the discharge parameters for different values of induction of external magnetic field. The calculation results are compared with similar results obtained using a 1.5D model in which the impact made by magnetic field of Hall current is ignored. It is inferred that the simpler 1.5D model may be employed in calculations of parameters of vacuum arc in a wide range of variation of arc current and of induction of external magnetic field.

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On the numerical simulation of the diffuse arc in a vacuum interrupter

Langlois

Chapelle

Jardy

et al. 2011

Journal of Applied Physics

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A 2D two-fluid numerical model is developed for the description of the diffuse arc in a vacuum interrupter under the possible influence of an axial magnetic field (AMF). This model incorporates the energy balance equations for both ions and electrons and takes into account the three components of the self-generated magnetic field. The possibility of both supersonic (at low current density) and subsonic (at high current density) plasma flow regimes is considered. Data from the literature are used to specify the values of the plasma parameters near the cathode, and the boundary conditions on the anode boundary rely on a simplified model of the anode sheath. Simulation results are presented for both ion flow regimes, with special attention to the current and plasma flow features. It is shown that there is always a contraction of the current flow, whereas the dynamics of the ions throughout the interelectrode gap is strongly influenced by their flow regime near the cathode. Finally, the influence of various operating parameters (presence of an AMF, gap length) on the current constriction at the anode is discussed.

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A Two-Dimensional Mathematical Model of a Short Vacuum Arc in External Magnetic Field

Cited by 9 publications

References 8 publications

A two-dimensional mathematical model of a short vacuum arc in external magnetic field: results of numerical calculations

A two-dimensional mathematical model of a short vacuum arc in external magnetic field: results of numerical calculations

A theoretical study of the impact of magnetic field of Hall current on the parameters of a high-current vacuum-arc discharge

On the numerical simulation of the diffuse arc in a vacuum interrupter

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