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, 2005, 31, 8, . 601­610

523.985


c 2005 . . . * , . .
. ..
04.03.2005 .

, . . , , (HXR), , . Yohkoh RHESSI, HXR- , HXR . : : , , , . COMPARISON OF THE FERMI AND BETATRON ACCELERATION EFFICIENCIES IN COLLAPSING MAGNETIC TRAPS, by S. A. Bogachev and B. V. Somov. The acceleration of charged particles in the solar corona during flares is investigated in terms of a model in which electrons and ions after their preacceleration in the region of magnetic reconnection are injected into a collapsing magnetic trap. Here, the particle energy rapidly increases simultaneously through the Fermi and betatron mechanisms. As a comparison of the efficiencies of the two mechanisms shows, the accelerated electrons in such a trap produce more intense hard X-ray (HXR) bursts than those in a trap where only the Fermi acceleration mechanism is at work. This effect explains the Yohkoh and RHESSI satellite observations in which HXR sources more intense than the HXR radiation from the chromosphere were detected in the corona. Key words: Sun: solar flares, magnetic reconnection, particle acceleration, X-ray radiation.

20-100 , , . EX K = E - mc2 ( E ­ ), KT 0.1 , , , .. , , , . :
*

: bogachev@sai.msu.ru

, , . . . . , (, 1971; , , 1972; , 1972). , , , , , . 601


602

,

() RR B0

Bm CHR (·) Y esc

Bm

Bm

B0

Bm

X

. 1. . (a) ­ : RR ­ , (CHR). () ­ .

, , (, , 1973). . Yohkoh RHESSI , , . HXR , : () (. , 2000). , , , . , , , ,

, (. , 2001; , 2002). , , , , , . , (, , 1997; , , 2001). ( ), (2003) , .. . , , , , . , . , , . HXR- . , . . , . , . . , . 1 . , (RR), , (; , 2000) KT 0.1 , , Keff 10 , .
31 8 2005






603

, , , Bm , B0 . , . , , .. ( ), , . , , ( ). , B0 , Bm , . 1. Bm , Bm /B0 ­ . , , , , , , . (. , , 2003). (RR) . . ( ), . b(t) = B (t)/B0 , (1) b(0) = 1, B (0) = B0 , bm = Bm /B0 ,


B (t) Bm . L l(t) = L(t)/L0 , (3) l(0) = 1 l = 0 , . () , (., , , 2000), : (4) p|| L = p0|| L0 = const p2 /B = p
2 0

/B0 = const.

(5)

(1) (3) (4) (5), , : p0|| (6) p|| = l (7) p = p0 b. , (6), . (7) . - , ­ . - : p0 p =l b (8) = l b tg 0 . tg = p|| p0|| l b < 1, - . , , . l b > 1, - . . (9) l b=1 . (9)
8 2005

(2)
31


604

,

-: tg = tg 0 . , , b(t) l(t) , , , , . , , K= 1 2m p2 + p ||
2

=

1 2m

p

2 0|| l2

+ bp

2 0

= (10)

= K0

cos 0 + b sin2 0 l2

2

, l 1 b 1. K0 = p2 /2m ­ 0 . (l b < 1) ( ), (l b > 1) ­ . l b = 1, , -: K = K0 /l2 . . , . - 1 1 = . (11) tg esc = Bm /B - 1 bm /b - 1 (8) (11), , 1 l2 b tg2 0 = bm /b - 1 1 = bm - b. (12) l2 tg2 0 (10) : K = K0 sin2 0 1 +b . l2 tg2 0

. , , , . , (11) . , . , . (13). , K0 , Kesc . , , ­ . (13) ­ , . : (14) Kmax = K0 bm . Keff 10 1 bm = Bm /B0 100. , , Bm /B0 = = 4. . (1998) , , , , (. ., 1999). , , - . . , , .. . , f0 (K0 ) : dN (K0 ,0 ) = N0 f0 (K0 )dK0 2 sin 0 d0 ,
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(12), Kesc = K0 bm sin2 0 . (13) , ,

(15)







605

f0 (K0 )dK0
0 0

2 sin 0 d0 = (16) sin2 + l2 cos2 b (22) (23) K0 = A K, A = K0 = A . K (24)

= 4
0

f0 (K0 )dK0 = 1,

(25) (26)

N0 ­ , . , -. , . . f0 (K0 ) f (K,) ( > esc ) 2f (K,)sin = 2 P f0 (K0 )sin 0 , 0 K0 P= K 0 0 K K . (17)

(19). : 1 sin 0 0 =- cos 0 = sin sin 1 1 . =- sin 1+tg2 0 (21), tg 0 tg sin 0 0 = sin 1 l l = = 3/2 2 b (sin )/b + l2 cos2 b A (27) 1 A .

(8) - , P 0 K0 . K (18) (17), P= f (K,) = sin 0 0 K0 f0 (K0 ). sin K (18)

(25), (26) (27) (19), - l (28) f (K,) = f0 (KA ) . b A , A (24) . (28) .


(19) f () =

K0 / K. (10). : K= (8) bl tg 0 = tg . (21) (20): K0 = sin2 + l2 cos2 K. b (22)
2 2 2

0

l f (K,)dK = b A



f0 (KA )dK.
0

(29) A - , . K0 = KA : f () = l bA
3/2 0

K0 l2

1+ bl tg 0 1+ tg2 0

2

2

.

(20)

f0 (K0 )dK0 .

(21)

sin2 K0 = + l2 cos2 . K b


(23)
31

(16) 1/4 . , l lb 1 1 = f () = 3/2 3/2 4 bA 4 sin2 + bl2 cos2 (30) , . . 2
8 2005


606

,

2.0 () 1.5 1.0 c 0.5 a 4 y 0 2.0 р 1.5 b 1.0 a 0.5 (·) b

, , .. , :
-esc

N =N

0 esc /2

f ()2 sin d =

(31)

= N0 l b
esc

sin d sin2 + bl2 cos2
3/2

.

esc ­ (11), , , (. . 1). sin d sin2 + bl2 cos2
3/2

=

d(tg2 ) 2(tg2 + bl2 )
3/2

t = tg2 , N = N0 l b


0

1

4 x

2

3

dt , (t + bl2 )3/2

(32)

t0

. 2. . (a) ­ , . a, b, c l = L/L0 = 1.0, 0.75, 0.50. () ­ , . . a, b, c b = B/B0 = 1, 2, 4.

t0 =

b . bm - b

, l bm - b . (33) N = N0 1+ (bm - b)l2 , b , . , (33) b = 1, l bm - 1 , (34) N = N0 1+ (bm - 1)l2 l 1 0. , , l = 1, b 1 bm . bm - b . (35) N = N0 bm - b +1 . 3 3 bm . . 3 b, b = 1 b = bm ,
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(b 1) . 2 (l 1). (l = 1, b = 1) . , . , - , , x. -, , x. (l b = 1) . N . HXR . - (30),






607

(b - 1)/(bm - 1), bm 0 1. , HXR- , , N0 , ( Npr ) . , , (33) Npr = 1 - 1 - 1/bm . (36) N0 , bm = 100 99.5% , bm = 4 ­ 87%. N , V : n = N/V , (37) n0 = N0 /V0 ­ . N V0 . (38) n = n0 N0 V N/N0 (33). V/V0 . L ­ , S ­ , L0 S 0 L0 B b V0 = = (39) =; V LS L B0 l : BS = B0 S0 . (33), (38) (39), b bm - b . (40) n = n0 1+(bm - b)l2 (b = 1) bm - 1 , n = n0 1+(bm - 1)l2 (l = 1) b bm - b . n = n0 bm - b +1

1.0 0.8 0.6 0.4 c 0.2 N/N0 0 1.0 1.0 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 (b ­1)/(bm ­l) 0.8 1.0 (·) 0.8 0.6 l a b c 0.4 0.2 0 () a b

. 3. . a, b, c bm = Bm /B0 = 100, 25, 10; (a) ­ , () ­ .

. , n
0

bm - 1.

(43)

(41)

b bm , . (40) l 0 b bm , : n 2n
0

bm 3

3/2

.

(44)

(42)

(41) (42) . 4 4 . . , . 4 4 ,
31

(44) HXR- : b
8 2005
m

3

1n 2 n0

2/3

.

(45)


608

,

10 () 8 6

a

b 4 2 n/n 0 1.0 (·) 80 60 40 20 0 0.2 0.4 0.6 (b ­1)/(bm­1) 0.8 b c 1.0
0

. - (28). K N0 :
-esc

c

F =N

0 0 esc

f (K,)KdK2 sin d;

(46)

0.8

0.6 l

0.4

0.2 a

0

100

- esc (. (11)), -, . (28),
/2

l F = 4N0 b
esc

sin d A



f0 (KA ) KdK.
0

K0 = KA :
/2

l F = N0 b
esc

sin d A2 A



4f0 (K0 )K0 dK0 .
0

(47) (47) :


. 4. . a, b, c bm = Bm /B0 = 100, 25, 10; (a) ­ , () ­ .

F0 =
0

f0 (K0 )K0 dK0
0

2 sin 0 d0 =

(48)

(40)­(42) . 4 , . , HXR-, . . , : . , HXR- .

= 4
0

f0 (K0 )K0 dK0 .

. , Teff "" , 3 F0 = kTeff . 2 , (47) (48),
/2

l F = N0 F0 b
esc

sin d, A2 A

(49)

A (24). (49): b2 b sin d sin d = . cos5 (tg2 + bl2 )5/2 A2 A
31 8 2005






609

20 () 15 10 5 0 1.0 a

(l = 1): F= F0 N 3 2b + bm bm - b +1 . (54)

b c 0.8 0.6 l (·) 0.4 0.2 0

F/F0

. 5 5. . (b = 1) (l = 1). l b , .

80 60 40 20 b c 0 0.2 0.4 0.6 (b ­1)/(bm­l) 0.8 1.0 a

. 5. . a, b, c bm = = Bm /B0 = 100, 25, 10; (a) ­ , () ­ .



b2 b (tg2 +1) sin d = d(tg2 ). (50) 2 (tg2 + bl2 )5/2 A2 A

(50) (49) t = tg2 . lb b t +1 dt, (51) F = N0 F0 2 (t + bl2 )5/2
t0

b . bm - b (51), bm F0 N 2b + 2 , F= 3 l (bm - b)+ 1 t0 =

. HXR-. , , ­ . , . , , . , , . , , . , . HXR , , , , .
1. (M.J. Aschwanden), Particle Acceleration and Kinematics in Solar Flares (Dordrecht: Kluwer Academ. Publ., 2002). 2. .., .., . . 78, 187 (2001).
8 2005

(52)

N ­ , (33). , (b = 1): bm F0 N 2+ 2 , (53) F= 3 l (bm - 1) + 1
4 31


610

, 10. .., .., . . 29, 621 (2003). 11. .(B.V. Somov, Yu.E.Litvinenko, T. Kosugi, et al.), ESA SP-448, 701 (1999). 12. , (S.I. Syrovatskiy and O.P. Shmeleva), Sov. Astron. 16, 273 (1972). 13. , (S. Tsuneta and T. Natio), Astrophys. J. Lett. 495, L67 (1998). 14. (H.S. Hudson), Solar Phys. 24, 414 (1972).

3. .., .., ., . . 24, 631 (1998). 4. (J.. Brown), Solar Phys. 18, 489 (1971). 5. , (D.H. Datlowe and R.P. Lin), Solar Phys. 32, 459 (1973). 6. . (S. Masuda, T. Kosugi, H. Hara, et al.), Nature 371, 495 (1994). 7. (L.I. Miroshnichenko), Solar Cosmic Rays (Dordrecht: Kluwer Academ. Publ., 2001). 8. (B.V. Somov), Cosmic Plasma Physics (Dordrecht: Kluwer Academ. Publ., 2000). 9. , (B.V. Somov and T. Kosugi), Astrophys. J. 485, 859 (1997).



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