Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://nuclphys.sinp.msu.ru/mirrors/1999_12c.pdf Äàòà èçìåíåíèÿ: Tue Jan 13 15:51:52 2009 Äàòà èíäåêñèðîâàíèÿ: Tue Oct 2 00:14:35 2012 Êîäèðîâêà: koi8-r

DEFLECTION OF CHARGED PARTICLES BY CRYSTALS
S. P. DENISOV Motion of relativistic charge particles in magnetic and electric fields and their deflection and focusing using bent crystals are considered. Éððîç ê,çðfl ,êéáëêá áíflçê,êðçðìêi à fléáëë°i ~ðçê^ , î,,ëêçëñî ê íáìç ê~áðìñî òñífli ê êi ñçìíñëáëêá ê ûñìøðê ñ,ì ò ê òñîñê êàñ,,ëøç°i ì êðçííñ,.


Ê. Õ. ÿæÃÞÊÈã
Åñðìñ,ðìêõ ,,ñðø ðç,áëë°õ øëê,á ðêçáç êî. Å.ã. Öñîñëñðñ,

1. ããæÿæÃÞæ

© ÿáëêðñ, Ê.Õ., 1999

. . 1976 (, ) .. . , , (, ) , .. . 1984 8 . 1989 70 . . 1996 .. , .. , .. , .. , .. , .. , .. .. . (), , 1 , : 1 = 109 . (R), ­ (R ).
2. ÈÌÄÖÈÃæÃÞæ ÑäÊÌÞßÓ ÛÖæÄÌÉÈÅäèÃÞÌÃÓÅ ÕÈÖæÅ

e, v p U B [1]

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dp e ----- = ­ e grad U + -- [ v â B ] . (1) dt c (1) . - grad U . -U / x, -U / y, -U / z. (1), v B, Fl . v B B sin , ­ v B. Fl [2] e F lx = -- ( y B z ­ z B y ) , c e F ly = -- ( z B x ­ x B z ) , c e F lz = -- ( x B y ­ y B x ) . c , M v E Mv vE 2 2 22 p = ----------------- = ------ , (2) ( pc ) = E ­ ( Mc ) , 2 2 c 1­ c ­ = / c. . B. , , , cp n R m = ------- , (3) eB pn ­ , B. (3), (1). , lm . , B z. p0 (x, y). , Rm = cp0 /(eB ) (. 1), , . . 1 , m lm eBl m sin m = ----- = ---------- . Rm cp 0 , ­ , ­

p0



l

m

m y m x . 1. . B Rm p

­ , 0 ,3 Z Bl m sin m = ------------------- , p0 c (4)

Z ­ . , 70 1°. , , 2 . (4) , 2 2 . ­ , . ( 10 ) . . , . . (. 2), lc dc , . Uc , y , U = 0, U = yUc / dc . E0 , p0 0

ÿæÃÞÊÈã Ê.Õ. ÈÌÄÖÈÃæÃÞæ ÀäÉÝýæÃÃÓÎ ÑäÊÌÞß ÄÉÞÊÌäÖÖäÅÞ

85


U = Uc

p

0

y py (td) x U=0

d

p0 p

. 2.

x t = 0 (. 2). (1), p x = p0 , eU c t p y = ­ ---------- , dc p z = 0, (5)

(x, y), x p0 . td (5), d py( td ) eU c t d tg d = ------------- = ­ -------- ---- . px p0 d c (6)

( c) td = lc / 0 . , x , . , p 2 = p 2 + p 2 , x y (2) (5) pxc p0 c x = --------- = --------------------------------------------- = 2 2 E E 0 + ( ceU c t / d c ) 0 = ------------------------------------------------------ . 2 1 + ( ceU c t / ( E 0 d c ) ) (7)
2 2

, , , [2], , . x (7). . 70 dc = 10 , 1 . , 1°. , eUc = 106 , (9) lc 120 . , 1 , . , , , . -, , ( 1 ) ? : , . ? , ­ . , . , , .
3. ÄäÃäÖÞÉÈãäÃÞæ ÑäÊÌÞß ã ÄÉÞÊÌäÖÖäÎ

(E Mc2) d 1, , , ceU c t ------------E0 d c 1. (8)

(8), , x = 0 , td = lc / 0 eU c l c tg d = ­ ---------- ---- . p0 0 d c (9)

. (8) d 1 E Mc2. , (8). , -

(. 3), . ­ . , . (. . 3). (100), (110) (111). 1964 . [3] . , 0 ( ), U, .

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(100)

(110)

(111)

. 3.

. . , z y (. . 3). x U = U(x). e M (x, z) 0 z. , E0 , p0 0 . (1), d px U ------- = ­ e ------ , dt x d pz ------- = 0. dt (10)

1 2 E t = -- p 0 0 + eU = const, 2 p0 d 2 x dU ---- ------- + e ------ = 0. -dx 0 dt 2

(12) (13)

2x 2 U ( x ) = U 0 ----- , d p x dp ---- , 2 (14)

dp ­ . (14) (. 4). (14) (13), x: p 0 d 2 x 8 eU 0 ---- ------- + ------------ x = 0. -2 0 dt 2 dp (15) p0 / 0 dx m ------- + ax = 0, 2 dt (m a ­ ). , x = 0: x = A sin ( 0 t + 0 ) , d p Et A = ---- -------- , 2 eU 0 2 c 2 eU 0 0 = ----- ------------ , d p E0 (16)
2

U x, U dU dU ------ = ------ = --------- . d x x dt x (11)

(15) m 8 eU 0 / d
2 p

a

(11), x = pxc2 / E, E = = c p x + p z + M c , (10). , , E + eU = const. px / pz
22 22 2 2 22

1 E Ez + p x c / ( 2 Ez ) ,
22

E z = c p z c + M c ­ , px c --------- + E z + eU = const. 2E z , (10), pz , , Ez , E t = p x c / ( 2 E z ) + eU . pz = = p0 Ez = E0 , , Et (10) :
22 22

0 ­ 0 ­ , . z = 0t, = dx / dz = dx /(0dt) : A 0 1 2E = --------- cos ( 0 t + 0 ) = ---- -------t cos ( 0 t + 0 ) . 0 E0 0 (16) , Et eU0 dp /2,

ÿæÃÞÊÈã Ê.Õ. ÈÌÄÖÈÃæÃÞæ ÀäÉÝýæÃÃÓÎ ÑäÊÌÞß ÄÉÞÊÌäÖÖäÅÞ

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U, B 25

20

. : , , , . . [4].
4. ÈÌÄÖÈÃæÃÞæ Þ ÍÈÄËÊÞÉÈãÄä ÕËÑÄÈã ÀäÉÝýæÃÃÓÎ ÑäÊÌÞß ÄÉÞÊÌäÖÖäÅÞ

15

10

5

0

-0,75

-0,25

x, å

0,25

0,75

. 4. (110) ( ­ , ­ )

, , . (12) , 0 , , U = 0 (x = 0). l = 2 eU 0 1 2 eU 0 ------------ = ---- ------------ . p0 0 0 E0 (17)

1976 .. , , , , . E0 , p0 v0 (x, z) 0 z (. 5). R dp , U, 3, pzz / R(z), . (. 5), z . pz = p0 z = 0 (. 3) : R(z) = R = const. x d px U p 0 0 ------- + e ------ + ---------- = 0. x R dt (. 3): p0 0 1 2 E t = -- p 0 0 + eU + ---------- x = const, 2 R (18)

l . - 0 . . 70 , , (110), dp = 1,92 å (1 å = 10-10 ) U0 = 22 . , , . (17) l = 25 ( ­ ). 70 , (110) 0,0014°. , : .

= dx / dz px / p0 1. U(x) (14),

x

p

0

0

0 F

z

c

. 5. (x, z ­ , Fc ­ )

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p0 d 2 x 8 U 0 p0 0 ---- ------- + --------- ex + ---------- = 0. -2 0 dt 2 R dp x = x ' ­ p 0 0 d p / ( 8 eU 0 R ) (15). , 2

x 0 = ­ p 0 0 d p / ( 8 eU 0 R ) :
2

x = x0 + A sin(0t + 0), A 0 (16) (18), 0 ­ . | x0 + A | max dp / 2, . R p0 0 R c = ------------ d p . 4 eU 0 (19)

Rc (18), , z (0 = 0 x0 = 0). R > Rc 0 , , | x0 + A | max dp / 2 x = 0: R c = l 1 ­ ----c , R (20)

? . ­ . , 0 > c = 20 , . 10­100 c . , . , ( 3), ( ), , . 100%- . , ? . -, "" 10- 3­10- 4. . -, E0 , l 1 / E 0 , , . , (, ) 450 50%. . -, , , . , , , (x, z) F (. 6, ). F B, B1 , B2 , , , O. , OF , . , , , , OF, , F.

l ­ (17). 0 > c . (20) , , . , 3, - , , dp . , Rc , 0 c . 70 , (110) . (19), Rc = 15 . R = Rc 1 c , R Rc . , R = 75 E0 = 70 = 1° lc lc = = R sin = 1,3 . 100 10 000 , (. 2). : , , ,
1 ­ , .

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B1 B B2 F



5 O . 6. ­ ; ­ () () , .

x = 2BF c , (21) c ­ (20). 70 x = 40 1 . 70 . . 6, . x (21). . 6, , , F , c .
5. ÀäÄÖØÑæÃÞæ

- , . [5]. .
ÖÞÌæÉäÌËÉä
1. .., .. . .: . .-. ., 1960. 63 . 2. .., .. . .: , 1981. . 147, 507. 3. . // . . 1969. . 99, . 2. . 249. 4. .., .., .. // . 1994. . 164, . 10. . 1017. 5. Biryukov V.M., Chesnokov Yu.A., Kotov V.I. Crystal Channeling and Its Application at High-Energy Accelerators. Berlin: Springer, 1997.

, , , . . , , - , , -

*** , , (), - . , , -3 t-. . 230 .

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ÊÈÉÈÊÈãÊÄÞÁ ÈåÉäÀÈãäÌæÖÇÃÓÁ ýËÉÃäÖ, <12, 1999