THE FIELD STRENGTH AND ELECTRON DENSITY CALCULATIONS FOR THE CORONA PULSES

(1)

HAL Id: jpa-00219150

https://hal.archives-ouvertes.fr/jpa-00219150

Submitted on 1 Jan 1979

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

THE FIELD STRENGTH AND ELECTRON DENSITY CALCULATIONS FOR THE CORONA PULSES

M. Laan, H. Korge, K. Kudu

To cite this version:

M. Laan, H. Korge, K. Kudu. THE FIELD STRENGTH AND ELECTRON DENSITY CALCULA-

TIONS FOR THE CORONA PULSES. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-351-C7-

352. �10.1051/jphyscol:19797173�. �jpa-00219150�

(2)

JOURNAL DE PHYSIQUE CoZZoque C7, suppZdment au n07, Tome 40, J u i Z Z e t 1979, page C7- 35 1

THE FlELD STRENGTH AND ELECTRON DENSTY CALCULATIONS FOR THE CORONA PULSES

M. Laan, H. Korge and K. Kudu.

T m t u S t a t e U n i v e r s i t y , Department of P h y s i c s , Y a r t u , E s t o n i a n S.S.R.

Introduction. I n our previous paper

[ I ]

t h e spatio-6emporal development of l u m i - nosity i n Trichel pulses and pre-onset streamers of

D.C.

coronas w a s determined.

The measurements were c a r r i e d out i n the point-to-plane gap i n laboratory air. I n t h i s paper we are going t o report about;

an attempt of t h e calculation of t h e main c h a r a c t e r i s t i c s of t h e corona pulses on t h e basis of luminosity d i s t r i b u t i o n meas- urements

[ I ]

. Such calculations f o r gas discharge i n nitrogen i n t h e homogeneous gap were made f o r t h e f i r s t time by Doran

[2].

I n our calculations t h e same proce- dure was used f o r the air. W e supposed only two processes - ionization,

and

at- t achment - are active within the volume element under observation and t h a t t h e photomultiplier current i s a l i n e a r

function of l i g h t iptensity.

So we were able t o evaluate the spatio- temporal d i s t r i b u t i o n of t h e reduced f i e l d strength (E/p), t h e r a t e o f change i n the number of electrons (dne/dt=d(+ - ^n-)/dt),

and the l i n e density of electrons (ne).

On the b a s i s of t h e curves E/p(x) a rough approximation of the spatio-temporal dis- t r i b u t i o n of the charged p a r t i c l e s con- centration (N+ -

^N-

- ^Ne)

^was

made, using the one dimensional Poisson equation.

Trichel pulse. The calculated f i e l d dis- t r i b u t f on d i f f e r s considerably from the 1;aplacian one. It is possib1e"to discern two stages i n the Trichel pulse develop- ment (A

and B, Fig. 1).

During stage

A

%he formation of the c h a r a c t e r i s t i c v i s i - b l e regions of the discharge pulse - ^the

negative glow, Paraday's dark space and t h e positive column - takes place. A t the moment t

=

2 ns t h e high f i e l d region is concentrated a t a distance of ~ ~ 0 . 2 5 mm from the point. In t h i s region the r a t e of change i n the number of electrons and ions has a maximum. As a r e s u l t , t h e pos- i t i v e space charge maximum moves towards t h e point. This process stops when t h e space charge concentration maximum

has

shif'ted t o x

^,N

0.05

~p.

During stage

A

attachment is not active

and

the reduc- t i o n in f i e l d strength i s due t o the in- tensive generation of electrons

and posi-

t i v e ions. During stage B, dne/dt reduces quickly and by %he moment; t = 20 ns at- t acchment becomes dominant.

A

streamer develops from a burst pulse when t h e number of electrons near t h e

~ o i n t exceeds

5.10~.

I n t h i s case the condition of piasma existence i s f u l f i l l e d near the point electrode t i p . By the mo- ment t = 14.5 ns counted from the detect-

lig.1. Trichel pulse. Spatio-temporal d i s t r i b u t i o n of t h e E/p, dne/dt, ne

and

(N+ - ^N- - %),the parameters expressing time counted from the beginning 09 the detectable luminosity level.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797173

(3)

able b e g h i n g typical distributions of the E/p, &/dt, ne and (N+ - ^N- - ^Ne)

have become established (Fig. 2). The char~actleristic regions ( I - ^V) ^of ^a

streamer have been indicated f o r the mo- ment t

^E18

ns (dotted curves).

In region I avalanches a r i s e due t o photo- ionisation. Region I1 of intensive ioni- zation has a considerable s p a t i a l extent L. The increasing ne compensates the po- s i t i v e space charge and produces a de- crease in E/p. Supposing the streamer channel diameter i s 50 urn, the ele t r o n concentration is of the order

of 10q4cm-3,

which about three times exceeds the order of (N - ^IT- - ^rJ,) for t h i s region. Come- quentfy, the discharge channel is quasi- neutral. I n region

111 a decrease

i n f i e l d strength produces an increase of attach- ment and hence causes a decrease

in

w / d t . I n region

I V

the electron d r i f t causes the accumulation of a negative space charge.

Between the positive space charge near t h e point (region V) and the negative

space charge the e l e c t r i c a l f i e l d strength enhances

a d

therefore &/dt and

ne

in- crease.

The r e s u l t s obtained for

the

pre-onset streamer

in

t h e best wag correspond t o the model of the streamer developed by Phelps

C3J. The accuracy of calculations signif- i c a n t l y decreased f o r x > 2 mm because of the considerable deviation of the streamer branches from the Sischarge gap axis. I n the zone near the point the distribution (N+ - ^N- -

^N ⁾

may be invalid

as

the dis- charge diameter changes sharply.

To veriFg the v a l i d i t y of our assumptions made above, t h e current of a Trichel pulse aad of a pre-onset streamer

w a s

calculated i n two different wws ^(Fig. 3) and w a s compared with the measured current. A more detailed emalysis of t h i s work i s given i n

[4

1. References.

1. B.Korge, K.Kudu, M.Laan. Development of

D.C.

Corona Pulses a t Atmospheric Bessure. Proc.

X I 1 1

I C P I G , Berlin, 1977, p.451JC52-

2. A.A.Doran. The Propagation of a Lumi- nous &ont through a Developing

Spark

Discharge fn

82.

Proc

I X I C P I G ,

Bucharest, 1969, p. 280.

3. C.T.Phelps and R.F.Criffiths. Depend- ence of Positive Corona Streamer Pro- pagation on

A i r

Pressure and Water Vapor Content.

3.

Appl. Phys., %,1976, pp. 2929-2934.

4.

THE FIELD STRENGTH AND ELECTRON DENSITY CALCULATIONS FOR THE CORONA PULSES

HAL Id: jpa-00219150

https://hal.archives-ouvertes.fr/jpa-00219150

Submitted on 1 Jan 1979

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

THE FIELD STRENGTH AND ELECTRON DENSITY CALCULATIONS FOR THE CORONA PULSES

M. Laan, H. Korge, K. Kudu

To cite this version:

M. Laan, H. Korge, K. Kudu. THE FIELD STRENGTH AND ELECTRON DENSITY CALCULA-

TIONS FOR THE CORONA PULSES. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-351-C7-

352. �10.1051/jphyscol:19797173�. �jpa-00219150�

Introduction. I n our previous paper

t h e spatio-6emporal development of l u m i - nosity i n Trichel pulses and pre-onset streamers of

coronas w a s determined.

The measurements were c a r r i e d out i n the point-to-plane gap i n laboratory air. I n t h i s paper we are going t o report about;

an attempt of t h e calculation of t h e main c h a r a c t e r i s t i c s of t h e corona pulses on t h e basis of luminosity d i s t r i b u t i o n meas- urements

. Such calculations f o r gas discharge i n nitrogen i n t h e homogeneous gap were made f o r t h e f i r s t time by Doran

I n our calculations t h e same proce- dure was used f o r the air. W e supposed only two processes - ionization,

at- t achment - are active within the volume element under observation and t h a t t h e photomultiplier current i s a l i n e a r

function of l i g h t iptensity.

So we were able t o evaluate the spatio- temporal d i s t r i b u t i o n of t h e reduced f i e l d strength (E/p), t h e r a t e o f change i n the number of electrons (dne/dt=d(+ - n-)/dt),

and the l i n e density of electrons (ne).

On the b a s i s of t h e curves E/p(x) a rough approximation of the spatio-temporal dis- t r i b u t i o n of the charged p a r t i c l e s con- centration (N+ -

- Ne)

made, using the one dimensional Poisson equation.

Trichel pulse. The calculated f i e l d dis- t r i b u t f on d i f f e r s considerably from the 1;aplacian one. It is possib1e"to discern two stages i n the Trichel pulse develop- ment (A

During stage

%he formation of the c h a r a c t e r i s t i c v i s i - b l e regions of the discharge pulse - the

negative glow, Paraday's dark space and t h e positive column - takes place. A t the moment t

shif'ted t o x

0.05

During stage

attachment is not active

the reduc- t i o n in f i e l d strength i s due t o the in- tensive generation of electrons

t i v e ions. During stage B, dne/dt reduces quickly and by %he moment; t = 20 ns at- t acchment becomes dominant.

streamer develops from a burst pulse when t h e number of electrons near t h e

~ o i n t exceeds

I n t h i s case the condition of piasma existence i s f u l f i l l e d near the point electrode t i p . By the mo- ment t = 14.5 ns counted from the detect-

lig.1. Trichel pulse. Spatio-temporal d i s t r i b u t i o n of t h e E/p, dne/dt, ne

(N+ - N- - %),the parameters expressing time counted from the beginning 09 the detectable luminosity level.

able b e g h i n g typical distributions of the E/p, &/dt, ne and (N+ - N- - Ne)

have become established (Fig. 2). The char~actleristic regions ( I - V) of a

streamer have been indicated f o r the mo- ment t

ns (dotted curves).

which about three times exceeds the order of (N - IT- - rJ,) for t h i s region. Come- quentfy, the discharge channel is quasi- neutral. I n region

i n f i e l d strength produces an increase of attach- ment and hence causes a decrease

w / d t . I n region

the electron d r i f t causes the accumulation of a negative space charge.

Between the positive space charge near t h e point (region V) and the negative

space charge the e l e c t r i c a l f i e l d strength enhances

therefore &/dt and

in- crease.

The r e s u l t s obtained for

pre-onset streamer

t h e best wag correspond t o the model of the streamer developed by Phelps

C3J. The accuracy of calculations signif- i c a n t l y decreased f o r x > 2 mm because of the considerable deviation of the streamer branches from the Sischarge gap axis. I n the zone near the point the distribution (N+ - N- -

may be invalid

the dis- charge diameter changes sharply.

To veriFg the v a l i d i t y of our assumptions made above, t h e current of a Trichel pulse aad of a pre-onset streamer

calculated i n two different wws (Fig. 3) and w a s compared with the measured current. A more detailed emalysis of t h i s work i s given i n

1.

References.

1. B.Korge, K.Kudu, M.Laan. Development of

Corona Pulses a t Atmospheric Bessure. Proc.

I C P I G , Berlin, 1977, p.451JC52-

2. A.A.Doran. The Propagation of a Lumi- nous &ont through a Developing

Discharge fn

Proc

Bucharest, 1969, p. 280.

3. C.T.Phelps and R.F.Criffiths. Depend- ence of Positive Corona Streamer Pro- pagation on

Pressure and Water Vapor Content.

Appl. Phys., %,1976, pp. 2929-2934.

M.Laan. Calculation of the Electric Pield Distsibution i n DFrect Current Corona Pulses. Acta Comment. Univ.

Tartuensis, B, 1979, p.77-106 ( i n BUSS~WL)

Fig.3. Measured (solid curves) end

l a t e d (o

current pulses of a Trichel pulse (a) and of a pre-onset streamer (8).

Pig. 2. Eke-onset streamer. Follow the

t e x t

So we were able t o evaluate the spatio- temporal d i s t r i b u t i o n of t h e reduced f i e l d strength (E/p), t h e r a t e o f change i n the number of electrons (dne/dt=d(+ - ^n-)/dt),

- ^Ne)

%he formation of the c h a r a c t e r i s t i c v i s i - b l e regions of the discharge pulse - ^the

(N+ - ^N- - %),the parameters expressing time counted from the beginning 09 the detectable luminosity level.

able b e g h i n g typical distributions of the E/p, &/dt, ne and (N+ - ^N- - ^Ne)

have become established (Fig. 2). The char~actleristic regions ( I - ^V) ^of ^a

which about three times exceeds the order of (N - ^IT- - ^rJ,) for t h i s region. Come- quentfy, the discharge channel is quasi- neutral. I n region

C3J. The accuracy of calculations signif- i c a n t l y decreased f o r x > 2 mm because of the considerable deviation of the streamer branches from the Sischarge gap axis. I n the zone near the point the distribution (N+ - ^N- -

calculated i n two different wws ^(Fig. 3) and w a s compared with the measured current. A more detailed emalysis of t h i s work i s given i n