LEADER, LIGHTNING, LIGHTNING PROTECTION LEADER, LIGHTNING, LIGHTNING PROTECTION E. Bazelyan and Yu. Raizer Solved and unsolved problems.

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