; 200 µs 0 1 ms 4 exponential 80 km m/s 10 km 1 ms 5 E k N = e z/h n 6 ; N, H n :, z: ( ) t ρ + (σe) = 0 E σ 1 σ σ σ e e (1/H e+1/h n )

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1 - [ : ( ) ] 1 (contact) (interaction) MTI c Mesosphere Thermosphere Ionosphere (MTI) Research Group, Japan 1 2 (1) : (2 ) (2) : (3 ) (3) : (2, 3 ) (4) : - (4 ) X 1

2 ; 200 µs 0 1 ms 4 exponential 80 km m/s 10 km 1 ms 5 E k N = e z/h n 6 ; N, H n :, z: ( ) t ρ + (σe) = 0 E σ 1 σ σ σ e e (1/H e+1/h n )z 4 (5) E H (1 1) + O(ε) (1) z3 ; H σ 1 O(ε) ; 6 E k0 /N 0 ; 100 km N 2:O 2 = 8 : 2 (Nσ) 1 7 X 2

3 E altitude, km breakdown electric field, V/m 1: E T 1 8 ε 0 /σ T T ε 0 /σ H H E > E k 2 T ε 0 /σ e (1/H e+1/h n )z, H E k e z/h n 8 T H (He+Hn)/He (2) H e, H n (H e + H n )/H e 2 3 ; T em, T el T ε 0 /σ(z cr ) T th T em T el 9 T th z cr 9 90 km T el ε 0 /σ X 3

4 z ii i. field relaxation t r (z) < T iii Electric field E E k 2: H T ε 0 /σ(z) < T (i) T ii H (iii) (70 90 km) H H discharge time T, s No sprite Halo electrostatic limit charge moment H, C km Streamer 3: H T (2) ; T 100 µs H 4 (e.g. Cummer and Lyons, 2005) C km Hiraki and Fukunishi, 2006, 3 H 100 C km 10 (2) T H 2 T T ; (detect) H : H T return stroke (1 ms ) 10 X 4

5 continuing current (up to 100 ms) ( M-component ) Ohkubo et al. (2005) 3 11 e.g. Pasko et al., 2000; Hayakawa 11 et al., ms CCD (Moudry et al., 2003; Cummer et al., 2006, 4 ) main branch tendril main branch tendril ; bead second branch 90 km leaf 5 ms main branch (i) main branch & second branch, (ii) tendril (i), (ii) 12 X 5

6 4: CCD (Cummer et al., 2006)main branch tendril main branch, tendril second branch, bead ; 13 main branch 13 ( H/z 3 ) ( exp( z/h n )) main branch ; 10 km km (1) z X 6

7 ( ) VHF (van der Velde et al., 2006) main branch main branch second branch tendril 15 main branch-tendril km 16 main branch X 7

8 T electron field E T c No sprite critical point Halo Structured H H c 5: (No sprite) (Halo); (Structured) T T cr n e 0 Halo (critical point) m (i) m = 0 (ii) (iii) m 0 m H T 18 (T cr, H cr ) (T > T cr, H > H cr ) T T cr m T 18 m H T m z 1,2 r 1 ; 6 z 1 z 2 T 19 (r, z) E = H cos 2 θ 2πε 0 (z 2 + r 2 ) 3/2 = H 4z 2 + r 2 2πε 0 (z 2 + r 2 ) 2 (3) r = 0 E k = E 0 e z/hn H πε 0 z1 3 = E 0 e z 1/H n ( H ) z 1 H n ln πε 0 z1,0 3 E 0 z 1 ln H H n + const (4) 19 X 8

9 z 2 Halo z 2 z 1 z 1 r 1 E E k 6: Halo-No sprite E E k z 1 z 2 ln z 1 z 2 ε 0 σ = T en e(z 2 )µ e (z 2 ) = ε 0 T z 2 = H eh n H e + H n ln σ ( ε0 σ 0 T z 2 = ln T H ehn He+Hn + const (5) ) = en e µ e ; n e (z) = n e0 e z/h e, µ e (z) = µ e0 e z/h n 20 Z = z 2 z 1 Z = H n ln HT He He+Hn H n ln HT const + const ; H e /(H e + H n ) 1/2 Z 0 r 1 z 2 E(z 2, r) = E k r 1 r 2 1 z2 2 4z µ e N e z/hn µ e N 1 H 4z2 (T ) 2 + r1 2 2πε 0 (z 2 (T ) 2 + r1 2 = b(t ) )2 b(t ) = E 0 e z 2(T )/H n r1 2 H z 2 (T ) = πε 0 b(t ) z 2(T ) 2 (6) m(t, H) m(t, H) = z2 (T ) z 1 (H) k(e/n)n e Ndz πr 2 1 z2 = const r 1 (T, H) 2 (T ) e cz νattt dz z 1 (H) c = 1 H e 1 H n = const r 1 (T, H) 2 e cz(t,h) νattt (7) k(e/n) e ν attt ; T 0 o(ε) (5) z 2 X 9

10 m(t, H) (T cr, H cr ) H T T > T cr T > 0 22 z 2 H n ln T 1/2 T 0 e cz H e z 2/H n z 2 2 r2 1 m(t, H) m H r 2 1 ; Tasaki, 2007 σ 0 E σ0 = (J z=2d i=1 σ i +µ 0 H)σ 0 = (zjψ+µ 0 H)σ 0 d: µ 0 H: J σ 0 ψ ψ = tanh(βzjψ+βµ 0 H) β = β mf = 1/zJ m(β, H) 22 T T cr m T cr T cr T 0 Ψ = N i=1 σ i N ; f LR (β, H) = min 1 ψ 1 { f(β, H) µ 0 Hψ} (ψ = Ψ/N) {} m(t, H) F F m 5 X 10

11 van der Velde, O. A., A. Mika, S. Soula, C. Haldoupis, T. Neubert, and U. S. Inan, Observations of the relationship between sprite morphology and in-cloud lightning processes, J. Geophys. Res., 111, D15203, doi: /2005jd006879, 2006.,, jp/ /d/, Cummer, S. A., and W. A. Lyons, Implications of lightning charge moment changes for sprite initiation, J. Geophys. Res., 110, A04304, doi: /2004ja010812, Cummer, S. A., N. Jaugey, J. Li, W. A. Lyons, T. E. Nelson, and E. A. Gerken, Submillisecond imaging of sprite development and structure, Geophys. Res. Lett., 33, L04104, doi: /2005gl024969, Hayakawa, M., D. I. Iudin, E. A. Mareev, and V. Y. Trakhtengerts, Cellular automaton modeling of mesospheric optical emissions: Sprites, Phys. Plasmas, 14, , Hiraki, Y., and H. Fukunishi, Theoretical criterion of charge moment change by lightning for initiation of sprites, J. Geophys. Res., 111, A11305, doi: /2006ja011729, Moudry, D., H. Stenbaek-Nielsen, D. D. Sentman, E. Wescott, Imaging of elves, halos and sprite initiation at 1ms time resolution, J. Atmos. Solar-Terr. Phys., 65, , Ohkubo, A., H. Fukunishi, Y. Takahashi, and T. Adachi, VLF/ELF sferic evidence for in-cloud discharge activity producing sprites, Geophys. Res. Lett., 32, L04812, doi: /2004gl021943, Pasko, V. P., U. S. Inan, and T. F. Bell, Fractal structure of sprites, Geophys. Res. Lett., 27, , Pasko, V. P., U. S. Inan, T. F. Bell, and Y. N. Taranenko, Sprites produced by quasielectrostatic heating and ionization in the lower ionosphere, J. Geophys. Res., 102, , Raizer, Y. P., Gas Discharge Physics, 1st ed., Springer-Verlag, New York, X 11

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