Comments on « the mechanism of the long spark formation »

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Comments on “ the mechanism of the long spark formation ”

E. Barreto, H. Jurenka

To cite this version:

E. Barreto, H. Jurenka. Comments on “ the mechanism of the long spark formation ”. Journal de

Physique, 1981, 42 (1), pp.153-153. �10.1051/jphys:01981004201015300�. �jpa-00208984�

153

Comments on « the mechanism of the long spark formation » (*)

E. Barreto and H. Jurenka

State University ^{of New York at} Albany,

1400 Washington Avenue, Albany, ^NY 12222, ^U.S.A.

(Reçu ^{le 5} juin 1980, accepté ^{le 22} septembre 1980)

J. Physique ⁴² (1981) ¹⁵³ JANVIER 1981.

Classification

Physics ^Abstracts

52.00

52.80

A recent publication by ^I. Gallimberti, ^{« The}

mechanism of the long spark formation », ^considers

the possibility of electron fluid waves in a weakly

ionized _gas [1]. Also,, it ^{describes a} mathematical

technique ^that incorporates fluid conservation laws together with transmission line equations ^{into a} single

non-linear equation ^{for a vector with four} compo.

nents : electron density, n, ^drift velocity, v, tempera- ture, T, ^and electrical potential, ^{U. We are} happy ^{that a}

« state-of-the art » paper brings ^{these two} concepts

to the attention of people working in electrical

discharges. Unfortunately, ^the system ^of equations

labelled (80) through (85) ^{seems to} incorporate ^serious

errors that cannot be traced to their source in unpu- blished references [116,117,119]. ^Our comments must then necessarily ^{be based on some of our} published

work in which ^we have used the ^same mathematicat technique [2].

1. Equation (84) defines the column vector

and the matrices A( Y ) ^and B(Y) ^{to be ûsed in} equa- tion (83). ^It is then stated that linearization is possible

around a stable solution Yo. Regardless of the actual

expansion used, equation (83) ^cannot be satisfied by

thé ^{B( Yo) term} defined in equation (84). ^{Even to a}

zéroth order approximation B(Yo) ^{is not zero and the} equation ^{to be solved} (equation (83)) ^{is not satisfied.}

Alternatively, ^an imposed B(YO) ^{= 0 condition} implies

a steady ^state trivial condition where the electron

density, ^drift velocity ^and temperature ^{are all zero.}

2. The transmission line equations ^used imply ^well-

known fixed values of capacitance and inductance _per unit length. ^The top equation (80) is obtained by integrating ^Maxwell’s equations ^{under the} assumption

that there are no field components along ^{the trans-}

mission line direction [3]. The bottom equation (80)

is Ohm’s law for ^a steady ^state condition. It is not

clear how these two equations ^{can be} incorporated together ^{with a} one-dimensional model for a transient process in which the electric field is parallel ^{to the fluid} velocity.

3. Equations.(81) incorporate ^{notation not defined.}

For instance v. ^{in the momentum} equation. ^{In the}

energy equation ^{we are unable to} obtain the

(2 evl3 k) (dU/dx) ^{term. In} fact, ^{we are not sure how} equations (81) ^are generated ^from equations (34)

because it is not clear whether the ES ^{term in} equation (34) represents ^{kinetic or} ionization _energy.

In our publication [2] ^{we work} directly ^{with Maxr}

well’s equations and define ^a different B(Y) ^{term such}

that B( Yo) ^{=- 0 as} required by ^the equation :

Our B(YO) ⁼ 0 condition implies that there is a steady

state Yo ⁼ (no, ^0, To, 0)T ⁱⁿ which the electric field and drift velocity ^are negligible. Physically ^{this is} justified,

in a typical weakly ^ionized plasma, by ^a large plasma frequency ^{and a small} shielding ^distance

Thus we assume that changes in the electron popula-

tion occur even before ionization takes place ^and

show that solitary ^{waves are} possible under conditions

compatible ^with experiment. ^We imply ^that, just ^{as in}

a neutral _gas, dissipation ^{can lead to a shock wave}

in the electron fluid. However, ^{we have not succeeded} in incorporating ionization or dissipation ^{into a} system ^of equations ^{that use} Taniuti’s reductive

perturbation ^method.

References

[1] GALLIMBERTI, I., « The mechanism of the long spark ^formation », J. Physique Colloq. ⁴⁰ (1979) ^C7-193.

[2] BARRETO, E., JURENKA, ^H. and REYNOLDS, ^S. I., ^« The formation of small sparks », J. Appl. Phys. ⁴⁸ (1977) ^4510.

[3] RAMO, ^{S. and} WHINNERY, J. R., ^Field and Waves in Modern Radio (John Wiley, NY) 1964, p. 340.

(*) ^Work supported by the Ofhce of Naval Research.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01981004201015300