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0 B = 0 B0 z 2 2 1 W (k) 1 (k) = (k)Im 1 - D1(k k) 2 4 B0/4 c2 kz kz a k, (k k )-2 kzkz cos2 (k, k ) + 2kk 1 - c2 sin2 (k, k ) a (k k) 2 1 cos (k, k ) 1 - c2 kz kz a 2 c2kzkz a D2(k k)(k k )2 - (kz kz)2 =(k) =(k) k (k, k ) k k W (k) Ew = W (k) = d3kW (k) Ew k 2 2 2 (k) = kD0(k) + (c2kz - 2)/va a (k) = 0 2 ca = va - (P 0 - P0)/0 P 0 P0 0 va = B0/ 40 D0(k) D1(k) D2(k) F0 2 2 8P0 4 kz v q v F0 D0(k) = 1 + + m d3v - 1(k) 2 2 B0 B0 v kz - 2 m 2 v m d3vkz q F0 2 D1(k) = -va 1 - 3(k) 0 v kz - m v 2 m d3vkz q v F0 D2(k) = - 1 - 3(k), 0 v kz - m 2 v 1(k) 3(k) -1 2 2 q d3v F0 d3v v F0 1(k) = q m v kz - v v kz - 2 v -1 2 q d3v F0 d3v F0 3(k) = q m v kz - v v kz - v 2 vakz (kz, k) = d2k - W (-kz, k ) + kz W (-kz, k ) 2 B0/4 kz -2 (k + k )2 kz cos2 (k, k ) + W -, k 4kz 16(k + k )2 2 4kk sin2 (k, k ) - (k + k )2 cos (k, k ), 2 = 4Pi/B0 1 Pi 2 vT ikz (kz, k) 2.25 d2kW (-kz, k ) cos2 (k, k ) 2 B0/4 1 vT i Ti vT i = Ti/mi > 1 E k S A(s) s S B u S B u 2 r2 - ra B = Ba, 2 uar 1 - Ma 2 2 1 - Ma ra/r2 u = r. 2 1 - Ma Ma = u 4/B = a/ Ba ua a Ma = 1 r = ra 2 S ra A(s)u = 0, s u2 u ur 1 2 u - = - (Pg + Pc) - r2B - , s u r s 8r2 s s u2 1 u2 g Pg BB c A u + + + - r + (u + va) PcA s 2 2 g - 1 4 c - 1 D Pc - = -c(T )n2, c - 1 s AB = 0, s 1 c D Pc Pc A (u + va) Pc - = (u + va), A s c - 1 c - 1 s s Pg Pc g c va = B/ 4 D = D cos2 2 cos = B/ B2 + B n T = B,D + H. B,D H 2 GMi B,D = - 2, i=1 r2 + ai + z2 + b2 i 3 -1 -2 G = 6.66810-8 GMH R H = 0 + ln 1 +, R < 100. Rb Rb ai = (0.0, 5.318) bi = (0.25, 0.387) Rb Mi = (1.411010, 8.561010)M MH = 1.071011 M 8.0 1011 M r0 2 - D = 3 1028 s - n0 T = 104 B0 = 2.0 10-6 -Pc0 = 5 10-13 g = 5/3 c = 4/3 r0 S - -2 - Fc = 1.3 10-5 u u T n z 3 - Pc0 = 5 10-13 n0 = 10-2 B0 = 2 10-6 Lc = -1.8 1041 1 N N p N 1 A(s)D cos2 - w + A(s)w + 2Q(p)(s) = 0. A(s) s s s 3 p A(s) s w Q(p) N(s, p) nc = 4 p2dpN nc D w = u + va u va - p Q(p) = (pm - p). 4c(mc)4 mc m pm Fc pm/mc Fc = y2-dy y2 + 1 - 1. 4- 3 p /c kW (k)|k=qB /pc =. t 4 mc ( - 2)A(s) cos Bt = B2 + B 4kW (k)/Bt 1 W (k) k W (k) -8( - 2) c2 Bt /4 p D = A(s) cos . 92 B0 /c mc B0 = qBt/mc Bt(s)A(s) cos = const S u(s) + va(s) w(s) = A(s) = A(s), u0 + va0 w D(p, s) N N p N Q(p) (Aw) - + + 2 () = 0, w0w s 3 p w D(p, s) = D (p, s) cos2 D(p, s)w-1 (Aw) = D(p) -1/s0. s K(p) = D(p)/(w0s0) N N p N Q(p) K(p) - + + 2 () = 0. 3 p w Q(p) = Q0(p/mc)- K(p) = K0(p/mc) 1/(-2) d Q0K0 (p/mc)- N(, p) = dy exp -y2- /K(p) w0(2 - )(1/(2 - )) d/ -d/2- 2-+0/2 - + 0/-2-+0/y y +, (2 - ) d = 0 d = +. 2 - p - (p) K(p) 1 < 2 < 1 N Q(p)/(p) Q(p)K1/( -2)(p) N(0, p) 1- 1/(-2) d/ ( d -1)/(2-) Q0K0 (p/mc)- 2-+/3 2- 2 - + 0/ N(0, p) =.

1 1- d/3 (2 - )w0(2 - ) + 2- 2- 2-+/ z < 15 A(s) = const cos 1 D = const(s) s = A(s) s2 cos Bt s-1 D s-2 s2 = 1/ 0 = - 3 - d = +. 2 - = 0 = 4.1 d = 4.65 = 1/2 = 4.0 d = 14/3 = 4.0 4.1 = 0 = 4.1 d = 4.65 -1/ - 8 d p c2 Bt /4 wN(0, p) = 0.96 ( - 2). 4c(mc)4 mc 92 B0 /c s v I(Ek) = 1.93 (0.939 + Ek( ))-2.7( )-1. c p mc 4.mc N(p) = N0, p - N0 = 7 10-11(mc)-3 1/ m3c3N0 w0 1 B = 9.5 10-7 . 2 - 7 10-11 40 s0 2 10- w0 = 40 s0 = 1 B0 = 210-6 -n0 = 10-2 1.1 10-6 -2 - p BD = 3.5 1026 . mc 2 10- X Q0 = cmn1 n1 = 4.65 1/ -0.55 1/s0 p s-X = 0.906cmn1 = 20 -1/2 w0D (p) mc 1 1/2 -1/2 -1/ B0 w0 n. -2 -1 -10-6 2 10-6 40 3 1020 X w0 = 40 s0 = 1 B0 = 2 10- = 1 = 4.1 -2 - pm = 106 mc Fc 10 = 10-5 Lc = 2RgFc Rg = 15 Lc = 1.3 1041 F = -[jd B]c-B jd F = -[jd B]c- jd s(p) s = 1 s = 15 3 103 s p1/3 1 s = B E = -[u B]/c u th jth F = [(jth - thu) B]/c th = -cr [ B] = 4(jth + jcr)/c cr jcr u [B [ B]] + (u)u = - - P - [(jcr - cru) B] t 4 c P Jd k B0 jdB( - ku0)2 = Va2k2 k. c 0 u0 Va = B0/ 4 k < kc = jdB0/c0Va2 max k = kc/jdBmax =. 2c0Va k-1 pc/qB0 k qB0/pc < k < kc kc > qB0/pc ucr cr >> 1 c B0/4 ucr cr ucr u1 0u z t = 0 z = -L Bb << B0 u pm z = 0 z = -L pm -3/ 1/Va esc u = u1 - 0. cp, PeV m 0. u, 103 km s- 10 1 p m u 643 1283 2563 p m -1/2 -1 -Va L Bp = pm. m - 5 esc = 2FE/0u3 FE 0u3/ p m u N(pm) (pm) (pm) = qB0/pm E0 a u, 103 b p, /c m < B2 >1/2 /B0 c a u b p m c 1< B2 >1/2 /B0, < u2 >1/2 /Va, cs/Va N(pm)/N0(pm), J/J0, (pm)/(pm) E0/B0.0.z/L -0.5 N(pm) J (pm) E0 z -u = 4900 B0 -u = 4900 R tm m0 T = m0R/u1 L = m0R = u1T L u 2 2 4 z u z z = 2 2562 512 - u1 = 3000 - VA = 10 - u = 4900 esc = 0. Y Z z XY u1 z z B Y Z 12.6B0 126B0 103B0/4 105B0/4 - u1 = 3000 - Va = 10 1/2 1/Bz, /B0, u2 /Va z, 1 /0, uz /Va, cs/Va 1z/Lz 0.5 z - u1 = 3000 - Va = 10 g g g a d obs T ub nc B0 ue ue ue pmcfpmcfpmcfBd Bd Bd Bd h 1 H 1 1 esc 0.05 0.14 0.05 0.14 0.05 0. a b - c -d e -f pmc g h b, c h ln-1 2B0u2, u1 < u Bbu 1/4 -escqu2B0L pmc = 2B0 ln - 1 + 2u - 1, 4cVa Bb u u1 > u u = (24cVa3/esc)1/ u1 ln (2B0/Bb) = 5 u1 >> u B2 Va 2esc0u2. 4 c u1 > u pmc (esc/0.05) (u1/1000 )2 n1/2Lpc = 21 H 1/Z 2Bln - 1 + 2u - Bb u Z u3 = 1730 nH - Lpc L L R T L = m0R = u1T 2/ -1/Va esc -u1 > (4cVa2/esc)1/3 = 1340. - 0. B0 = 5 - B0 = 10 esc esc esc = 0.01 esc = 0.05 esc = 0.14 esc = 0.14 = s = 2.5 esc = 0. esc = 0.01 Pc 0u N N v 1 1 p + u b N + p2 F - u N = N - N. t 2 p2 p 2 v p u b = B/B F p u F = qE - b + (u)u.

v t F v + b p 2F 2 (p) = , exp + b - vp d = v. (p, ) - || < 0 << F = u v/2 0 0 const B/B << 1 l l p2 1 B(s) Dpp = (u)2 ds 1 - 6 l Bmax u || < p pu t t 2/ (p)2 (u)Dpp p2 3 t B/B iDijf = 0, Dij Dij = (D - D)bibj + Dij. D D b b = B/B D = D D < A2 > D /D A = (B - B0)/B0 B0 =< B > D D D = D 1 + C1 < A2 > + C2 < A2 >2 +..., D D C1, C2, A< D >> D D D < D + D Dmm ln-1 mL D D A2 2 L A2 L D D + ln-1 4L2 L D L L Dm m r2 = 4Dm|z|, (r1 - r2)2 = (r1 - r2)2 |z=0 exp{2m|z|}, (r1 - r2)2 << L2. D Dm D D Dm D / D D exp 2m D L2. 1 D ln2 mL. D m D D 0 H R uR(R, ) = uR()U(R/g()) u(R, ) = u()U(R/g()) (R, ) = n()0(R/g()) p(R, ) = n()P (R/g()) U(R0) 0(R0) P (R0) = /2 g() uR() u() n() g(/2) = n(/2) = 1 R = R0g() R0 P 0U2 R0 ng2u sin = const. uR u = -n-1 + u2 u uR u2 - n-1 u-1 = n-1 + ( + 2) - uRu tg u u2 u2 R + + n-1 = const 2 2 - U2(R/g()) g = /2 uR(/2) u(/2) = 0 = /2 uR = 0 = /2 = -2/(2 - 1) 0 < < / uR = u cos u = -(1 - -1)u sin n = sin2/(-1) g = sin-/(-1) u R R0 uU(R/g()) = 5/3 = -10/7 r z M = 2( - 1)/(2 - 1) < -2/(2 - 1) uR = 0 = /2 = -2/(2 - 1) M = 1 M 0.756 = 5/3 70 R < 300 -0.43 -0.17 - R > 1 R < 300 = 5/3 = -10/7 r z 5.13.8 6246 70 33 21 400 255 - u = 900 - 1042 -1 - 4M 2M 105

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