E. Bazelyan and Yu Raizer EFFECT CORONA ON CONNECTING LEADER AND UPWARD LIGHTNING FROM HIGH STRUCTURES

OUTLINE -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 ACTIVITY -Europe: 3 – 5 strokes /km 2 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 m Ostankino Tower in Moscow undergoes 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 - -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 inception Rod’s top behaves as electrode with U = E 0 h = 1 MV for h = 100 m E 0 =100 V/cm Field at the top E top  E 0 h/(2r 0 ) E top  30 kV/cm for these E 0, h and r 0 = 15 cm

CONDITIONS FOR LEADER FORMATION 1.Streamer flash (at E top > 30 – 50 kV/cm) 2.U =E 0 h > 400 kV and 400 kV falls on the length d  1 m 3.Leader vitality E L  E 0 Leader velocity v L ~ (  U tip ) 1/2

Corona over high grounded structure hinders upward leader formation Why? Glow corona is always stabilizing field at electrode top

Effects of corona on leader E top = E cor < E flash – prevents streamer flash Only 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 CORONA theory and numerical simulation -Only stationary corona have been considered previously -Corona from grounded rod under thundercloud is non-stationary: ion cloud expands “unrestrictedly” Model for numerical simulation U(t)=E 0 (t)h; U=0 at r   Spherical model for analytical theory

Equations of spherical model -Ionization is happened in the thin layer nearby electrode top - Field at electrode top is stabilized The main approximation, - quasi-stationary local current i(r,t) = 4  r 2  E  i(t) – - results in R(t), i(t) for any U(t) - function

for U = At Strong dependence i upon dU/dt ! for U(t) = const Example: E 0max = 100 V/cm  = 10 s h = 200 m U max = 2 MV  = 1.5 cm 2 (V s) -1 R = 32 m i max = 0.35 mA Q = 1.75 mC for t = 10 s Solution

Results of numerical simulation

Critical current for corona-to-streamer transitions Critical current corresponds If i > i cr ionization wave (“spherical streamer”) is incepted i cr  6 mA for r 0 = 1 cm (E cor = 42.8 kV/cm) Condition i > i cr requires so high dE 0 /dt, E 0max and h that thundercloud itself can never provoke streamer flash

Empirical confirmation of corona influence Almost 100% probability, i.e. 1 trigger lightning for ~ 5 s 1 upward lightning for 40 thunderstorm hours upward lightning for 40 thunderstorm hours

Corona by combined action of thundercloud and approaching downward leader (numerical simulation) i cr

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, in reasonable agreement with empiric radius of lightning attraction, 3h

Influence of corona on upward leader vitality Field by thundercloud, E 0, necessary to sustain vitality of leader born from rod of height h

COMMUNITY OF CONNECTING AND UPWARD LEADERS Connecting leader E 0 due to cloud, E lid due to downward Leader E lid > E 0 Upward lightning E lid << E 0 dE lid /dt >> dE 0 /dt -Upward lightning from high structure is provoked by far downward lightning, providing high dE 0 /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 LEADER 1. To joint with downward lightning 2. To stop in some distance 3. To reach thundercloud and to convert into lightning Numerical results Case 2

Case 3. Upward leader from 540 m TV tower in Moscow went to cloud

SOME ATTEMPTS TO IMPROVE LIGHTNING ROD Some authors and firms advertise lightning rod with very pointed top convincing that this facilitates inception of connecting leader NO, r 0 < 1 cm is useless since leader is unviable

MULTI-ELECTRODE LIGHTNING ROD - A lot (N ~ 5000) of needles l = 10 cm, r 0 = 1 mm on surface r 1 ~ 5 m - Corona ion cloud R >>r 1 - Corona current i does not depend on N, r 1, r 0, l - Current from one needle i 1 = i/N << i cr  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