E. Bazelyan and Yu Raizer

EFFECT CORONA ONEFFECT CORONA ONCONNECTING LEADERCONNECTING LEADER

AND UPWARD LIGHTNING AND UPWARD LIGHTNING FROM HIGH STRUCTURES FROM HIGH STRUCTURES

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

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

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

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

Corona over high grounded structurehinders upward leader formation

Why?Glow corona is always stabilizing field at electrode top

cmkVcmr

EE ignitioncor /][

..

0

5401827

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

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

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

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

Results of numerical simulationResults of numerical simulation

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

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

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

Ion density at joint action of thundercloud and approaching downward lightning

Maximum horizontal displacement of downward lightning from rod for initiation of upward (connecting) leader

D 4h, inreasonable agreementwith empiric radius oflightning attraction, 3h

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

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

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

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

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

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