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Applied Scientific Research

, Volume 22, Issue 1, pp 185–200 | Cite as

Theoretical investigation of the first order magnetic self-striction in a low pressure mercury vapor arc with remote walls

  • M. F. Hoyaux
Article

Abstract

The conditions of magnetic self-striction in an arc of finite length, not confined laterally by walls, are investigated with a recently developed theory of ambipolar diffusion in a magnetic field, including all first order corrections. Indications are given of how numerical predictions can be made; the case of mercury vapor is treated as an example, using earlier measurements of cylindrical arcs.

Keywords

Electron Temperature Carrier Density Acceptable Solution Positive Column Ambipolar Diffusion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

b, b

mobility of the electrons

b+

mobility of the positive ions

e

modulus of the electron charge

j

current density

2l

distance between fictitious electrodes (Fig. 3)

0

index denoting the center of the discharge

( )0

index characterizing low arc current, magnetic effects negligible

( )I

index denoting strong current, magnetic effects (and others) important

p

reduced pressure of the neutral gas or vapor (in Torr)

u, v, w

curvilinear coordinates, Fig. 2

x

u/l

y

N/N 0

B

self-magnetic induction

Da

coefficient of ambipolar diffusion

E

“primitive” electric field

G

auxiliary function of T, defined in [1, 2]

I

total arc current

K

Boltzmann constant

N

density of carrier pairs

R

radius of the cylindrical arc used for comparison

T

electron temperature

U

“primitive” potential [1, 2]

V

true potential

Z

see Eq. (10)

α

ζ i0 l 2/D a0

β

b +(b )2 E 0 μel 2 N 0/D a0

ζi

“effective” number of ionizing events per electron per unit time

μ

magnetic permeability

(1)

index or superscript indicating: at unit reduced pressure (1 Torr)

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References

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    Hoyaux, M. F., Am. J. Phys. 35 (1967) 232.CrossRefGoogle Scholar
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    Hoyaux, M. F., Arc Physics, p. 105, Springer, New York 1968.Google Scholar
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    Holway, L. H., Jr., Physics Fluids 8 (1965) 1207.CrossRefGoogle Scholar
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    Hoyaux, M. F., The Gvosdover effect in a low pressure arc constrained by its own magnetic field, to be published in Applied Scientific Research.Google Scholar
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    Hoyaux, M. F., Rev. Gén. Electr. 60 (1951) 279, 317.Google Scholar
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    Hoyaux, M. F. and P. Gans, The Effect of the Self-Magnetic Field Upon the Characteristics of a Positive Column with Axial Symmetry, EOARDC Report TN-54,1, Ateliers de Constructions Electriques de Charleroi, Charleroi (Belgium) 1954.Google Scholar
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    Hoyaux, M. F. and P. Gans, The Influence of the Gvosdover Effect Upon the Characteristics of a Positive Column with Axial Symmetry in the Domain in which the Self-Magnetic Field is Important, EOARDC Technical Report TN-55,5, Ateliers de Constructions Electrique de Charleroi, Charleroi (Belgium) 1954.Google Scholar
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    Hoyaux, M. F., Arc Physics (loc. cit.), p.Google Scholar
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    Tonks, L. and I. Langmuir, Phys. Rev. 34 (1929) 1929.CrossRefGoogle Scholar
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    Hoyaux, M. F. and P. Gans, Some Properties of the Mercury Vapour Arc at Very Low Pressures, Proceedings of the Fourth International Conference on Ionization and Gases, IIB, p. 364, Uppsala August 1959.Google Scholar
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    Hoyaux, M. F., Arc Physics (loc. cit.) p.Google Scholar

Copyright information

© Martinus Nijhoff 1970

Authors and Affiliations

  • M. F. Hoyaux
    • 1
  1. 1.University of PittsburghPittsburghUSA

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