LEADER,LEADER, LIGHTNING, LIGHTNING,

LIGHTNING PROTECTIONLIGHTNING PROTECTION

E. Bazelyanand

Yu. Raizer

Solved and unsolved problems

OUTLINEOUTLINE

Possibility of a streamer breakdown

Leader mechanism of a long spark and lightning

The main unsolved problems in leader physics

Some essential unsolved problems in lightning physics

The present needs in lightning protection

Why a long spark and lightning can not be Why a long spark and lightning can not be the simplest streamer-like channelthe simplest streamer-like channel

-Electron lives t ~ 10 –7 s in cold air

- Channel loses conduction at x ~ vst ~ 1- 100 cm behind tip ( vs ~ 107 – 109 cm/s )

-Only air T 5000 K can save channel conduction

Energy resource for growing channel:

22

11 05.0

2U

UCW

1.0/ln

2 01

rLÑ

J/cm U [MV]

pF/cm

-Heating balance W1 r020w(T), w(5kK)=12 kJ/g –specific

enthalpy - W1 is sufficient to heat r0 0.033U cm, U - [MV]

- Corresponding radial field MV/cm5rLr

UEr /ln

immediately expands channel .Really rtip Utip /2Emax 3Utip [MV] cm and T 3K (Emax 150 kV/cm)

Cold air short plasma life no long conducting channel

Streamer breakdownStreamer breakdown

- Streamer bridges air gap d if U > Esd

Es+ = 5 kV/cm Es

- = 10 kV/cm

Bridging gap breakdown = short circuit

Channel should have a falling V-I characteristic to be converted to arc what requires T 5000 K

-Channel can not be heated by the “return stroke” because its energy resource even less than for primary streamer ionization wave.

-Channel can be heated after bridging by following current only if 20 kV 4Es

+, otherwise air plasma decays. dUE /

Streamer breakdown: numerical modelingStreamer breakdown: numerical modeling

1. “Return stroke” along streamer channel1. “Return stroke” along streamer channel

2. Heating plasma channel after 2. Heating plasma channel after “return stroke” “return stroke”

Cause of j minimum: great contribution of N2

* (born in the streamer tip) into ionization, ne and j fall when N2

* disappear, ne and j grow again at T > 3000 K due to N + O e + NO+ ionization

Streamer breakdown can “outrun” leader one (much more effective) only in short gaps or at the very strong fields Eaver =U/d

3. Time of heating3. Time of heating

LEADER MECHANISM OF SPARK AND LEADER MECHANISM OF SPARK AND LIGHTNINGLIGHTNING

Typical leader parameters

Laboratory Lightning

Length 10 m 3-6 kmTip potential 1.5 10-50 MVVelocity 2104 3105 m/sCurrent 1 10-100 ALength ofstreamer zone 3 10-100 mChannel radius 0.3 1 cmTemperature 5000 10000 K Length of streamer zone

s

ts E

UR ~

Es+ = 5 kV/cm Es

- = 10 kV/cm

Advantages of the leader mechanismAdvantages of the leader mechanism

- No relation between rchan and U,- rchan can be small: Er ~ 30 kV/cm << U/rchannel

- TL >> T S though energy resources of leader and streamer are close at the same U (since rchan.L << rchan.S)

-High T results in • no attachment • weak recombination • increase of ionization by electron impact • new ionization mechanism N + O e + NO+

-Leader lives a long time and propagates far at the weak external electric field E ~ 100 V/cm

-Leader breakdown of a long gap requires U much less than streamer one

Streamer-leader transition – clue process Streamer-leader transition – clue process determining positive leader advancementdetermining positive leader advancement

Leader tip ejects weak streamers with fs ~ 109 – 1010 s-1

(experiment 1982)

“Young” conducting streamers form a leader tip of rtip ~ lattach ~ vsattach ~ 10710 –7 ~ 1 cm

Leader current IL ~ fsqs ~ 1 A(qs ~ 10-9 C– charge carried by one streamer)

Summary current of numerous streamers is constricted due to ionization-thermal instabitity

IL const during constriction because the streamer zone is a“current source” with huge resistance Utip/IL ~ 1 MV/1 A ~ 1 M

Instability time ins ~ 10 –6 s (computer modeling and estimate )

Leader velocity

scmvlr

vins

atts

ins

att

ins

tipL /~~~~ 610

Minimal possible channel radius

cmr ins2104 ~~min

- max from heat diffusion and ambipolar diffusion coefficients

Minimal voltage to sustain positive leader - rmin2w(5kK) =C1Umin

2/2

Umin 300 kV – estimate Umin 400 kV - experiment

Casual connections and simplest model forCasual connections and simplest model forlong leaderlong leader

Voltage balance

U = ELL + Utip (1)

L xt – leader length EL – channel field

Developed hot leader channel is similarto that in arcEL b/IL b 300 VA/cm (2)

Charge conservation law:

IL = LvL C1[Utip – Uext(xt)]vL C1UtvL (3)

Leader velocity vL is function of Ut or IL but can not depend upon Eext ~ 100 V/cm << ES 10 kV/cm, Ei 30 kV/cm

Empirical formula vL = a(Ut )1/2 a = 1500 cm/s (vL ~ IL1/3) (4)

dL/dt = vL (5)

Leader model (1) – (5) admits - to compute lightning propagation, - to find optimal regime for leader propagation and minimal breakdown voltage of large air gaps, d

5/2

5/2

0min 2

/ln3

3

5d

a

RdbU s

U d Eopt L5/ 2 ) ( UU opttip 5/3)(

5/3. ~ dI optL

- very good agreement with measured U50%(d) for d ~ 10 –100 mand reasonable estimate for lightning

Umin 20 MV for d = 3 km

Umin 0.73d 2/5 MV, d – [m]

CREEPING LEADERCREEPING LEADER

Usual leader -Usual leader - high Umin = 400 kV and U ~ 1-3 MV to bridge 1-30 m are result of small C1 ~ 0.1 pF/cm for leader in free space

Creeping leader requires U ~ 10 – 20 kVto move 1-3 m for = 10-4 cm whenC1 ~ 10 pF/m

Creeping leaderCreeping leader

Some of the main unsolved problemsSome of the main unsolved problems

Adequate theory of streamer-leader transition, current constriction and leader velocity.

All published computations of leader evolution (very complicateand tangled) consist evident or (more often) hidden unproved assumptions and fitting parameters.

Stepped negative leader

-90% of downward lightning are negative.- Both lightning and laboratory negative leaders propagate by steps. Laboratory steps – 0.2 – 2 m Lightning steps - 20 – 50 m

Streak photos of negative leaderStreak photos of negative leader

Advancement of negative stepped leader

“Double step forward - single step backward”

Double step is very fast, single –with vL

+ so the mean vL- vL

+

Artificially induced stepArtificially induced step

Why positive leader elongates quasi-continuouslyWhy positive leader elongates quasi-continuouslybut negative one – by stepsbut negative one – by steps

-plasma germs for streamer pair are probably generate in both cases near to front of streamer zone where there arelocal E > 30 kV/cm

-but streamers can develop at the first case only

-advancement of negative leader via auxiliary positive space leader is more “profitable”.

Problem: how the space leaders are formed

LIGHTNINGLIGHTNING

Basic mechanisms and allproblems concerning of the firstlightning leader are practicallythe same as for laboratory longleader .

Amongst a lot unsolved problems we note two:

1. What is a mechanism of the first downward leader inception?

Cloud is not conductor. Only pair of leaders can be originated.What is a nature of the primary plasma conductor? The problem is close to the problem of space leaders inception inthe negative spark.

2. What is mechanism of non-conducting cloud discharging during lightning process?

How does the net of multibranched streamers-leaders develop?

LIGHTNING PROTECTIONLIGHTNING PROTECTION

Hazard Can lightning rod protect ? - human

- forest - structures- transmission lines- electronic and microelectronic systems- aircrafts

nonoyes (partly)yes partly)

nono

Two principal way of protection:

1. to catch lightning not let it to object lightning rod

2. to take lighting away, to annihilate far it from object no means

This is the main problem