Survey on actual knowledge and physical problems

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Survey on actual knowledge and physical problems

K. Berger

To cite this version:

K. Berger. Survey on actual knowledge and physical problems. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-57-C7-62. �10.1051/jphyscol:19797429�. �jpa-00219431�

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JOURNAL DE PHYSIQUE Colloque C7, suppkment au no 7, Tome 40, Juillet 1979, page C7-57

Survey on actual knowledge and physical problems

K. Berger

31 Gstadstrasse, CH 8702, Suisd

RksumB. - Rtsultats de la recherche moderne sur la foudre, valeurs statistiques des parambtres des impulsions du courant de la foudre, leur influence sur la protection contre la foudre.

Problkmes non rtsolus : coup de foudre pilote (stepped leader), vitesse de propagation de la foudre, temps de montee du courant de la foudre, d&itions internationales des notions de la foudre.

Abstract. - Survey on results of modern lightning research, statistical values of parameters of lightning current impulses, their significance for lightning protection.

Unsolved physical problems, stepped leader, stroke velocity, rise time. International definitions.

First part : Lightning research. - How is lightning initiated ? What is reliable knowledge about it ? What phenomenon is at the base of the strong electric field which causes lightning ?

It is wellknown that during a thunderstorm a strong updraft of warm humid air causes production and separation of electric charges when passing a region with - 5

. . .

- 100 freezing. Negative ions or particles remain concentrated in restricted areas or cells, light positive particles follow the wind and are deposited in higher and calmer regions. This is the case for heat thunderstorms as well as for cold or warm front thunderstorms.

Between negatively and positively charged clouds or cells an electric field has been built up which also influences the earth. Above flat countries the field is at its maximum near the negative cells. With growing space charge a downward progressing discharge will develop : The leader of a downward lightning stroke. Above steep mountains or high towers the induced electric field below the negative cloud may grow at the tower tip not only to produce corona discharges (so-called St-Elmos fires) but also to initiate real lightning discharges, so-called upward strokes or upward flashes. Like downward leaders these are relatively well conducting channels out from the cell with a speed of about 111 000

...

113 000 of velocity of light (1 00

. . .

300 m/ms or 100

. . .

300 km/s).

Discharges which do not reach (strike) the earth are cloud-flashes; discharges to or from the earth are earth-JEashes. In multiple flashes every stroke of an earth flash is initiated by a leader stroke or shortly leader. Currents in negative downward first leaders are between less than 100 A up to several 100 kA.

Currents in upward leaders below positive clouds may reach 1 000 A or even more. The relative well conducting leader channel is often on a very high potential (< 100 MV). When it approaches the earth a kind of breakdown will happen. More exactly, in most cases another leader will initiate at the earth, growing upwards and joining then the downward progressing leader. This kind of upward leader is called connecting leader (Fangentladung) (de'chavge d'interception). On tall structures (TV- or Radio-Towers) this connecting

leader may have lengths of 100 m or more. Sometimes upward and downward leaders miss themselves and a so-called loop appears in the photographs.

The observation of connecting leaders is in relation with the notion of the so-called striking distance on which there is still controversion among the physical engineers.

The highly charged leader channel, after joining the connecting leader, discharges then abruptly and initiates the return stroke. The high current impulse at its earth point is the base for disposition and dimensioning of most lightning protection devices.

Velocity of progression of the return stroke is very high, about 10

. . .

60

%

of velocity of light.

The current impulse of the return strokes is well characterized by _- 4 - parameters :

1) Current amplitude

i^

(kA).

2) Rise time (ps) or current steepness di/dt (kA/ps).

3) Electric charge

S

i dt (C).

4) Current square impulse

1

i 2 . dt (A2. s or kA2. s),

J

or current square integral, in USA often called action integral.

The signification of these afore-mentioned parameters regarding lightning protection is as follows :

1) The crest value of lightning current

f

is responsible for ohmic voltage drops especially in the earthing ground resistance (50

kA

x 10 f2 = 500 kV).

2) The steepness of lightning current dildt deter- mines all kind of inductive voltage drops : Voltage drop in lightning current conductors, induced voltages on magnetically coupled loops a.s.f.

3) The electric charge Q =

1

i dt of lightning current is a mesure for the energy which is transmitted J

by the lightning arc to metallic surfaces, causing melting effects. Charge Q is responsible also for diffusion of electric fields through metallic screens (skin effect screens).

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797429

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C7-58 K. BERGER

4) The current square impulse i2 dt is at the

impulse heating of ohmic resistors.

base of every mecanical effect, and for electrical

S

Some curves on frequency of occurrence of these parameters, as evaluated from the Monte San Sal- vatore research are given in annex 1 and will be reproduced by projection. More details are available in the Bulletin SEV 1972/1973/1978 and in the Cigre- Electra 41 (1975). Annex 2 to this Conference Paper

or 0.5 kA2 . s for negative flashes

S

^iZ.dt

⁼

10' A Z . s or 10 kA2. s for positive flashes.

For engineering purposes it is necessary t o remember that positive flashes are rather seldom in the flat and warm or moderate zones, but have been observed in Sweden and Japan. There is a tendency to base usual protection on negative flashes only.

presents a ^'list 'of all principal definitions about Second part : Three physical problems not yet lightning in 3 languages. solved sufficiently

According to the available measurements from

San Salvatore. some avvroximate values which cor- AS The problem the leaders.

respond to probabilities of occurrence of a few

%

2) The problem of velocity of leader and return

may be given as follows : strokes.

dildt ^N100 kA/ps or 10" A/s , 3) The problem of current rise in first and subsequent strokes (front of current wave).

i ^ ~

150kA.

Analog few %-values for charge and current 1. STEPPED LEADERS are observed in the first square impulse of complete flashes are stroke of negative downward flashes. They do not

S

appear in subsequent leaders if the no-current interval

i. dt 1. 150 Cb (for negative flashes) between strokes is less than 1 or 2 tenths of a second.

They reappear with smaller steps if the no-current interval is long, say several tenths of a second. What i. dt N 500 Cb (for positive flashes) is the reason of this stepping ?

1 .1 TheJirst stroke-leader has to open the lightning channel by ionisation (corona discharge) and to

Rg. 1. - Lightning currents (first strokes).

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SURVEY ON ACTUAL KNOWLEDGE A N D PHYSICAL PROBLEMS

2. - Steepness of all negatlve strokes in a flash dildt (max).

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K. BERGER

Annex 114

Rg. 4. - Current square impulse

S

i2.dt of all positive and negative flashes.

Annex 115

Fig. 5. - Steepness dildtfmax) of 713 negative foilowing strokes in upward flashes.

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S U R V E Y ON ACTUAL KNOWLEDGE AND PHYSICAL PROBLEMS C7-61

produce a well-conducting channel (streamer or leader) with 100 or a few 100 A continuing current.

Stepping is a kind of instability in this channel progression. It may be caused :

a) by an instability in the long feeding arc which supplies the corona-tip of the channel or

b) by an instability during transition from corona to the streamer, before or near the tip of the channel.

Streak camera-photographs from San Salvatore show the most bright point of a new step to appear at the tip of the new step. This remembers the plasma formation by the well-known reversal of the electron avalanches, published by Meek and Raether. But there is no agreement because the steps with lightning are several m long up to more than 10 m as compared with only a few cm in the lab.

The author has the impression that in the transition process the energy transmission from positive ions to the gas molecules has not taken into account sufficiently until now. Indeed the ions do not ionise, but according to their mass they may transmit the whole kinetic energy they got in the electric field, to neutral molecules by central impulses. Their energy is only 4 &? times smaller than that of the electrons because of their smaller free kinetic path. But their acceleration and velocities are about 1 O4 times smaller than that of electrons. Transmission of energy to neutral molecules therefore is slowlier. May be that in the normal stepping interval of 40

...

50 ps transition of energy to the gas molecules i.e. gas heating near the avalanche is sufficient to cause an appreciable enhancement of the Townsend-Coefficient a. This initiates an instability a local gas temp. + a. The effect is analog to the Meek-Raether-instability but it takes more time (40 ps ?). The author suggests an analysis of this effect of energy transmission from

+

ions to the gas and the enhancement of a-ionisation until the field collapses in a new step.

1 . 2 Subsequent strokes dispose of an appreciable residual charge of ions in the channel and in the surrounding corona-space charge. Furthermore temperature of the channel is still enhanced. Both effects facilitate ionisation and leader transition at a lower field intensity. This opinion is proved by the reap- pearance of steps if the cooling and de-ionizing time between strokes becomes longer.

2. VELOCITY OF LEADERS AND RETURN STROKES. -

A) Velocity of the first leader is determined by the stepping process. Between two steps corona pro- gresses rel. slowly at about 100

...

300 km/s.

B) Velocity of subsequent leaders is at least 10 times faster. A possible explanation is residual temperature and residual charge within the channel and outside in the corona shell, which could not be extracted by the preliminary stroke completely.

Mathematical treatment of these progression velocities of leaders on a physical base is extremely difficult.

C) Velocity of the return stroke, which is between 10 and 50

%

that of light, has been found an experi- mental treatment by C. F. Wagner : He supposes the energy which is necessary to ionize and heat the channel to be able to carry the high impulse current of 10 to 200 kA to be responsible for the reduced velocity of waves when compared with the velocity of travelling waves on a metallic conductor. This energy is furnished at the front of the return stroke travelling wave, and therefore cuts permanently slices of charge and energy from it. Some measurements of this phenomenon were made in the high voltage laboratory with rather low impulse current values of a few kA only. An energy of 2 Ws was found to be necessary for each cm of channel and each kA of impulse current (2 Ws cm-I kA-l). Velocity of return strokes is calculated on this base in function of impulse current.

A report to the 15th European Conference on Lightning Protection presented 2 weeks ago at Uppsala by R. Fieux confirms some correlation between current amplitude and progressing speed of the return stroke of triggered lightning flashes, corresponding to the theory of C. F. Wagner : Energy absorption in the front of the travelling wave. This theory should still be confirmed by direct comparison of progression velocity and return stroke measurements.

I was much interested to find in the Journal to this Conference an article by Mr. P. Hubert and G . Monget about measurements from St-Privat-d'Allier of return- stroke velocities in function of current (p. C7-421).

2 flashes with a total of 11 impulse currents between 3-19 kA were analysed :

the 2 first strokes present velocities of about 20

%

of velocity of light,

the 9 subsequent strokes have velocities between 23 and 47

%

of velocity of light,

these values seem to confirm the theoretical calculation by Lundholm and Rusk and the measurements in a laboratory by C . F. Wagner.

3. CURRENT FRONT (RISE TIME) IN FIRST AND SUBSE- QUENT STROKES. - Shape of front current rise does not correspond with the double exponential curve which is generally admitted for calculations. First strokes always begin with a positive exponential rise.

They present a slowlier current rise (less steep wave shape of current) than subsequent strokes. The difference is at least one order of magnitude (at least 10 x ). Only first strokes have so-called connect- ing leaders (Fangentladungen) which progress from an earthed object upward towards the downcoming leader. A simple treatment of the resulting current curve bases on a breakdown between earth and a

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C7-62 K. BERGER

metallic conductor in place of the downcoming leader, where the distance to the meeting point is treated as a simple inductivity L, and the lightning channel as a metallic conductor with surge impedance Z . A better physical treatment of this striking pheno- menon with a physical explication of Z as used by C . F. Wagner is still wanted.

Subsequent strokes have no connecting leaders.

Their current wave has front durations (rise times) between about 0,1

...

1 ps. These values do not show much difference with those of travelling waves on transmission lines.

The difference of front duration between first and subsequent leader could possibly give a measure for the length of the connecting leader.

Regarding steepness of currents dildt there is a very good agreement between French measurements at St-Privat-d'Allier, Italian measurements on Mte Orsa near Varese, and our 1 1 years statistiques from Mount San Salvatore in CH.

With these examples of still open problems I thank you for the possibility to expose our lightning problems to your international cercle of physicists.

Now some coloured pictures of lightning will be shown.

Annex 2 I. Lightning

A. Definitions. - 1 . LIGHTNING. - 1 . 1 Lightning flash is an atmospheric discharge consisting of one or more lightning strokes (single stroke flash, multiple flash).

1 . 2 Lightning channel is the path of the lightning current in the atmosphere.

1 . 3 Lightning stroke (stroke) is a partial discharge in a lightning channel, led by a leader stroke.

1 .4 Leader stroke (leader) is a pre-discharge of low light and current intensity, which produces the lightning channel of the lightning stroke.

1.5 Return stroke (main stroke) is the high light and current intensity discharge following the leader stroke.

1 . 6 Connecting leader is a discharge expanding towards the leader stroke of a downward flash from the earth or from earthed objects.

1 . 7 Downward $ash is a lightning flash, whose first leader stroke proceeds from the cloud to the earth.

1.8 Upwardflash is a lightning flash, whose first leader stroke extends from the earth,,, generally from high earthed pointed structures, towards the electrically charged cloud.

1 .9 Point of strike is the point where the lightning stroke contacts the earth or an earthed object.

2. LIGHTNING CURRENT. - 2 . 1 Lightning current is the current flowing at the point where the lightning strikes.

2.2 Lightning impulse current is the high amplitude and short duration proportion of lightning current.

2 . 3 Continuing current is the current of low amplitude and long duration which follows the impulse current without interruption.

2 . 4 Front is the rising part of the lightning impulse current.

2.5 Tail is the falling part of the lightning impulse current.

2.6 Rise time (front duration) is the time from the beginning until the peak value of the lightning impulse current is reached.

2.7 Lightning flash duration is the time from the beginning of the first lightning stroke to the end of the last lightning stroke.

2.8 Currentpeak (lightning current) is the maximum value of the lightning impulse current i.

2.9 Current steepness (current rise) is the maximum value of the rise of the lightning current di/dt(max) during the rise time (steepest tangent to the current curve).

2.10 Electric charge of a lightning flash is the integral of the lightning current over the flash duration

2.11 Current square impulse is the integral from

P

the square of the current over the time

J

iQt.