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

OUTLINE  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 the simplest streamer-like channel -Electron lives t ~ 10 –7 s in cold air - Channel loses conduction at  x ~ v s t ~ cm behind tip ( v s ~ 10 7 – 10 9 cm/s ) -Only air T  5000 K can save channel conduction Energy resource for growing channel: J/cm U [MV] pF/cm

-Heating balance W 1   r 0 2  0 w(T), w(5kK)=12 kJ/g –specific enthalpy - W 1 is sufficient to heat r 0  0.033U cm, U - [MV] - Corresponding radial field MV/cm immediately expands channel. Really r tip  U tip /2E max  3U tip [MV] cm and  T  3K (E max  150 kV/cm) Cold air  short plasma life  no long conducting channel

Streamer breakdown - Streamer bridges air gap d if U > E s d E s + = 5 kV/cm E s - = 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  4E s +, otherwise air plasma decays.

Streamer breakdown: numerical modeling 1. “Return stroke” along streamer channel

2. Heating plasma channel after “return stroke” Cause of j minimum: great contribution of N 2 * (born in the streamer tip) into ionization, n e and j fall when N 2 * disappear, n e 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 E aver =U/d 3. Time of heating

LEADER MECHANISM OF SPARK AND LIGHTNING Typical leader parameters Laboratory Lightning Length 10 m 3-6 km Tip potential MV Velocity 2   10 5 m/s Current A Length of streamer zone m Channel radius cm Temperature K Length of streamer zone E s + = 5 kV/cm E s - = 10 kV/cm

Advantages of the leader mechanism - No relation between r chan and U, - r chan can be small: E r ~ 30 kV/cm << U/r channel - T L >> T S though energy resources of leader and streamer are close at the same U (since r chan.L << r chan.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 determining positive leader advancement Leader tip ejects weak streamers with f s ~ 10 9 – s -1 (experiment 1982) “Young” conducting streamers form a leader tip of r tip ~ l attach ~ v s  attach ~ 10 7  10 –7 ~ 1 cm Leader current I L ~ f s q s ~ 1 A (q s ~ C– charge carried by one streamer) Summary current of numerous streamers is constricted due to ionization-thermal instabitity I L  const during constriction because the streamer zone is a “current source” with huge resistance U tip /I L ~ 1 MV/1 A ~ 1 M 

Instability time  ins ~ 10 –6 s (computer modeling and estimate ) Leader velocity Minimal possible channel radius  - max from heat diffusion and ambipolar diffusion coefficients Minimal voltage to sustain positive leader -  r min 2 w(5kK) =C 1 U min 2 /2 U min  300 kV – estimate U min  400 kV - experiment

Casual connections and simplest model for long leader Voltage balance U = E L L + U tip (1) L  x t – leader length E L – channel field Developed hot leader channel is similar to that in arc E L  b/I L b  300 VA/cm (2) Charge conservation law: I L =  L v L  C 1 [U tip – U ext (x t )]v L  C 1  U t v L (3) Leader velocity v L is function of  U t or I L but can not depend upon E ext ~ 100 V/cm << E S  10 kV/cm, E i  30 kV/cm Empirical formula v L = a(  U t ) 1/2 a = 1500 cm/s (v L ~ I L 1/3 ) (4) dL/dt = v L (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 - very good agreement with measured U 50% (d) for d ~ 10 –100 m and reasonable estimate for lightning U min  20 MV for d = 3 km U min  0.73d 2/5 MV, d – [m]

CREEPING LEADER Usual leader - high U min = 400 kV and U ~ 1-3 MV to bridge 1-30 m are result of small C 1 ~ 0.1 pF/cm for leader in free space Creeping leader requires U ~ 10 – 20 kV to move 1-3 m for  = cm when C 1 ~ 10 pF/m Creeping leader

Some of the main unsolved problems Adequate theory of streamer-leader transition, current constriction and leader velocity. All published computations of leader evolution (very complicate and 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 leader

Advancement of negative stepped leader “Double step forward - single step backward” Double step is very fast, single – with v L + so the mean v L -  v L +

Artificially induced step

Why positive leader elongates quasi-continuously but negative one – by steps -plasma germs for  streamer pair are probably generate in both cases near to front of streamer zone where there are local 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

LIGHTNING Basic mechanisms and all problems concerning of the first lightning leader are practically the same as for laboratory long leader. 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 in the negative spark.

2. What is mechanism of non-conducting cloud discharging during lightning process? How does the net of multibranched streamers-leaders develop?

LIGHTNING PROTECTION Hazard Can lightning rod protect ? - human - forest - structures - transmission lines - electronic and microelectronic systems - aircrafts no yes (partly) yes partly) no 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