- Email: [email protected]
A momentum analyser of high resolution
NUCLEAR
1N57RUMEN75
AND
ME7H0D5
A M0MEN7UM
96 (1971) 2 2 1 - 2 2 2 ;
~
N0R7H-H0LLAND
PU8L15H1N6
C0.
ANALY5ER 0F H16H RE50LU710N*
W. C. M1LLER and J. M. P 1 0 W A 7 Y t
Department 0f Phy51c5, Un1ver51ty0f N0tre Dame, N0tre Dame, 1nd1ana 46556, U.5.A. Rece1ved 1 June 1971 A tw0 ma9net 5y5tem ha5 6een deve10ped t0 91ve 5t19mat1c f0cu551n9 w1th un1t ma9n1f1cat10n and a m0mentum d15per510n 0ver 3.5 t1me5 that 06ta1ned w1th a 51n91e ma9net.
7he u5e 0f 5ect0r-5haped, un1f0rm ma9net1c f1e1d5 fc,r m0mentum ana1y515 0f char9ed part1c1e5 pr0duced 6y e1ectr05tat1c, and 6y 0ther acce1erat0r5 15 4u1te c0mm0n. 1n th05e 51tuat10n5 re4u1r1n9 900d re501ut10n, 1t ha5 6een the pract1ce t0 de519n the f1e1d 50 that the part1c1e traject0r1e5 have a 1ar9e rad1u5 0f curvature, p, 1n the f1e1d, 51nce w1th 06ject and 1ma9e 511t5 10cated at c0nju9ate p01nt5, the d15per510n 15 pr0p0rt10na1 t0 th15 rad1u5. 1n the d1rect10n para11e1 t0 the f1e1d (hereaf1er referred t0 a5 the vert1ca1 d1rect10n) c0nver9ence can 6e effected 6y hav1n9 n0n-n0rma1 entrance and ex1t 1nt0 and 0ut 0f the f1e1d. A5 the an91e5 6etween the mean traject0ry and the n0rma15 t0 the 5ect0r ed9e5 at entrance and ex1t are 1ncrea5ed, the c0nju9ate p01nt5 m0ve away fr0m the f1e1d re910n w1th a re5u1t1n9 1ncrea5e 1n d15per510n. 1n the 5ymmetr1c ca5e 0f e4ua1 entrance and ex1t an91e5 and e4ua1 06ject and 1ma9e d15tance5, the m0mentum d15per510n, D = Ax(3p/p) -1 (where Ax 15 the h0r120nta1 tran5ver5e d15p1acement at the 1ma9e p1ane due t0 a fract10na1 chan9e 0f m0mentum Ap/p) 15 2p at n0rma1 entrance and ex1t, and can 6e•, 1ncrea5ed 6y 1ncrea51n9 the entrance and ex1t an91e5. 1f the5e an91e5 are ch05en 50 a5 t0 pr0duce a vert1ca1 1ma9e 1n the h0r120nta1 1ma9e p1ane (••d0u61e f0cu551n9•• 0r ••5t19mat1c f0cu551n9••) the d15per510n 15 1ncrea5ed t0 4p. Further 1ncrea5e 1n the5e an91e5 w0u1d 1ncrea5e the d15per510n; h0wever, the vert1ca1 1ma9e w0u1d n0t 6e at the h0r120nta1 1ma9e p1ane. A typ1ca1 m0mentum ana1y5er f0r a 15 MV tandem e1ectr05tat1c acce1erat0r ha5 a def1ect10n an91e 0f 90 °, a rad1u5 0f curvature 0f 1 m, entrance and ex1t an91e5 0f a60ut 26 °, 06ject and 1ma9e 511t5 each at a d15tance 0f 2 m fr0m the f1e1d 60undar1e5, and thu5 ha5 un1t h0r120nta1 ma9n1f1cat10n and ha5 a d15per510n 0f 4 m. 1f a 1ar9e def1ect10n an91e 15 re4u1red then the entrance and ex1t an91e5 needed t0 pr0duce a 5t19mat1c * W0rk 5upp0rted 6y the Nat10na1 5c1ence F0undat10n and the 0ff1ce 0f Nava1 Re5earch under C0ntract N00014-67-A042-0005. t Pre5ent addre55:DePau1 Un1ver51ty, Ch1ca90, 1111n015. 0C708ER 1971
225
1ma9e a150 6ec0me 1ar9e. F0r the 5ymmetr1c 5t19mat1c f0cu551n9 ca5e at a def1ect10n 0f 135 ° the5e an91e5 are a60ut 50 ° , and appr0ach 90 ° a5 the def1ect10n an91e appr0ache5 180 °. Any reduct10n 0f the5e an91e515 at the expen5e 0f a 5t19mat1c 1ma9e and decrea5e5 the d15per510n t0 1e55 than 4p. We have deve10ped a 535 ° def1ect10n 5y5tem wh1ch ha5 un1t h0r120nta1 ma9n1f1cat10n, un1t vert1ca1 ma9n1f1cat10n and a m0mentum d15per510n 0f a60ut 15p. 7h15 enhancement 1n d15per510n and hence 1n re501ut10n ha5 6een effected 6y a 5tra19htf0rward app11cat10n 0f the 10n-0pt1c5 techn14ue 1) and 0f the matr1x techn14ue2). 51nce the meth0d 15 n0t 11m1ted t0 a part1cu1ar def1ect10n an91e 0r t0 a part1cu1ar 9e0metry, 0ther5 may 6e a61e t0 app1y 1t t0 51m11ar 51tuat10n5. C0n51der a def1ect10n thr0u9h an an91e ~ t0 6e made up 0f tw0 def1ect10n5 4~1+ 4~2 = ~ w1th a dr1ft 0f L 6etween the tw0 def1ect0r5. 7reat1n9 the def1ect0r5 a5 1en5e5, 10cate the 06ject 511t5 at the f1r5t f0ca1 p01nt 0 f t h e f1r5t 1en5, 50 that ray5 fr0m th15 p01nt are para11e1 t0 the 0pt1c ax15 1n the dr1ft 5pace and thu5 w111 6e 1ma9ed at the 5ec0nd f0ca1 p01nt 0f the 5ec0nd 1en5. 7h15 5y5tem ha5 the f0110w1n9 advanta9e5: 5. 51nce there are tw0 5et5 0f entrance and ex1t an91e5, the d15tance fr0m the f1e1d 60undar1e5 t0 the f0ca1 p01nt5 can 6e 1ncrea5ed w1th a re5u1t1n9 1ncrea5e 1n d15per510n. 2. 51nce the f0cu551n9 C0nd1t10n5, the h0r120nta1 ma9n1f1cat10n and the d15per510n are 1ndependent 0f the d15tance 6etween the ma9net5, th15 d15tance can 6e adju5ted 50 that a vert1ca1 1ma9e 15 f0rmed at the h0r120nta1 1ma9e p1ane. We have 5tud1ed the 135 ° 5y5tem 5h0wn 1n f19. 1 wh1ch wa5 de519ned t0 ana1y5e the e1ectr0n 6eam pr0duced 6y the M0de1 F N Van de 6 r a a f f Acce1erat0r 1n 0ur 1a60rat0ry. 80th 5ect0r-5haped ma9net1c f1e1d5 have a def1ect10n an91e 0f 67.5 ° and are 1dent1ca1, w1th e4ua1 entrance and ex1t an91e5 0f 30 ° . 06ject 511t5 1n the f1r5t f0ca1 p1ane 0f the f1r5t ma9net are
222
W.
C.
M1LLER
AND
1ma9ed h0r120nta11y at the 5ec0nd f0ca1 p1ane 0f the 5ec0nd ma9net w1th a ma9n1f1cat10n 0f ( - 1 ) . A vert1ca1 1ma9e 0f the 06ject 511t5 15 pr0duced 6y the f1r5t ma9net at L / 2 fr0m the f1r5t ma9net•5 ex1t ed9e and th15 1ma9e 15 1ma9ed a9a1n at the h0r120nta1 1ma9e p1ane 6y the 5ec0nd ma9net w1th an 0vera11 ma9n1f1cat10n 0f + 1. 7he ca1cu1ated d15per510n 15 14.6p. A techn14ue wa5 deve10ped 1n th15 1a60rat0ry 6y Demp5ey 3) f0r 5e1ect1n9 the rad1u5 0f curvature 0f the ma9net ed9e5 t0 e11m1nate 5ec0nd 0rder a6errat10n5. 7he ca1cu1ated rad1u5 0f curvature 0f the5e ed9e5 wa5 50 1ar9e that a 5tra19ht-ed9e wa5 deemed 5at15fact0ry. A 6eam tran5p0rt c0mputer pr09ram, 51m11ar t0 that de5cr11~ed 6y 5wen50n 4) wa5 u5ed t0 de5cr16e the 6eam 1n 60th h0r120nta1 and vert1ca1 pha5e 5pace at var10u5 p01nt5 a10n9 the traject0ry. 7he f0cu551n9 pr0pert1e5 and the 1ar9e d15per510n were c0nf1rmed. 1nc1u510n 0f 5ec0nd 0rder term55) 1n th15 pr09ram c0nf1rmed the ch01ce 0f 5tra19ht ma9net ed9e5 (and 1nd1cated 5evere 5ec0nd 0rder effect5 f0r 5ma11er rad1u5 0f curvature ed9e5). 7he 1ncrea5e 1n 1ma9e 512e due t0 5ec0nd 0rder effect5 wa5 1e55 than 1%. A f1r5t and 5ec0nd 0rder 6eam enve10pe c0mputer 1
1
r
1 1/
J.
M.
P10WA7Y
pr09ram wa5 perf0rmed a5 part 0f the 5y5tem c05t 6y the ma9net manufacturer* pr10r t0 c0n5truct10n. 7h15 pr09ram 15 rep0rted t0 1nc1ude fr1n9e f1e1d effect5. 7he re5u1t5 are 1n exce11ent a9reement w1th 0ur re5u1t5. 7he enhancement 1n re501v1n9 p0wer 15 due t0 the 1ar9e d15tance 6etween the 5ec0nd ma9net and the 1ma9e p1ane w1th0ut a c0nc0m1tant 1ncrea5e 1n h0r120nta1 ma9n1f1cat10n. 1n the 5y5tem de5cr16ed a60ve the e4ua11y 1ar9e d15tance 6etween the 06ject 511t5 and the f1r5t ma9net c0u1d 6e a d15advanta9e 1f 5pace 6etween the acce1erat0r and the ana1y5er 15 11m1ted. 7h15 d15advanta9e c0u1d 6e c1rcumvented, f0r examp1e, 6y reduc1n9 the traject0ry rad1u5 1n the f1r5t ma9net. 1f a11 an91e5 were pre5erved then the d15per510n w0u1d 6e the 5ame; h0wever, the h0r120nta[ ma9n1f1cat10n w0u1d 6e 1ncrea5ed pr0p0rt10na1 t0 (p1) -~. 7he d15tance 6etween ma9net5 w0u1d 6e d1fferent; h0wever, the vert1ca1 ma9n1f1cat10n w0u1d 6e unchan9ed. A1ternate1y, the entrance and ex1t an91e5 0f e1ther the f1r5t ma9net 0r 0f 60th ma9net5 c0u1d 6e chan9ed 50 that the f1r5t f0ca1 p01nt 0f the f1r5t ma9net 15 c105er t0 the ma9net. F0r examp1e, 1f 1n f19. 1, //1 = f13 = 60 °, //2 =/5•4 = 0°, 1j = 1 . 4 5 p , 12 = 7.56p, L --- 0.2p, the d15per510n 15 11.6p, h0r120nta1 ma9n1f1cat10n 15 ( - 1 ) and vert1ca1 ma9n1f1cat10n 15 (+3.5). 7h15 5y5tem ha5 n0t 6een 5tud1ed f0r 5ec0nd 0rder effect5. 7he auth0r5 w15h t0 thank Dr. H. Me1ner wh0 1nc1uded the 5ec0nd 0rder term5 1n the 6eam tran5p0rt pr09ram. Reference5
"~51
1
F19. 1. 5ymmetr1c, 5t19mat1cf0cu551n95y5tem. p1 =/92; (f1~=t~2 =67.5~; f1~ = [J2 = f13 =f14 = 30°; L=1.55p; 1, = 1 , = 5.26p ; D = 14.6p.
1) R. Her209, 2. Phy51k 89 (1934) 447; K. 7. 8ra1n6r1d9e, Exper1menta1 nuc1ear phy51c5, v01. 1 (ed. E. 5e9re; W11ey, New Y0rk, 1953) p. 559. 2) 5. Penner, Rev. 5c1. 1n5tr. 32 (1961) 150; H.A. En9e, F0cu51n9 0 f c h a r 9 e d part1c1e5, v01. 11 (ed. A 5ept1er; Academ1c Pre55, New Y0rk, 1967) p. 203. :3) D. F. Demp5ey, Rev. 5c1. 1n5tr. 26 (1955) 1141. 4) D.A. 5wen50n, MURA-645 (1962) unpu6115hed. 5) K. L. 8r0wn, Rev. 5c1. 1n5tr. 36 (1965) 271 ; Cf. H. A. En9e, 10c. c1t. * Var1an Rad1at10n D1v1510n,5pectr0ma9net1c P1ant, Hayward, Ca11f0rn1a.
1N57RUMEN75
AND
ME7H0D5
A M0MEN7UM
96 (1971) 2 2 1 - 2 2 2 ;
~
N0R7H-H0LLAND
PU8L15H1N6
C0.
ANALY5ER 0F H16H RE50LU710N*
W. C. M1LLER and J. M. P 1 0 W A 7 Y t
Department 0f Phy51c5, Un1ver51ty0f N0tre Dame, N0tre Dame, 1nd1ana 46556, U.5.A. Rece1ved 1 June 1971 A tw0 ma9net 5y5tem ha5 6een deve10ped t0 91ve 5t19mat1c f0cu551n9 w1th un1t ma9n1f1cat10n and a m0mentum d15per510n 0ver 3.5 t1me5 that 06ta1ned w1th a 51n91e ma9net.
7he u5e 0f 5ect0r-5haped, un1f0rm ma9net1c f1e1d5 fc,r m0mentum ana1y515 0f char9ed part1c1e5 pr0duced 6y e1ectr05tat1c, and 6y 0ther acce1erat0r5 15 4u1te c0mm0n. 1n th05e 51tuat10n5 re4u1r1n9 900d re501ut10n, 1t ha5 6een the pract1ce t0 de519n the f1e1d 50 that the part1c1e traject0r1e5 have a 1ar9e rad1u5 0f curvature, p, 1n the f1e1d, 51nce w1th 06ject and 1ma9e 511t5 10cated at c0nju9ate p01nt5, the d15per510n 15 pr0p0rt10na1 t0 th15 rad1u5. 1n the d1rect10n para11e1 t0 the f1e1d (hereaf1er referred t0 a5 the vert1ca1 d1rect10n) c0nver9ence can 6e effected 6y hav1n9 n0n-n0rma1 entrance and ex1t 1nt0 and 0ut 0f the f1e1d. A5 the an91e5 6etween the mean traject0ry and the n0rma15 t0 the 5ect0r ed9e5 at entrance and ex1t are 1ncrea5ed, the c0nju9ate p01nt5 m0ve away fr0m the f1e1d re910n w1th a re5u1t1n9 1ncrea5e 1n d15per510n. 1n the 5ymmetr1c ca5e 0f e4ua1 entrance and ex1t an91e5 and e4ua1 06ject and 1ma9e d15tance5, the m0mentum d15per510n, D = Ax(3p/p) -1 (where Ax 15 the h0r120nta1 tran5ver5e d15p1acement at the 1ma9e p1ane due t0 a fract10na1 chan9e 0f m0mentum Ap/p) 15 2p at n0rma1 entrance and ex1t, and can 6e•, 1ncrea5ed 6y 1ncrea51n9 the entrance and ex1t an91e5. 1f the5e an91e5 are ch05en 50 a5 t0 pr0duce a vert1ca1 1ma9e 1n the h0r120nta1 1ma9e p1ane (••d0u61e f0cu551n9•• 0r ••5t19mat1c f0cu551n9••) the d15per510n 15 1ncrea5ed t0 4p. Further 1ncrea5e 1n the5e an91e5 w0u1d 1ncrea5e the d15per510n; h0wever, the vert1ca1 1ma9e w0u1d n0t 6e at the h0r120nta1 1ma9e p1ane. A typ1ca1 m0mentum ana1y5er f0r a 15 MV tandem e1ectr05tat1c acce1erat0r ha5 a def1ect10n an91e 0f 90 °, a rad1u5 0f curvature 0f 1 m, entrance and ex1t an91e5 0f a60ut 26 °, 06ject and 1ma9e 511t5 each at a d15tance 0f 2 m fr0m the f1e1d 60undar1e5, and thu5 ha5 un1t h0r120nta1 ma9n1f1cat10n and ha5 a d15per510n 0f 4 m. 1f a 1ar9e def1ect10n an91e 15 re4u1red then the entrance and ex1t an91e5 needed t0 pr0duce a 5t19mat1c * W0rk 5upp0rted 6y the Nat10na1 5c1ence F0undat10n and the 0ff1ce 0f Nava1 Re5earch under C0ntract N00014-67-A042-0005. t Pre5ent addre55:DePau1 Un1ver51ty, Ch1ca90, 1111n015. 0C708ER 1971
225
1ma9e a150 6ec0me 1ar9e. F0r the 5ymmetr1c 5t19mat1c f0cu551n9 ca5e at a def1ect10n 0f 135 ° the5e an91e5 are a60ut 50 ° , and appr0ach 90 ° a5 the def1ect10n an91e appr0ache5 180 °. Any reduct10n 0f the5e an91e515 at the expen5e 0f a 5t19mat1c 1ma9e and decrea5e5 the d15per510n t0 1e55 than 4p. We have deve10ped a 535 ° def1ect10n 5y5tem wh1ch ha5 un1t h0r120nta1 ma9n1f1cat10n, un1t vert1ca1 ma9n1f1cat10n and a m0mentum d15per510n 0f a60ut 15p. 7h15 enhancement 1n d15per510n and hence 1n re501ut10n ha5 6een effected 6y a 5tra19htf0rward app11cat10n 0f the 10n-0pt1c5 techn14ue 1) and 0f the matr1x techn14ue2). 51nce the meth0d 15 n0t 11m1ted t0 a part1cu1ar def1ect10n an91e 0r t0 a part1cu1ar 9e0metry, 0ther5 may 6e a61e t0 app1y 1t t0 51m11ar 51tuat10n5. C0n51der a def1ect10n thr0u9h an an91e ~ t0 6e made up 0f tw0 def1ect10n5 4~1+ 4~2 = ~ w1th a dr1ft 0f L 6etween the tw0 def1ect0r5. 7reat1n9 the def1ect0r5 a5 1en5e5, 10cate the 06ject 511t5 at the f1r5t f0ca1 p01nt 0 f t h e f1r5t 1en5, 50 that ray5 fr0m th15 p01nt are para11e1 t0 the 0pt1c ax15 1n the dr1ft 5pace and thu5 w111 6e 1ma9ed at the 5ec0nd f0ca1 p01nt 0f the 5ec0nd 1en5. 7h15 5y5tem ha5 the f0110w1n9 advanta9e5: 5. 51nce there are tw0 5et5 0f entrance and ex1t an91e5, the d15tance fr0m the f1e1d 60undar1e5 t0 the f0ca1 p01nt5 can 6e 1ncrea5ed w1th a re5u1t1n9 1ncrea5e 1n d15per510n. 2. 51nce the f0cu551n9 C0nd1t10n5, the h0r120nta1 ma9n1f1cat10n and the d15per510n are 1ndependent 0f the d15tance 6etween the ma9net5, th15 d15tance can 6e adju5ted 50 that a vert1ca1 1ma9e 15 f0rmed at the h0r120nta1 1ma9e p1ane. We have 5tud1ed the 135 ° 5y5tem 5h0wn 1n f19. 1 wh1ch wa5 de519ned t0 ana1y5e the e1ectr0n 6eam pr0duced 6y the M0de1 F N Van de 6 r a a f f Acce1erat0r 1n 0ur 1a60rat0ry. 80th 5ect0r-5haped ma9net1c f1e1d5 have a def1ect10n an91e 0f 67.5 ° and are 1dent1ca1, w1th e4ua1 entrance and ex1t an91e5 0f 30 ° . 06ject 511t5 1n the f1r5t f0ca1 p1ane 0f the f1r5t ma9net are
222
W.
C.
M1LLER
AND
1ma9ed h0r120nta11y at the 5ec0nd f0ca1 p1ane 0f the 5ec0nd ma9net w1th a ma9n1f1cat10n 0f ( - 1 ) . A vert1ca1 1ma9e 0f the 06ject 511t5 15 pr0duced 6y the f1r5t ma9net at L / 2 fr0m the f1r5t ma9net•5 ex1t ed9e and th15 1ma9e 15 1ma9ed a9a1n at the h0r120nta1 1ma9e p1ane 6y the 5ec0nd ma9net w1th an 0vera11 ma9n1f1cat10n 0f + 1. 7he ca1cu1ated d15per510n 15 14.6p. A techn14ue wa5 deve10ped 1n th15 1a60rat0ry 6y Demp5ey 3) f0r 5e1ect1n9 the rad1u5 0f curvature 0f the ma9net ed9e5 t0 e11m1nate 5ec0nd 0rder a6errat10n5. 7he ca1cu1ated rad1u5 0f curvature 0f the5e ed9e5 wa5 50 1ar9e that a 5tra19ht-ed9e wa5 deemed 5at15fact0ry. A 6eam tran5p0rt c0mputer pr09ram, 51m11ar t0 that de5cr11~ed 6y 5wen50n 4) wa5 u5ed t0 de5cr16e the 6eam 1n 60th h0r120nta1 and vert1ca1 pha5e 5pace at var10u5 p01nt5 a10n9 the traject0ry. 7he f0cu551n9 pr0pert1e5 and the 1ar9e d15per510n were c0nf1rmed. 1nc1u510n 0f 5ec0nd 0rder term55) 1n th15 pr09ram c0nf1rmed the ch01ce 0f 5tra19ht ma9net ed9e5 (and 1nd1cated 5evere 5ec0nd 0rder effect5 f0r 5ma11er rad1u5 0f curvature ed9e5). 7he 1ncrea5e 1n 1ma9e 512e due t0 5ec0nd 0rder effect5 wa5 1e55 than 1%. A f1r5t and 5ec0nd 0rder 6eam enve10pe c0mputer 1
1
r
1 1/
J.
M.
P10WA7Y
pr09ram wa5 perf0rmed a5 part 0f the 5y5tem c05t 6y the ma9net manufacturer* pr10r t0 c0n5truct10n. 7h15 pr09ram 15 rep0rted t0 1nc1ude fr1n9e f1e1d effect5. 7he re5u1t5 are 1n exce11ent a9reement w1th 0ur re5u1t5. 7he enhancement 1n re501v1n9 p0wer 15 due t0 the 1ar9e d15tance 6etween the 5ec0nd ma9net and the 1ma9e p1ane w1th0ut a c0nc0m1tant 1ncrea5e 1n h0r120nta1 ma9n1f1cat10n. 1n the 5y5tem de5cr16ed a60ve the e4ua11y 1ar9e d15tance 6etween the 06ject 511t5 and the f1r5t ma9net c0u1d 6e a d15advanta9e 1f 5pace 6etween the acce1erat0r and the ana1y5er 15 11m1ted. 7h15 d15advanta9e c0u1d 6e c1rcumvented, f0r examp1e, 6y reduc1n9 the traject0ry rad1u5 1n the f1r5t ma9net. 1f a11 an91e5 were pre5erved then the d15per510n w0u1d 6e the 5ame; h0wever, the h0r120nta[ ma9n1f1cat10n w0u1d 6e 1ncrea5ed pr0p0rt10na1 t0 (p1) -~. 7he d15tance 6etween ma9net5 w0u1d 6e d1fferent; h0wever, the vert1ca1 ma9n1f1cat10n w0u1d 6e unchan9ed. A1ternate1y, the entrance and ex1t an91e5 0f e1ther the f1r5t ma9net 0r 0f 60th ma9net5 c0u1d 6e chan9ed 50 that the f1r5t f0ca1 p01nt 0f the f1r5t ma9net 15 c105er t0 the ma9net. F0r examp1e, 1f 1n f19. 1, //1 = f13 = 60 °, //2 =/5•4 = 0°, 1j = 1 . 4 5 p , 12 = 7.56p, L --- 0.2p, the d15per510n 15 11.6p, h0r120nta1 ma9n1f1cat10n 15 ( - 1 ) and vert1ca1 ma9n1f1cat10n 15 (+3.5). 7h15 5y5tem ha5 n0t 6een 5tud1ed f0r 5ec0nd 0rder effect5. 7he auth0r5 w15h t0 thank Dr. H. Me1ner wh0 1nc1uded the 5ec0nd 0rder term5 1n the 6eam tran5p0rt pr09ram. Reference5
"~51
1
F19. 1. 5ymmetr1c, 5t19mat1cf0cu551n95y5tem. p1 =/92; (f1~=t~2 =67.5~; f1~ = [J2 = f13 =f14 = 30°; L=1.55p; 1, = 1 , = 5.26p ; D = 14.6p.
1) R. Her209, 2. Phy51k 89 (1934) 447; K. 7. 8ra1n6r1d9e, Exper1menta1 nuc1ear phy51c5, v01. 1 (ed. E. 5e9re; W11ey, New Y0rk, 1953) p. 559. 2) 5. Penner, Rev. 5c1. 1n5tr. 32 (1961) 150; H.A. En9e, F0cu51n9 0 f c h a r 9 e d part1c1e5, v01. 11 (ed. A 5ept1er; Academ1c Pre55, New Y0rk, 1967) p. 203. :3) D. F. Demp5ey, Rev. 5c1. 1n5tr. 26 (1955) 1141. 4) D.A. 5wen50n, MURA-645 (1962) unpu6115hed. 5) K. L. 8r0wn, Rev. 5c1. 1n5tr. 36 (1965) 271 ; Cf. H. A. En9e, 10c. c1t. * Var1an Rad1at10n D1v1510n,5pectr0ma9net1c P1ant, Hayward, Ca11f0rn1a.