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