e. bazelyan and yu raizer effect corona on connecting leader and upward lightning from high...
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E. Bazelyan and Yu Raizer
EFFECT CORONA ONEFFECT CORONA ONCONNECTING LEADERCONNECTING LEADER
AND UPWARD LIGHTNING AND UPWARD LIGHTNING FROM HIGH STRUCTURES FROM HIGH STRUCTURES
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OUTLINEOUTLINE
-Lightning activity
- Cause and conditions of an upward leader inception
- Corona over high structure: its influence on the upward leader
- Upward lightning and connecting leader: relation and difference
- Attempts to improve a lightning rod
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LIGHTNING ACTIVITYLIGHTNING ACTIVITY-Europe: 3 – 5 strokes /km2 per year
- Grounded structure of height h attracts lightning from 3h –radius
- 30m structure experiences 1 stroke/10 years, 100 m – 1stroke/year
- Very high structure ejects lightning itself
- 540 m Ostankino Tower in Moscow undergoes 25-30 stokes/year, 90% due to upward lightning
-Downward lightning strikes object exciting connecting leader and jointing with it
-Lightning rod towers over defending object and takes stroke on itself
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Conceivable ways to control lightning -Conceivable ways to control lightning --to eliminate lightning by acting on thundercloud- to influence on connecting and upward leaders
The 2nd task is “more realistic” what dictates interest to upward leaders
Cause of upward leader inceptionCause of upward leader inception
Rod’s top behaves as electrode with U = E0h = 1 MV for h = 100 m E0 =100 V/cm
Field at the top Etop E0h/(2r0)
Etop 30 kV/cm for these E0, h and r0 = 15 cm
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CONDITIONS FOR LEADER FORMATIONCONDITIONS FOR LEADER FORMATION
1. Streamer flash (at Etop > 30 – 50 kV/cm)2. U =E0h > 400 kV and 400 kV falls on the length d 1 m3. Leader vitality EL E0
Leader velocity vL ~ (Utip )1/2
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Corona over high grounded structurehinders upward leader formation
Why?Glow corona is always stabilizing field at electrode top
cmkVcmr
EE ignitioncor /][
..
0
5401827
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Effects of corona on leaderEffects of corona on leader
Etop = Ecor < Eflash – prevents streamer flashOnly very high dE/dt can counteract
Smoothness of U(r) near the rod’s top results in: - obstacle for 400kV/1 m - obstacle for leader vitality
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NON-STATIONARY CORONANON-STATIONARY CORONAtheory and numerical simulationtheory and numerical simulation
-Only stationary corona have been considered previously
-Corona from grounded rod under thundercloud is non-stationary: ion cloud expands “unrestrictedly”
Model fornumerical simulation
U(t)=E0(t)h; U=0 at r
Spherical model foranalytical theory
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Equations of spherical model
-Ionization is happened in the thin layer nearby electrode top
- Field at electrode top is stabilized
01 2
2
Errrt 0
22
1
Errr
REEdrEdrU f
R
rr
00
)(REE f
R
r
drrQ0
24dt
dQi ff Ev
dt
dR
The main approximation , - quasi-stationary local current i(r,t) = 4r2E i(t) – - results in R(t), i(t) for any U(t) - function
constErE cor )( 0
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tA
R3
t
Ai
32
3
0
for U = At
Strong dependence i upon dU/dt !
tR ~ ti
1~ for U(t) = const
Example: E0max = 100 V/cm = 10 s h = 200 m Umax = 2 MV = 1.5 cm2 (V s)-1
R = 32 m imax = 0.35 mA Q = 1.75 mC for t = 10 s
Solution
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Results of numerical simulationResults of numerical simulation
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Critical current for corona-to-streamer transitionsCritical current for corona-to-streamer transitions
Critical current corresponds
00
rrdt
dE
If i > icr ionization wave (“sphericalstreamer”) is incepted
2008 corcr Eri
icr 6 mA for r0 = 1 cm (Ecor = 42.8 kV/cm)
Condition i > i cr requires so high dE0/dt, E0max and h thatthundercloud itself can never provoke streamer flash
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Empirical confirmation of corona influenceEmpirical confirmation of corona influence
Almost 100%probability, i.e.1 trigger lightning for ~ 5 s
1 upward lightningfor 40 thunderstormhours
25-30 upward lightningfor 40 thunderstormhours
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Corona by combined action of thundercloud Corona by combined action of thundercloud and approaching downward leader and approaching downward leader
(numerical simulation)(numerical simulation)
icr
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Ion density at joint action of thundercloud and approaching downward lightning
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Maximum horizontal displacement of downward lightning from rod for initiation of upward (connecting) leader
D 4h, inreasonable agreementwith empiric radius oflightning attraction, 3h
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Influence of corona on upward leader vitalityInfluence of corona on upward leader vitality
Field by thundercloud, E0,necessary to sustain vitalityof leader born from rod ofheight h
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COMMUNITY OF CONNECTING AND COMMUNITY OF CONNECTING AND UPWARD LEADERSUPWARD LEADERS
Connecting leader
E0 due to cloud,Elid due to downwardLeader
Elid > E0
Upward lightning
Elid << E0
dElid/dt >> dE0/dt
-Upward lightning from high structure is provoked by far downward lightning, providing high dE0/dt
-Upward lightning and connecting leader have the same origin:they both are incepted owing to downward lightning
-Upward lightning heads for thundercloud Connecting leader heads for close downward one
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LOT OF THE BORN UPWARD LEADERLOT OF THE BORN UPWARD LEADER1. To joint with downward lightning2. To stop in some distance3. To reach thundercloud and to convert into lightning
Numerical resultsCase 2
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Case 3. Upward leader from 540 m Case 3. Upward leader from 540 m TV tower in Moscow went to cloud TV tower in Moscow went to cloud
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SOME ATTEMPTS TO IMPROVE LIGHTNING SOME ATTEMPTS TO IMPROVE LIGHTNING RODROD
Some authors and firms advertise lightning rod with very pointedtop convincing that this facilitates inception of connecting leader
NO, r0 < 1 cm is useless since leader is unviable
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MULTI-ELECTRODE LIGHTNING RODMULTI-ELECTRODE LIGHTNING ROD
- A lot (N ~ 5000) of needles l = 10 cm, r0 = 1 mm on surface r1 ~ 5 m
- Corona ion cloud R >>r1
- Corona current i does not depend on N, r1, r0, l
- Current from one needle i1= i/N << icr
No streamer flash No connecting or upward leader No lightning stroke
Object placed under the system is protected, excepting case of the direct lightning hit