Hng dan c ban s dung

MCNP

cho he ieu hanh Windows

Nhom NMTP

(Tai lieu lu hanh noi bo)

Hng dn c bn s dng

MCNP

cho h iu hnh Windows

ng Nguyn Phng

TPHCM 06/2015

Computers are useless. They can only give you answers.

Pablo Picasso (1968)

MC LC

Li ni u 5

1 Gii thiu v MCNP 71.1 Chng trnh MCNP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.2 Lch s ca chng trnh MCNP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.2.1 Phng php Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.2.2 MCNP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.2.3 MCNPX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.2.4 MCNP6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.3 Cch thc ci t chng trnh MCNP . . . . . . . . . . . . . . . . . . . . . . . . . . 121.4 Cch thc thi chng trnh MCNP . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.4.1 S dng Visual Editor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.4.2 S dng cu lnh trong Command Prompt . . . . . . . . . . . . . . . . . . . 13

2 C s phng php Monte Carlo 172.1 C s ca phng php Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.2 S ngu nhin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2.1 Cc loi s ngu nhin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.2.2 Nhng iu cn lu khi m phng s ngu nhin . . . . . . . . . . . . . . . 192.2.3 Phng php to s ngu nhin . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3 Phn b xc sut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.3.1 Bin ngu nhin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.3.2 Hm mt xc sut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.3.3 Lut s ln . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.3.4 nh l gii hn trung tm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.3.5 Ly mu phn b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.3.6 c lng mu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.3.7 chnh xc ca c lng . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.3.8 Khong tin cy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3 Cu trc chng trnh MCNP 273.1 Cch thc hot ng ca MCNP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.1.1 Cc th tc chnh trong MCNP . . . . . . . . . . . . . . . . . . . . . . . . . . 273.1.2 Cch thc m phng vn chuyn ht . . . . . . . . . . . . . . . . . . . . . . . 28

3.2 D liu ht nhn v phn ng ca MCNP . . . . . . . . . . . . . . . . . . . . . . . . 29

MC LC 2

3.2.1 Cc th vin d liu c s dng . . . . . . . . . . . . . . . . . . . . . . . . 293.2.2 Cc bng d liu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.3 Input file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.3.1 Cu trc input file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.3.2 V d cu trc input file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.3.3 Mt s lu khi xy dng input file . . . . . . . . . . . . . . . . . . . . . . . 35

3.4 Output file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4 nh ngha hnh hc 374.1 Surface Cards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.1.1 Cc mt c nh ngha bi phng trnh . . . . . . . . . . . . . . . . . . . 374.1.2 Macrobody . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.2 Cell Cards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.3 Mt s card nh ngha tnh cht ca cell . . . . . . . . . . . . . . . . . . . . . . . . 44

4.3.1 Material Cards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.3.2 Cell Volume Card (VOL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.3.3 Surface Area Card (AREA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.4 Chuyn trc ta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.4.1 Coordinate Transformation Card (TRn) . . . . . . . . . . . . . . . . . . . . . 464.4.2 Cell Transformation Card (TRCL) . . . . . . . . . . . . . . . . . . . . . . . . 47

4.5 Lattice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.5.1 Universe & Fill Card (U & FILL) . . . . . . . . . . . . . . . . . . . . . . . . . 484.5.2 Lattice Card (LAT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5 nh ngha ngun 495.1 Mode Cards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495.2 Cc kiu nh ngha ngun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495.3 Ngun tng qut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

5.3.1 nh ngha . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505.3.2 M t phn b ngun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505.3.3 Ngun mt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.4 Ngun ti hn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565.5 Card ngng chng trnh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

6 nh ngha tally 596.1 Cc loi tally . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

6.1.1 Tally F1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606.1.2 Tally F2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 616.1.3 Tally F4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 616.1.4 Tally F5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 616.1.5 Tally F6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646.1.6 Tally F7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656.1.7 Tally F8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

6.2 Cc card dng cho khai bo tally . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 666.3 FMESHn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 726.4 Lattice Tally . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

7 S dng chng trnh Visual Editor 757.1 Chng trnh Visual Editor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

7.1.1 Cc menu chnh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 757.1.2 Hin th ha ca input file . . . . . . . . . . . . . . . . . . . . . . . . . . . 757.1.3 Mt s file chnh ca Visual Editor . . . . . . . . . . . . . . . . . . . . . . . . 78

7.2 Chnh sa input file bng Visual Editor . . . . . . . . . . . . . . . . . . . . . . . . . 79

3 MC LC

7.2.1 Ca s Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 797.2.2 Ca s cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 807.2.3 Khai bo vt liu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 817.2.4 Khai bo importance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 827.2.5 Chuyn trc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

7.3 Mt s ha 2D c trng . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 847.3.1 Hin th vt ca ht . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 847.3.2 th tally . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 847.3.3 th tit din . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

7.4 ha 3D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 867.4.1 nh 3D Ray Tracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 867.4.2 nh ng hc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

8 K thut gim phng sai 918.1 Cc k thut gim phng sai . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 918.2 Phn chia theo hnh hc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 928.3 Phn chia theo nng lng . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 938.4 t ngng kho st . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 948.5 Ca s trng s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 958.6 Bin i exponential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 978.7 Hiu chnh cc hiu ng vt l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 988.8 Va chm bt buc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 998.9 Hiu chnh pht bremsstrahlung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1008.10 Hiu chnh s to photon t neutron . . . . . . . . . . . . . . . . . . . . . . . . . . . 1008.11 Ly mu tng quan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1018.12 Mt cu DXTRAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

9 Cch c ouput file ca MCNP 1039.1 Kt qu u ra ca MCNP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

9.1.1 Cc bng thng tin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1039.1.2 In ra cc kt qu theo chu k . . . . . . . . . . . . . . . . . . . . . . . . . . . 1069.1.3 V kt qu tally . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

9.2 chnh xc ca kt qu v cc nhn t nh hng . . . . . . . . . . . . . . . . . . 1079.3 nh gi thng k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

9.3.1 Sai s tng i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1089.3.2 Figure of Merit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1099.3.3 Variance of Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1099.3.4 Probability Density Function . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

9.4 Cc kim nh thng k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

10 Mt s v d m phng MCNP 11310.1 V d bi ton ph gamma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11310.2 V d bi ton ngng . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11610.3 V d bi ton tnh liu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

Ti liu tham kho 124

A Bng tnh cht cc nguyn t 127

B Mt s vt liu thng dng 131

C B h s chuyn i thng lng sang liu 135

D Ma trn quay trc ta 137

MC LC 4

Li ni u

Trong nhng nm gn y, vic nghin cu v ng dng phng php m phng Monte Carlo chocc bi ton vt l ht nhn ngy cng tr nn ph bin do nhng li ch m cc phng php nymang li. Cc chng trnh m phng Monte Carlo tr thnh cc cng c hu hiu gii quytcc bi ton phc tp m khng th gii c bng nhng phng php thng thng, chng hnnh m phng tng tc ca bc x vi vt cht nhiu vng nng lng khc nhau, tnh tonti u l phn ng, kho st p ng ca detector,...

Tp ti liu Hng dn c bn s dng MCNP cho h iu hnh Windows c xydng vi mc ch cung cp cho ngi c nhng kin thc c bn s dng mt trong nhngcng c m phng Monte Carlo cho bi ton vn chuyn bc x thng dng nht hin nay lchng trnh MCNP. Ti liu ny c hnh thnh t vic tng hp cc lun vn cng nh ghichp ca cc thnh vin trong nhm NMTP (https://sites.google.com/site/nmtpgroup/)vi mc ch h thng ho kin thc ln kinh nghim thu c sau gn 10 nm lm vic vi chngtrnh MCNP. Phn ln ni dung ca ti liu ny u c ly t cc ti liu MCNP Manual(vol I, II, III). Ni dung ca ti liu tp trung vo 3 mc tiu chnh:

Hng dn cch ci t v thc thi chng trnh MCNP.

Cch vit mt input file n gin.

Cch c cc bng s liu thng k, nhn xt tin cy ca cc kt qu thu c t MCNP.

Tc gi xin gi li cm n n tt c cc thnh vin trong nhm c bit l c Trng Th HngLoan v cc thnh vin Nguyn c Chng , Trn i Khanh , ng Trng Ka My , Phm Hu Phong , Phan Th Qu Trc, L Thanh Xun v nhng bi dch v ghi chp vcng qu gi gp phn to nn ti liu ny. Hi vng vi ti liu ny, ngi c s thu thp cnhng kin thc qu gi c ch cho cng vic ca mnh.

Do ti liu c tng hp t nhiu ngun khc nhau nn chc chn s khng trnh khi nhngsai st v ni dung cng nh hnh thc. Ngoi ra, do gii hn ca ti liu cng nh kin thc catc gi, vn cn nhiu ni dung lin quan ti chng trnh MCNP cha c trnh by trong y.Hi vng rng, ti liu ny s c b sung, ng gp bi chnh cc c gi n ngy cng chon thin hn.

ng Nguyn Phng

LI NI U 6

1Gii thiu v MCNP

Mc ch ca chng ny l nhm gii thiu nhng nt chnh ca chng trnh m phng vnchuyn ht bng phng php Monte Carlo MCNP (https://mcnp.lanl.gov/). Phn u cachng s c dnh cho vic trnh by tng quan lch s pht trin, tnh hnh ng dng cng nhcc phin bn chnh ca chng trnh MCNP tnh cho n thi im hiu nay. Bn cnh , trongchng ny ti cng trnh by cch thc ci t v thc thi chng trnh MCNP trn h iu hnhWindows thng qua cu lnh v chng trnh Visual Editor. Phin bn MCNP c s dng trongti liu ny l phin bn MCNP5.1.4.

1.1 Chng trnh MCNP

MCNP (Monte Carlo NParticle) l chng trnh ng dng phng php Monte Carlo mphng cc qu trnh vt l ht nhn i vi neutron, photon, electron (cc qu trnh phn r htnhn, tng tc gia cc tia bc x vi vt cht, thng lng neutron,...). Chng trnh ban uc pht trin bi nhm Monte Carlo v hin nay l nhm Transport Methods Group (nhmXTM ) ca phng Applied Theoretical & Computational Physics Division (X Division) Trungtm Th nghim Quc gia Los Alamos (Los Alamos National Laboratory M). Trong mi haihoc ba nm h li cho ra mt phin bn mi ca chng trnh.

Chng trnh MCNP c khong 45.000 dng lnh c vit bng FORTRAN v 1000 dng lnh C,trong c khong 400 chng trnh con (subroutine). y l mt cng c tnh ton rt mnh, cth m phng vn chuyn neutron, photon v electron, gii cc bi ton vn chuyn bc x khnggian 3 chiu, ph thuc thi gian, nng lng lin tc trong cc lnh vc t thit k l phn ngn an ton bc x, vt l y hc vi cc min nng lng neutron t 1011 MeV n 20 MeV (ivi mt s ng v c th ln n 150 MeV), photon t 1 keV n 100 GeV v electron t 1 keVn 1 GeV. Chng trnh c thit lp rt tt cho php ngi s dng xy dng cc dng hnhhc phc tp v m phng da trn cc th vin ht nhn. Chng trnh iu khin cc qu trnhtng tc bng cch gieo s ngu nhin theo quy lut thng k cho trc v m phng c thchin trn my tnh v s ln th (trial) cn thit thng rt ln.

Chng trnh MCNP c cung cp ti ngi dng thng qua Trung tm Thng tin An ton Bcx (Radiation Safety Information Computational Center RSICC) Oak Ridge, Tennessee (M)v ngn hng d liu ca C quan Nng lng Nguyn t (Nuclear Energy Agency NEA/OECD) Paris (Php). Ngy nay, ti Los Alamos c khong 250 ngi dng v trn th gii c hn 3000ngi dng trong hn 200 c s ng dng.

1.2. Lch s ca chng trnh MCNP 8

Ti Vit Nam, trong khong hn 10 nm tr li y, cc tnh ton m phng bng chng trnhMCNP c trin khai nhiu c s nghin cu nh Vin Nghin cu Ht nhn Lt, Trungtm Nghin cu & Trin khai Cng ngh Bc x TPHCM, Vin Khoa hc & K thut ht nhnH Ni, Vin Nng lng Nguyn t Vit Nam,. . . v c bit l ti B mn Vt l Ht nhn K thut Ht nhn (Trng i hc Khoa hc T nhin TPHCM) chng trnh MCNP ca vo ging dy nh l mt phn ca mn hc ng dng phn mm trong Vt l Ht nhn bc o to cao hc. Cc nghin cu ng dng MCNP ti Vit Nam ch yu tp trung vo cclnh vc nh tnh ton cho l phn ng, ph ghi nhn bc x, phn b trng liu bc x, phntch an ton che chn,...

1.2 Lch s ca chng trnh MCNP

1.2.1 Phng php Monte Carlo

Tn gi ca phng php ny c t theo tn ca mt thnh ph Monaco, ni ni ting vicc sng bc, c l l do phng php ny da vo vic gieo cc s ngu nhin. Tuy nhin vic gieos ngu nhin gii cc bi ton xut hin t rt lu ri.

Vo khong th k 18, ngi ta thc hin cc th nghim m trong h nm mt cy kim trongmt mt cch ngu nhin ln trn mt mt phng c k cc ng thng song song v suy ragi tr ca pi t vic m s im giao nhau gia cc cy kim v cc ng thng1.

Trong khong nhng nm 1930, Enrico Fermi s dng phng php Monte Carlo gii quytcc bi ton khuch tn neutron nhng khng xut bn bt c cng trnh no v vn ny.

Phng php Monte Carlo ch c thc s s dng nh mt cng c nghin cu khi vic ch tobom nguyn t c nghin cu trong sut thi k chin tranh th gii ln th hai. Cng vic nyi hi phi c s m phng trc tip cc vn mang tnh xc sut lin quan n s khuch tnneutron ngu nhin trong vt liu phn hch. Nm 1946, cc nh vt l ti Phng th nghim LosAlamos, dn u bi Nicholas Metropolis, John von Neumann v Stanislaw Ulam, xut vic

1c bit n vi tn gi Bi ton cy kim Buffon (Buffons needle problem), trong bi ton ny ngi ta thngu nhin cc cy kim c chiu di l ln trn mt mt sn c k cc ng thng song song cch nhau mt on t(vi l t) v tnh xem xc sut ca cy kim ct ngang ng thng l bao nhiu.Gi x l khong cch t tm cy kim n ng thng gn nht v l gc to bi cy kim v ng thng, ta

c hm mt xc sut (probability density function) ca x v nh sau

0 x t2

:2

tdx

0 theta pi2

:2

pid

Hm mt xc sut kp hp (joint probability density function)

4

tpidxd

iu kin cy kim ct ngang ng thng x l2

sin , xc sut cy kim ct ngang ng thng s thu c

bng cch ly tch phn hm mt xc sut kt hp pi/20

(l/2) sin 0

4

tpidxd =

2l

tpi

Ga s ta gieo N kim, trong c n kim ct cc ng thng

n

N=

2l

tpi

pi =2lN

tn

9 CHNG 1. GII THIU V MCNP

Hnh 1.1: Minh ha bi ton tnh s pi vi cc cy kim v ng thng song song

ng dng cc phng php s ngu nhin trong tnh ton vn chuyn neutron trong cc vt liuphn hch. Do tnh cht b mt ca cng vic, d n ny c t mt danh Monte Carlov y cng chnh l tn gi ca phng php ny v sau. Cc tnh ton Monte Carlo c vitbi John von Neumann v chy trn my tnh in t a mc ch u tin trn th gii ENIAC(Electronic Numerical Integrator And Computer) (Hnh 1.2).

Hnh 1.2: My tnh in t ENIAC c t ti BRL building 328

Cc tng ca phng php ny c pht trin v h thng ha nh vo cc cng trnh caHarris v Herman Kahn vo nm 1948. Cng vo khong nm 1948, Fermi, Metropolis v Ulamthu c c lng ca phng php Monte Carlo cho tr ring ca phng trnh Schrodinger.

Mi cho n nhng nm 1970, cc l thuyt mi pht trin v phc tp ca tnh ton bt ucung cp cc tnh ton c chnh xc cao hn, nhng c s l lun thuyt phc cho vic s dngv pht trin phng php Monte Carlo. Ngy nay, cng vi s pht trin ca my tnh in t,cc phng php Monte Carlo ngy cng c p dng rng ri trong cc nghin cu khoa hc vcng ngh, c bit l cng ngh ht nhn.

1.2.2 MCNP

Ti Trung tm Th nghim Quc gia Los Alamos, phng php Monte Carlo c bt u ngdng t nhng nm 1940, v chng trnh MCNP l mt trong nhng sn phm ra i t vic ngdng ny. Tin thn ca n l mt chng trnh Monte Carlo vn chuyn ht mang tn l MCSc pht trin ti Los Alamos t nm 1963. Tip theo MCS l MCN c vit nm 1965. Chngtrnh MCN c th gii bi ton cc neutron tng tc vi vt cht hnh hc 3 chiu v s dng ccth vin s liu vt l.

1.2. Lch s ca chng trnh MCNP 10

MCN c hp nht vi MCG (chng trnh Monte Carlo gamma x l cc photon nng lngcao) nm 1973 to ra MCNG chng trnh ghp cp neutron-gamma. Nm 1973, MCNG chp nht vi MCP (chng trnh Monte Carlo photon vi x l vt l chi tit n nng lng1 keV) m phng chnh xc cc tng tc neutron-photon v cho ra i chng trnh vi tngi MCNP (c ngha l Monte Carlo neutron-photon). Mi cho n nm 1990, khi qu trnh vnchuyn electron c thm vo, MCNP mi mang ngha Monte Carlo N-Particle nh chng tabit ngy nay.

Cc phin bn ca MCNP

MCNP3 c vit li hon ton v cng b nm 1983 thng qua Radiation Safety InformationComputational Center (RSICC). y l phin bn u tin c phn phi quc t, cc phinbn tip theo MCNP3A v 3B ln lt c ra i ti Phng Th nghim Quc gia Los Almostrong sut thp nin 1980.

MCNP4 c cng b nm 1990, cho php vic m phng c thc hin trn cc cu trcmy tnh song song. MCNP4 cng b sung vn chuyn electron thng qua vic tch hpgi ITS (Integrated TIGER Series).

MCNP4A c cng b nm 1993 vi cc im ni bt l phn tch thng k c nngcao, kh nng phn phi chy song song trn cc cm my (cluster) hay my trm(workstation).

MCNP4B c cng b nm 1997 vi vic tng cng cc qu trnh vt l ca photon va vo cc ton t vi phn nhiu lon,...

MCNP4C c cng b nm 2000 vi cc tnh nng ca electron c cp nht, cc x lcng hng gn nhau (unresolved resonance), hnh hc khi (macrobody),...

MCNP4C2 c b sung thm cc c trng mi nh hiu ng quang ht nhn (photonucleareffect) v cc ci tin ca s trng s (weight window), c cng b nm 2001.

MCNP5 c vit li hon ton bng Fortran 90 v cng b vo nm 2003 cng vi vic cpnht cc qu trnh tng tc mi chng hn nh cc hin tng va chm quang ht nhn(photonuclear collision physics), hiu ng gin n Doppler (Doppler broadenning),... MCNP5cng tng cng kh nng tnh ton song song thng qua vic h tr OpenMP v MPI.

Ngoi ra cn c thm phin bn MCNPX c pht trin ban u t d n Accelerator Productionof Tritium (APT)vi cc mc nng lng v chng loi ht c m rng

Phin bn MCNPX u tin c pht hnh rng ri l MCNPX2.1.5 vo nm 1999, datrn phin bn MCNP4B.

Phin bn MCNPX2.4.0 pht hnh vo nm 2002 da trn MCNP4C, c trn h iu hnhWindows, h tr Fortran 90.

MCNPX2.5.0 vo nm 2005 c ti 34 loi ht, cc phin bn tip theo MCNPX2.6.0 phthnh nm 2008 v MCNPX2.7.0 nm 2011.

T nm 2006 bt u c nhng n lc nhm hp nht hai chng trnh MCNP v MCNPX vivic a MCNPX2.6.B vo trong MCNP5. Kt qu ca nhng n lc ny l phin bn MCNP61.0 ra i vo thng 5/2013.

1.2.3 MCNPX

MCNPX l mt phin bn m rng ca MCNP c pht trin t Phng Th nghim Quc giaLos Alamos (M) vi kh nng m phng c nhiu loi ht hn. MCNPX c pht trin nhl mt s kt hp ca MCNP v h thng ngn ng lp trnh LAHET (LCS) vo nm 1994.

11 CHNG 1. GII THIU V MCNP

Chng trnh MCNPX c th m phng c vn chuyn ca 34 loi ht: neutron, proton, electron,photon, 5 loi ht lepton, 11 loi ht baryon, 11 loi ht meson v bn loi ht ion nh (deuteron,triton, helium-3 v alpha) lin tc v nng lng v hng. Chng trnh cho php x l chuynv dng hnh hc 3 chiu ca vt cht trong cc b mt s cp hay th cp, hnh xuyn, dng li.N s dng d liu tit din lin tc vi cc m hnh vt l cho nng lng m rng trn 150 MeV.Bng 1.1 lit k cc loi ht c m phng bi MCNPX. Trong trng hp khai bo cc phnht th ta t du tr () pha trc k hiu ht.

Bng 1.1: Cc loi ht c m phng trong MCNPX

IPT Loi ht K hiu Khi lng Ngng nng Thi gian(MeV) lng (MeV) sng (s)

Cc ht trong MCNP1 neutron N 939.5656 0.0 887.01 anti-neutron N 939.5656 0.0 887.02 photon P 0.0 0.001 3 electron E 0.511 0.001 3 positron E 0.511 0.001

Lepton4 muon | 105.6584 0.1126 2.197 1064 anti-muon | 105.6584 0.1126 2.197 1065 tau * 1777.1 1.894 2.92 10136 electron neutrino U 0.0 0.0 7 muon neutrino V 0.0 0.0 8 tau neutrino W 0.0 0.0

Baryon9 proton H 938.2723 1.0 9 anti-proton H 938.2723 1.0 10 lambda0 l 1115.684 1.0 2.63 101011 sigma+ + 1189.37 1.2676 7.99 101112 sigma 1197.436 1.2676 1.479 101013 cascade0 X 1314.9 1.0 2.9 101014 cascade Y 1321.32 1.4082 1.64 101015 omega O 1672.45 1.7825 8.22 101116 lambda+c C 2285.0 2.4353 2.06 101317 cascade+c ! 2465.1 2.6273 3.5 101318 cascadec ! 2470.3 1.0 9.8 101419 lambda+b R 5641 1.0 1.07 1012

Meson20 pion+ / 139.57 0.1488 2.6 10820 pion / 139.57 0.1488 2.6 10821 pion0 Z 134.9764 0.0 8.4 101722 kaon+ K 493.677 0.5261 1.24 10822 kaon K 493.677 0.5261 1.24 10823 K0 short % 497.672 0.000001 0.89 101024 K0 long 497.672 0.000001 5.17 10825 D+ G 1869.3 1.9923 1.05 101226 D @ 1864.5 1.0 4.15 101327 D+s F 1968.5 2.098 4.67 101328 B+ G 5278.7 5.626 1.54 101229 B0 B 5279.0 1.0 1.5 1012

1.3. Cch thc ci t chng trnh MCNP 12

30 B0s Q 5375 1.0 1.34 1012Ion nh

31 deuteron D 1875.627 2.0 32 triton T 2808.951 3.0 12.3 y33 helium-3 S 2808.421 3.0 34 alpha A 3727.418 4.0

1.2.4 MCNP6

Ni mt cch n gin, MCNP6 l phin bn hp nht ca MCNP v MCNPX. Hin nay MCNP6c tt c 37 loi ht, c chia thnh cc nhm: cc ht c bn (elementary particles), cc httng hp (composite particle) hay hadrons v cc ht nhn (nuclei). Hnh 1.3 trnh by cc khongnng lng tng ng cho tng loi ht v m hnh vt l trong MCNP6.

Hnh 1.3: Bng cc loi ht, di nng lng v m hnh tng tc vt l trong MCNP6

1.3 Cch thc ci t chng trnh MCNP

Trong phn ny ti s hng dn cch ci t phin bn chng trnh MCNP5.1.4 trn h iuhnh Windows, cch thc tin hnh nh sau

M a ci t MCNP5, vo th mc MCNP\MCNP_Win\Windows_Installer, chy chngtrnh setup.exe ci chng trnh MCNP5. Bm Next gi nguyn cc mc nh.

Sau khi ci t xong chng trnh MCNP5, tr ra ngoi a, v vo trong th mcMCNP_MCNPX_Win_Data\Disk1, chy file setup.exe chy chng trnh ci t th vin choMCNP5.

hon tt vic ci t MCNP5, nu khng c thay i g th file thc thi chng trnhs mc nh nm trong C:\Program Files\LANL\MCNP5\bin, trong th mc ny nhp ichut vo vised.exe chy chng trnh MCNP5.

Cch khai bo ng dn vo th vin d liu

Trn thanh cng c, chn Data Material.

13 CHNG 1. GII THIU V MCNP

Trn thanh cng c ca Material, chn Files.

Khai bo cc ng dn ti file xsdir trong th mc MCNPDATA nh trong Hnh 1.4 richn Apply.

Hnh 1.4: Khai bo ng dn cho xsdir

1.4 Cch thc thi chng trnh MCNP

1.4.1 S dng Visual Editor

Chy chng trnh Visual Editor bng cch nhp i chut vo vised.exe trong th mcbin hoc vo Start All Programs MCNP5 VisEd.

M input file c sn bng cch vo File Open, hin th input file hoc son tho trc tiptrn editor bng cch nhp vo Input trn thanh menu (Hnh 1.5).

Hin th plot bng cch nhp vo Update Plots trn menu hoc nhp vo Update trn ccca s Vised (Hnh 1.6).

V 3D bng cch nhp vo 3D View trn menu (Hnh 1.7).

Chy chng trnh bng cch nhp vo Run trn menu.

Mt s option trn thanh cng c ca s Vised (s dng bng cch nhp vo tng ng):

Zoom: phng to hoc thu nh hnh nh bng cch nhp v ko chut trn hnh v, hoc cth c thc hin qua thanh trt Zoom out Zoom in trn ca s.

Origin: thay i gc to v hnh bng cch nhp chut vo v tr bt k trn hnh v.

Surf : hin th cc ch s mt.

Cell : hin th cc ch s cell.

Color : hin th mu.

1.4.2 S dng cu lnh trong Command Prompt

Command Prompt l mt ca s dng lnh DOS chy trn nn Windows cho php bn thchin cc dng lnh nh trong DOS. Bn cnh vic s dng Visual Editor, MCNP cn c th cthc thi thng qua vic nhp cc lnh thng qua vic s dng ng dng ny.

Cch thc thc thi MCNP trong Command Prompt nh sau:

Vo Start All Programs Accessories Command Prompt

1.4. Cch thc thi chng trnh MCNP 14

Hnh 1.5: Giao din chng trnh Visual Editor

Hnh 1.6: ha ca Visual Editor

S dng lnh cd di chuyn n a cha chng trnh MCNP.V d: cd c:\mcnp (trong trng hp th mc mcnp nm a d: th ta chuyn a bngcch g d: v bm enter)

Thc thi chng trnh MCNP bng cch g lnh mcnp (trong trng hp s dng chngtrnh MCNP5 th g lnh mcnp5)V d: mcnp inp=file1 outp=file1o runtpe=file1r mctal=filetally xsdir=xsTrong inp l tu chn khai bo tn file input, oupt l tn ca file output xut ra, runtpel tn ca file cha cc thng tin trong sut qu trnh chy chng trnh, mctal l tn cafile cha kt qu tally v xsdir l tn ca th mc cha cc tit din.

Ngoi ra, ta c th khai bo tt bng cch s dng tu chn name

15 CHNG 1. GII THIU V MCNP

Hnh 1.7: ha 3D ca Visual Editor

V d: mcnp name=file1, chng trnh s t ng chy file file1 v to ra file output, runtpebng cch thm vo cc k t o, r ngay sau tn ca file input (trong trng hp ny haifile s c tn l file1o v file1r).

Ta c th vit tt tn cc tu chn bng cch s dng k t u tin.V d: mcnp i=file1 o=file1o r=file1r hay mcnp n=file1

Trong trng hp chng ta s dng text editor son tho, file input c to ra s mcnh c ui .txt. Trong trng hp ny ta cn chuyn thnh file khng c ui m rng trckhi chy MCNP thng qua lnh copy hay ren.V d: copy file1.txt file1

Khi chy li file input c, cn xo hoc i tn cc file ouput v runtpe c to ra trc ,nu khng MCNP s t ng thay i tn output mi c to ra trnh ghi chng ln ccfile c.

Hnh 1.8: Giao din trn nn DOS ca MCNP

n gin ta c th to cc batch file (c ui .bat) cha cc dng lnh thc thi chng trnh

1.4. Cch thc thi chng trnh MCNP 16

MCNP cho DOS. Cch thc thc hin nh sau:

M trnh son tho text (notepad, wordpad).

G vo cc dng lnh thc thi MCNP, v d: mcnp n=file1 ip

Lu li file text di tn c ui .bat (v d run_mcnp.bat) vo trong th mc c chaMCNP.

Nhp i chut vo file va to chy chng trnh, nu mun sa i dng lnh trong file,ch cn m file vi trnh son tho text v chnh sa.

Mt s tu chn khc Bn cnh cc tu chn khai bo input, output file, chng ta cn sdng mt s tu chn iu khin qu trnh thc thi MCNP:

i c v kim tra li trong input file.p v hnh hc m t trong input file.x cc bng tit din tng tc.r chy bi ton vn chuyn ht.z v cc kt qu tally t file RUNTPE hay MCTAL (xem Phn 3.4).

v cc tit din trong input file.

Cc tu chn ny c th c kt hp vi nhau chng hn nh ip (v hnh hc v kim tra litrong input file), ixz (c input file, c v v cc tit din tng tc), ...

V d: mcnp n=file1 ip (c file1 v v hnh hc m t trong file ).

Cch v hnh hc m t trong input Mt s lnh v hnh hc trong MCNP

origin x y z chn gc to , mc nh 0 0 0basis x1 y1 z1 x2 y2 z2 chn mt phng v, mc nh 0 1 0 0 0 1extent h v thang chia v, mc nh 100 100

(nu khng khai bo v th mc nh v = h)label s c des ghi cc ch s ln hnh v

V d: or 0 -2 10 (chn gc to v hnh ti (0,-2,10), gc to lun nm gia hnh v).

Hnh 1.9: ha trn nn DOS ca MCNP

2C s phng php Monte Carlo

MCNP l mt chng trnh m phng vn chuyn ht bng phng php Monte Carlo, do mts kin thc c s v phng php ny l cn thit c th hiu c cch thc hot ng cngnh phn tch cc kt qu thu c sau khi thc thi chng trnh.

Khi lm vic vi chng trnh MCNP, hot ng ca ngi dng ch yu l hai khu: cung cpd liu u vo v phn tch d liu u ra. i vi vic cung cp d liu u vo, mt trongnhng thng tin quan trng cn cung cp chnh l cch thc ly mu phn b (phn b v trngun, phn b nng lng, phn b xc sut pht,...). Trong chng ny, ti s trnh by mt snt chnh v s ngu nhin, phn b xc sut v cch ly mu phn b bng phng php MonteCarlo. Cn i vi d liu u ra, vic hiu r cch thc c lng kt qu m phng Monte Carlol cn thit c th nh gi cc kt qu thu c t chng trnh. Do phn cui ca chngs c dnh cho vic trnh by cc khi nim c lng mu v nh gi chnh xc ca ktqu c lng thu c.

2.1 C s ca phng php Monte Carlo

Phng php Monte Carlo c xy dng da trn nn tng

Cc s ngu nhin (random numbers): y l nn tng quan trng, gp phn hnh thnhnn thng hiu ca phng php. Cc s ngu nhin khng ch c s dng trong vicm phng li cc hin tng ngu nhin xy ra trong thc t m cn c s dng lymu ngu nhin ca mt phn b no , chng hn nh trong tnh ton cc tch phn s(numerical integration).

Lut s ln (law of large numbers): lut ny m bo rng khi ta chn ngu nhin cc gi tr(mu th) trong mt dy cc gi tr (qun th), kch thc dy mu th cng ln th cc ctrng thng k (trung bnh, phng sai,...) ca mu th cng gn vi cc c trng thngk ca qun th. Lut s ln rt quan trng i vi phng php Monte Carlo v n m bocho s n nh ca cc gi tr trung bnh ca cc bin ngu nhin khi s php th ln.

nh l gii hn trung tm (central limit theorem): nh l ny pht biu rng di mt siu kin c th, trung bnh s hc ca mt lng ln cc php lp ca cc bin ngunhin c lp (independent random variables) s c xp x theo phn b chun (normaldistrbution). Do phng php Monte Carlo l mt chui cc php th c lp li nn nhl gii hn trung tm s gip chng ta d dng xp x c trung bnh v phng sai ca cckt qu thu c t phng php.

2.2. S ngu nhin 18

Cc thnh phn chnh ca phng php m phng Monte Carlo (Hnh 2.1) gm c

Hm mt xc sut (probability density function PDF): mt h vt l (hay ton hc)phi c m t bng mt b cc PDF.

Ngun pht s ngu nhin (random number generator RNG): mt ngun pht cc s ngunhin ng nht phn b trong khong n v.

Quy lut ly mu (sampling rule): m t vic ly mu t mt hm phn b c th.

Ghi nhn (scoring hay tallying): d liu u ra phi c tch lu trong cc khong gi trca i lng cn quan tm.

c lng sai s (error estimation): c lng sai s thng k (phng sai) theo s php thv theo i lng quan tm.

Cc k thut gim phng sai (variance reduction technique): cc phng php nhm gimphng sai ca p s c c lng gim thi gian tnh ton ca m phng MonteCarlo.

Song song ho (parallelization) v vector ho (vectorization): cc thut ton cho php phngphp Monte Carlo c thc thi mt cch hiu qu trn mt cu trc my tnh hiu nngcao (high-performance).

Hnh 2.1: Nguyn tc hot ng ca phng php Monte Carlo

2.2 S ngu nhin

Trong phng php m phng Monte Carlo, chng ta khng th no thiu c cc s ngu nhin.Cc s ngu nhin c mt trong cc hin tng t nhin nh nhiu lon in t, phn r phngx,... gii mt bi ton bng phng php Monte Carlo iu quan trng nht l chng ta cnto ra cc s ngu nhin phn b u (uniform distribution) trn khong (0,1).

2.2.1 Cc loi s ngu nhin

C 3 loi s ngu nhin chnh

S ngu nhin thc (real random number): cc hin tng ngu nhin trong t nhin.

S gi ngu nhin (pseudo-random number): cc dy s xc nh m n vt qua c cckim tra v tnh ngu nhin.

S gn ngu nhin (quasi-random number): cc im c s phn b tt (c s khng nhtqun thp).

19 CHNG 2. C S PHNG PHP MONTE CARLO

2.2.2 Nhng iu cn lu khi m phng s ngu nhin

C hai iu chng ta cn lu khi m phng cc s ngu nhin

My tnh khng th to ra cc dy s ngu nhin tht s m ch l cc s gi ngu nhin.

Bn thn cc s khng phi l ngu nhin m ch c dy s mi c th c xem l ngunhin

Mt dy s ngu nhin tt phi hi t y cc yu t sau y

Chu k lp li phi di tc l vic gieo s ngu nhin phi to ra c nhiu s trc khi lpli dy s c ca n cho khng c phn no ca dy b trng trong tnh ton.

Cc s c to ra phi hng ti phn b u, tc l mt dy s bt k gm vi trm sphi hng ti phn b ng nht trong ton vng kho st.

Cc s khng tng quan vi nhau, tc l cc s trong dy phi c lp v mt thng k vicc s trc n.

Thut ton phi truy xut nhanh, tc l thi gian my tnh to ra s ngu nhin phi nh

Cc s gi ngu nhin trong phng php Monte Carlo ch cn t ra mc ngu nhin, nghal tun theo phn b u hay theo phn b nh trc, khi s lng ca chng ln.

2.2.3 Phng php to s ngu nhin

to c mt dy s ngu nhin, chng ta c th dng nhiu phng php khc nhau. yti xin trnh by mt phng php c dng ph bin nht. Phng php ny c s dngtrong nhiu ngn ng lp trnh, chng hn nh C, Fortran,... chnh l phng php ng dtuyn tnh (linear congruential generator). Thut ton ca phng php ny nh sau

x0 = s gieo ban u, l s nguyn l < M (2.1)xn = axn1 + cmodM (2.2)n = xn/M (2.3)

y a v c l cc s nguyn v M thng l mt s nguyn c gi tr ln, s gieo ban u x0 cth c t bi ngi dng trong qu trnh tnh ton.

Thc s y khng phi l mt thut ton to s ngu nhin tt nht nhng u im ca thutton ny l n gin, d s dng, tnh ton nhanh v dy s ngu nhin do n to ra l kh tt.

Ta c th thy rng trong dy s c to ra bi phng php ny mi s ch c th xut hin duynht mt ln trc khi dy b lp li. Do chu k ca phng php ng d tuyn tnh (chiu dica dy s cho n khi s u tin b lp li) M . c ngha l trong trng hp tt nht th xns ly tt c cc gi tr c trong on [0,M 1]. i vi phng php ng d tuyn tnh th chuk cc i s ph thuc vo di k t ca my tnh. V d: chu k ln nht i vi my 16 bit c chnh xc n (single precision) l 216 = 65536 i v vi chnh xc kp (double precision)l 232 = 4.29 109.

2.3 Phn b xc sut

2.3.1 Bin ngu nhin

Cc bin ngu nhin (random variable hay stochastic variable) l cc bin m gi tr m n nhnc mt cch ngu nhin. Mt bin ngu nhin c th bao gm mt tp hp cc gi tr m migi tr i km vi mt xc sut (probability) trong trng hp gi tr ri rc hoc mt hm mt xc sut (probability density function) trong trng hp gi tr lin tc (xem Hnh 2.2).

2.3. Phn b xc sut 20

Hnh 2.2: Minh ha phn b xc sut ca bin ri rc (tri) v lin tc (phi)

Gi s ta tin hnh php o mt bin ngu nhin x (trong thc nghim) hay gieo ngu nhin gitr ca bin ny (trong phng php Monte Carlo) N ln, ta s thu c mt tp hp cc gi trca bin nh sau {x1, x2, . . . , xn}.

Gi tr k vng (expected value hay expectation) hay cn gi l gi tr trung bnh (mean) cabin x (thng c k hiu l ) chnh l gi tr m ta k vng s thu c khi lp li N lnphp o vi N tin n v cc. Hay ni mt cch khc, gi tr k vng chnh l trung bnh ctrng s (weight average) ca tt c cc gi tr kh d (possible values) ca bin x, trng s cdng y chnh l xc sut fi tng ng vi cc gi tr ca bin.

E(x) =

Ni=1

xifi

Ni=1

fi

(2.4)

Phng sai (variance) c dng nh gi mc phn tn ca tp hp gi tr thu c,gi tr ca phng sai bng 0 c ngha l tt c cc gi tr ca tp hp l ng nht. Phng saithng c k hiu l 2.

V ar(x) = E[(x E(x))2

]=

Ni=1

(xi )2fiNi=1

fi

= E(x2) [E(x)]2 (2.5)

lch chun (standard deviation) k hiu l cn bc hai ca phng sai, c cng th nguynvi gi tr ca bin x nn thng c dng km vi gi tr trung bnh biu din kt qu thuc.

2.3.2 Hm mt xc sut

Hm mt xc sut (Probability Density Function PDF)1 ca mt bin ngu nhin lin tc lmt hm m t kh nng (xc sut) nhn mt gi tr ca bin .

Hm mt xc sut c xem nh l chun ha khi

+

f(x)dx = 1 (2.6)

1i khi cn c gi l hm phn b xc sut (probability distribution function) hay hm xc sut (probabilityfunction), tuy nhin khng c quy nh no thng nht cho cc tn gi. Hm xc sut i khi cn c dng chhm mt tch ly (cumulative distribution function)

21 CHNG 2. C S PHNG PHP MONTE CARLO

Hm mt tch ly (cumulative density function hay cumulative distribution function CDF)c tnh nh l tch phn ca hm mt xc sut (Hnh 2.3)

F (x) =

x

f(t)dt (2.7)

Hnh 2.3: So snh hai hm PDF v CDF, gi tr ca hm CDF ti v tr x chnh l tch phn cahm PDF t n x

Trong trng hp ta c hm g(x) vi x l bin ngu nhin vi mt f(x), gi tr trung bnh cahm g(x) s c tnh theo cng thc

E[g(x)] =

+

g(x)f(x)dx E[g(x)] =Nk=1

gkfk (2.8)

2.3.3 Lut s ln

Lut s ln (Law of Large Numbers LLN) m t kt qu thu c khi thc hin php o mt sln ln, theo gi tr trung bnh ca cc kt qu thu c s cng gn vi gi tr k vng khi sphp o cng ln (v d trong Hnh 2.4). Lut s ln c vai tr quan trng v n m bo cho sn nh v mt lu di ca gi tr trung bnh ca cc s kin ngu nhin.

2.3.4 nh l gii hn trung tm

Theo nh l gii hn trung tm (Central Limit Theorem CLT), tng ca cc bin ngu nhinc lp (independent random variable) v phn phi ng nht (identically distribution) theo cngmt phn phi xc sut, s hi t v mt bin ngu nhin no (Hnh 2.5).

Gi s ta c N tp hp cc bin ngu nhin c lp Xi (X1, X2, ..., XN ), mi tp hp u c phnb tng minh (arbitrary) vi xc sut P (x1, x2, ..., xN ) c tr trung bnh i, phng sai hu hn

2.3. Phn b xc sut 22

Hnh 2.4: Minh ha Lut s ln khi thc hin th nghim tung ng xu, th biu din t l phntrm xut hin mt nga (head) nhiu hn mt sp (tail) theo s ln tung

2i tng ng. Khi i lng c dng chun ha

Xnorm =

Ni=1

xi Ni=1

iNi=1

2i

(2.9)

s c mt hm phn b tch ly gii hn xp x theo phn b chun.

Hnh 2.5: Minh ha nh l gii hn trung tm, trung bnh ca cc phn b t X1 n X5 s cdng phn b chun

Mt cch n gin hn, nh l gii hn trung tm c th hiu nh l phn b ca vic ly mungu nhin s tin v phn b chun khi kch c mu c tng ln, d cho phn b thc hay cngi l phn b qun th (population) ca bin khng phi l phn b chun.

Lu : in kin ca nh l gii hn trung tm l c tr trung bnh v phng sai ca phn bphi tn ti hu hn.

2.3.5 Ly mu phn b

Phn b mu (sampling distribution) hay cn gi l phn b mu hu hn (finite-sample distribu-tion) l phn b xc sut thng k ca cc gi tr trong mu ngu nhin c ly ra t mt phnb qun th. Phn b mu ph thuc vo cc yu t nh phn b ca bn thn qun th, cchthc ly mu, kch c mu,...

23 CHNG 2. C S PHNG PHP MONTE CARLO

Gi s ta c mt qun th c phn b chun vi tr trung bnh v phng sai 2, c k hiu lN(, 2). Sau chng ta ly cc mu c kch thc n cho trc t qun th ny v tnh ton ccgi tr trung bnh xi cho mi mu c ly, cc gi tr ny c gi l cc gi tr trung bnh camu (sample mean) v phn b ca cc gi tr trung bnh ny c gi l phn b ca cc gi trtrung bnh mu. Phn b ny s tun theo phn b chun N(, 2/n)2 do phn b qun th lphn b chun (mc d theo nh lut gii hn trung tm, nu kch thc mu n ln, phn btrung bnh mu vn c th c xp x theo phn b chun d cho phn b qun th c l phnb chun hay khng). Trong trng hp kch thc mu nh, phn b trung bnh mu c chotrong Bng 2.1.

lch chun ca phn b trung bnh mu c gi l sai s chun (standard error)3, trong trnghp cc mu c lp vi nhau ta c

x =n

(2.10)

vi l lch chun ca qun th v n l kch c mu.

Bng 2.1: Mt s v d phn b mu ngu nhin c ly t qun th

Phn b qun th Phn b mu

Normal(, 2) X Normal(,2

n

)Bernoulli(p) nX Binomial(n, p)

Normal(1, 21) v Normal(2, 22) X1 X2 Normal

(1 2,

21n

+22n

)

2.3.6 c lng mu

Trung bnh mu (sample mean) l gi tr c lng ca trung bnh qun th (population mean) da trn mt mu c chn ngu nhin t qun th ny. c lng trung bnh ca mu tas dng cng thc

x =1

N

Ni=1

xi (2.11)

vi xi l cc gi tr trong mu v N l kch thc mu4.

Gi tr x ny s phn b quanh gi tr trung bnh ca qun th vi

x = E(x) = (2.12)

2x = V ar(x) =2

N(2.13)

D cho phn b ca x l ng nht vi gi tr trung bnh ca qun th nhng phng sai s nhhn nhiu nu kch thc ca mu l ln.

2Lu phn b chun ny khc vi phn b chun ca qun th3Cn phn bit vi lch chun ca qun th vn c gi vi tn standard deviation4Gi tr x cn c xem l trung bnh khng trng s ca cc gi tr, ngc li vi l trung bnh c trng s,

xem cng thc (2.4)

2.3. Phn b xc sut 24

Phng sai mu (sample variance) thng c k hiu l S2 hay S2N c xc nh bi cngthc5

S2 =1

N

Ni=1

(xi x)2 (2.14)

Nu ta xem x nh l mt c lng ca trung bnh qun th vi

E(x) = (2.15)

th S2 cng c xem nh l mt c lng ca phng sai qun th , tuy nhin y li l mtc lng b chch (biased estimator)

E[S2] = E

[1

N

Ni=1

(xi x)2]

= E

[1

N

Ni=1

((xi ) (x ))2]

= E

[1

N

Ni=1

(xi )2 (x )2]

= 2 E [(x )2] = N 1N

2 < 2 (2.16)

iu ny c ngha l E(S2) 6= 2, k vng ca S2 khng phi l phng sai 2 ca qun th6. hiu chnh cho s chch ny, chng ta thay th S2 bng

s2 =1

N 1Ni=1

(xi x)2 (2.17)

T s gia phng sai cha hiu chnh trn phng sai hiu chnh (S/s)2 = N/(N 1) c gil h s hiu chnh Bessel (Bessels correction).

2.3.7 chnh xc ca c lng

Sai s (error) hay cn gi l bt nh (uncertainty) th hin khng chnh xc ca mtc lng so vi gi tr thc ca n. Sai s thng hay c chia lm hai loi l sai s ngu nhin(random error) hay cn gi l sai s thng k (statistical error) v sai s h thng (systematicerror).

2total = 2statistical +

2systematic (2.18)

Sai s ngu nhin lin quan n kch thc hu hn ca mu, trong khi sai s h thng li linquan n vic mu thhu c khng i din y cc tnh cht ca qun th (v nhiu l donh sai s thit b, con ngi,...). Sai s h thng thng kh c nh lng tuy nhin trong mts trng hp c th ta cng c th c lng c gi tr ca n.

chnh xc (accuracy) dng nh gi gn (closeness) hay chch (bias) ca gi trtrung bnh c lng so vi gi tr thc ca i lng vt l, i khi cn c m t bi sai s h

5Cn lu phn bit gia cc i lng 2 (phng sai ca qun th), 2x (phng sai ca phn b trung bnhmu) v S2 (phng sai mu)

6L do l v trung bnh mu x l mt c lng bnh phng cc tiu tuyn tnh (linear least squares) ca , gitr ca x c chn sao cho tng

(xi x)2 t gi tr nh nht. Do vy, khi a thm s hng vo trong tng, gi

tr ca tng ch c th tng ln, c bit khi 6= x ta c

1

N

Ni=1

(xi x)2 < 1N

Ni=1

(xi )2

25 CHNG 2. C S PHNG PHP MONTE CARLO

thng (systematic error). Trong Monte Carlo, ta khng th c lng chnh xc ny mt cchtrc tip c.

Cc nhn t chnh nh hng ln chnh xc gm c

chnh xc ca code (m hnh vt l,...)

M hnh bi ton (hnh hc, ngun,...)

Sai s c nguyn nhn t ngi dng

tp trung (precision)7 l bt nh ca ca cc thng ging thng k trong vic ly mu.Mi tng quan gia chnh xc v tp trung c mnh ha trong Hnh 2.6 v Hnh 2.7.

Hnh 2.6: Minh ha chnh xc v tp trung ca mt phn b c lng

Hnh 2.7: Minh ha cc mc ca chnh xc v tp trung

2.3.8 Khong tin cy

Khong tin cy (Confidence Interval CI) l mt khong gi tr m c th cha trong n gi trca tham s cn c lng (unknown parameter). rng ca khong tin cy cho chng ta thngtin v bt nh ca php tnh c lng tham s8.

7Trong thc t, nhiu khi precision cng c gi l chnh xc, tuy nhin n d b ln ln vi accuracy nn tis gi precision l tp trung phn bit.

8Nhiu ngi cho rng xc sut c cho bi khong tin cy chnh l xc sut m gi tr trung bnh ca qun thri vo trong khong tin cy , suy ngh ny l khng ng. Gi tr trung bnh ca qun th l mt hng s, nkhng thay i, do xc sut gi tr trung bnh qun th ri vo trong khong tin cy ch l mt trong 2 gi tr0 hoc 1.

2.3. Phn b xc sut 26

Cc khong tin cy thng dng i vi phn b chun nh sau (Hnh 2.8)9

P (xn 1 < < xn + 1) = 68% (2.19)P (xn 2 < < xn + 2) = 95% (2.20)P (xn 3 < < xn + 3) = 99% (2.21)

Hnh 2.8: Minh ha khong tin cy ca phn b chun

9Cc gi tr xc sut nh 68%, 95%, 99% c cho bi khong tin cy tnh theo ch ng trong trng hpphn b mt chiu (1-dimension)

3Cu trc chng trnh MCNP

Trong chng ny chng ta s i tm hiu cc thnh phn chnh ca chng trnh MCNP nh ccth vin d liu, cc th tc thc thi, file d liu u vo (input file) v file d liu u ra (outputfile). Bn cnh , chng ta cng s c c hi tm hiu cc bc tin hnh m phng cng nhcu trc ca cc file d liu ca chng trnh MCNP.

3.1 Cch thc hot ng ca MCNP

3.1.1 Cc th tc chnh trong MCNP

MCNP c vit trn nn tng ngn ng lp trnh ANSI-Standard Fortran 90. Di y l mt sth tc (subroutine) chnh trong MCNP

IMCN khi ng

c input file (INP) v ly kch thc (PASS1).

Khi to kch thc ca cc bin (SETDAS).

c li input file (INP) ln na ly cc thng s u vo (RDPROB).

Khi ng th tc cho ngun pht ((ISOURC).

Khi ng th tc cho tally (ITALLY).

Khi ng th tc cho vt liu (STUFF) k c khi lng m cha cn ti cc file d liu.

Tnh th tch v din tch ca cell (VOLUME).

PLOT ha hnh hc.

MCNP_RANDOM to v qun l cc s ngu nhin.

XACT tnh ton tit din

c cc th vin (GETXST).

Loi b cc d liu neutron nm ngoi khong nng lng kho st trong bi ton (EXPUNG).

a vo gin n Doppler v tnh ton tit din ton phn tng ng trong trng hp nhit trong bi ton cao hn nhit ca s liu c trong th vin (BROADN).

3.1. Cch thc hot ng ca MCNP 28

Truy xut cc th vin multigroup (MGXSPT).

Truy xut cc th vin electron (XSGEN), tnh ton cc qung chy, tn x, phn b gc,...

MCRUN chy chng trnh

Pht ht t ngun (STARTP).

Tm khong cch n bin (TRACK), i qua b mt (SURFAC) vo cell k tip (NEW-CEL).

Tm tit din ton phn ca neutron (ACETOT), tn x neutron (COLIDN) v to photontng ng nu c (ACEGAM).

Tm tit din ton phn ca photon (PHOTOT), tn x photon (COLIDP) v to electrontng ng nu c (EMAKER).

S dng xp x bremsstrahlung trong trng hp khng kho st electron (TTBR).

Theo vt ca electron (ELECTR).

S dng cc tn x multigroup nu c chn (MGCOLN, MGCOLP, MGACOL).

Tnh ton cc tally detector (TALLYD) hoc DXTRAN.

Tnh ton cc tally mt, cell hoc cao xung (TALLY).

Tun t in ra cc file output, cc kt qu thng k tm thi trong qu trnh chy, cp nht cc chuk k tip trong bi ton ngng (KCALC), DXTRAN,... In kt qu thng k cui cng (SUMARY,ACTION), kt qu tally (TALLYP).

3.1.2 Cch thc m phng vn chuyn ht

Phn ny trnh by mt cch s lc qu trnh m phng vn chuyn ht cho bi ton vn chuynneutron/photon/electron:

u tin, i vi mi lch s ht, MCNP s to ra mt dy cc s ngu nhin phc v cho qutrnh tnh ton. Bin flag IPT s c gn gi tr tng ng vi loi ht ang c kho st: 1 choneutron, 2 cho photon v 3 cho electron.

K , cc th tc ngun pht tng ng s c gi (ngun c nh, ngun mt, ngun t nhngha,...). Tt c cc thng s ca ht (hng pht, v tr, nng lng, trng s,...) s c khito gi tr bng cch ly mu ngu nhin theo phn b c khai bo trong input file. Mt s kimtra s c tin hnh nhm xc nh rng ht ngun nm ng trong cell hoc mt c xc nhtrong input.

Tip theo, cc thng s ban u ca 50 lch s ht u tin s c in ra. Sau cc thng tintm tt s c ghi li (nng lng, thi gian, trng s,...). Cc thng s cn ghi nhn trong qutrnh m phng s c khi to, th tc DXTRAN s c gi (nu c s dng) to ra cc httrn mt cu.

By gi l lc qu trnh m phng vn chuyn ht bt u. i v ngun pht electron, cc electrons c kho st ring. Cn i vi cc ngun pht neutron hoc photon, im giao ca vt ccht vi cc mt bin ca cell s c tnh ton. Khong cch dng nh nht (DLS) t v tr htn mt bin ca cell s cho bit mt k tip (JSU) m ht hng ti. Khong cch n mt cuDXTRAN gn nht cng c tnh ton. Cc tit din tng tc trong cell (ICL) c tnh tonda vo cc bng s liu ca neutron v photon. Tit din ton phn c xc nh trong trnghp c s dng exponential transform, v khong cch n v tr va chm k tip cng c xcnh. di vt ca mt ht trong cell c xc nh nh l khong cch n ln va chm k tip,khong cch n mt JSU, qung ng t do trung bnh, khong cch n hnh cu DXTRAN,

29 CHNG 3. CU TRC CHNG TRNH MCNP

hoc l khong cch n ngng di nng lng. Cc tally ghi nhn vt s c tnh ton, v ccthng s mi ca ht cng s c cp nht. Nu khong cch n mt hnh cu DXTRAN cngloi bng vi di vt nh nht, ht s c kt thc. Nu ht vt qu thi gian ngng, vtcng c ngt ti . Nu ht ri khi mt hnh cu DXTRAN, bin flag ca DXTRAN s cgn gi tr 0 v qu trnh cutoff trng s s c tin hnh, ht s kt thc ti y hoc s tiptc vi trng s c tng ln. Cc hiu chnh trng s cng c thc hin trong trng hp cs dng exponential transform.

Nu di vt nh nht bng khong cch n mt bin, ht s c vn chuyn n mt JSUtrong trng hp c tally mt, v vo trong cell k tip. Lc ny, cc tnh ton mt phn x, bintun hon, phn chia hnh hc, Russian roulette s c p dng. Trong trng hp b phn chia,chng trnh s ghi nhn li vt ca tt c cc ht c phn chia v kho st ln lt tip theo.

Nu khong cch n ln va chm k tip nh hn khong cch n mt bin, hoc cc ht mangin tch n khong cch t ti ngng di ca nng lng kho st, ht s c m phng vachm. i vi neutron, cc tnh ton va chm s xc nh loi ht nhn bia tham gia vo va chm,ly mu vn tc nhn bia trong trng hp tng tc vi kh t do chuyn ng nhit, ghi nhncc photon to ra (ACEGAM), xt xem hiu ng bt neutron l khng hay c trng s, x l ccva chm nhit theo S(, ), xt tn x n hi hay khng n hi. i vi bi ton ngng, ccsn phm phn hch s c lu li cho cc tnh ton tip theo. Cc thng s ca ht to ra trongva chm (nng lng, hng bay,...) cng s c lu li. Cc va chm c s tham gia ca nhiuht s c x l ring r.

Cc tnh ton va chm ca photon cng tng t nh ca neutron, bao gm c m hnh vt ln gin ln chi tit. Cc m hnh vt l n gin ch bao gm cc tng tc ca photon vi ccelectron t do (khng tnh cc hiu ng lin kt ca electron vi nhn). Cn m hnh vt l chi titc bao gm c cc tha s dng (form factor) v hiu ng lin kt ca electron trong qu trnh tnxa Compton, bn cnh cn c thm cc hiu ng tn x kt hp (Thomson) v s pht hunhquang theo sau hiu ng quang in. Phin bn MCNP5 cn c thm cc hiu ng quang ht nhn(photonuclear), cc ht th cp to ra t phn ng quang ht nhn c ly mu theo cng cchthc vi va chm neutron khng n hi. Cc electron to ra do tn x Compton, to cp v hiung quan in c xem nh li nng lng hon ton ti ch (nu IDES=1 trong PHYS card)hoc xp x pht bc x hm (nu IDES=0) hoc c kho st vn chuyn (nu mode E c sdng v IDES=0).

Sau khi ht qua mt bin hoc sau khi qu trnh va chm c kho st, ht s tip tc ctnh khong cch n mt bin k tip v c nh th tip din. Khi ht b mt trong qu trnh vachm hoc trong cc qu trnh tnh ton gim phng sai, chng trnh s kim tra xem c cnht th cp no c to ra trong qu trnh m phng ht hay khng, nu khng cn th lchs ht s kt thc. Cc thng tin s c tng hp v a vo tally kt qu, cc bng thng k.

Cui mi lch s ht, chng trnh s kim tra cc iu kin kt thc (s lch s ht, thi gian chychng trnh,...) c tha hay cha. Nu tha, MCRUN s kt thc v kt qu s c in ra.

3.2 D liu ht nhn v phn ng ca MCNP

3.2.1 Cc th vin d liu c s dng

MCNP s dng cc th vin s liu ht nhn v nguyn t nng lng lin tc. Cc ngun cungcp d liu ht nhn ch yu cho MCNP gm c

The Evaluated Nuclear Data File (ENDF)

The Evaluated Nuclear Data Library (ENDL)

The Activation Library (ACTL)

3.2. D liu ht nhn v phn ng ca MCNP 30

Applied Nuclear Science (T2) Group ti Phng Th nghim Los Alamos.Cc d liu ht nhn c x l theo nh dng thch hp i vi MCNP bng chng trnh NJOY(https://t2.lanl.gov/nis/codes/NJOY12/index.html).

3.2.2 Cc bng d liu

Cc bng s liu ht nhn c cho i vi cc tng tc neutron, cc tng tc photon v cctng tc photon c to ra do neutron, php o liu hay kch hot neutron v tn x nhitS(, ).

C hn 500 bng d liu tng tc neutron kh d cho khong 100 ng v v nguyn t khc nhau,c chia lm 9 nhm: neutron nng lng lin tc (continuous-energy neutron), neutron phn ngri rc (discrete-reaction neutron), tng tc quang nguyn t nng lng lin tc (continuous-energy photoatomic interaction), tng tc electron nng lng lin tc (continuous-energy electroninteraction), tng tc quang ht nhn nng lng lin tc (continuous- energy photonuclear in-teraction), liu neutron (neutron dosimetry), nhit S(, ) (S(, ) thermal), neutron multigroupv photoatomic multigroup.

Mi bng s liu c trong MCNP c lp danh sch trong file xsdir. Ngi dng c th la chncc bng s liu c th qua cc k hiu nhn dng duy nht i vi mi bng ZAID. Cc k hiunhn dng ny c cha s nguyn t Z, s khi A v k hiu xc nhn th vin ID.

Cc k hiu ZAID c dng ZZZAAA.nnX vi ZZZ l s hiu nguyn t (v d carbon c k hiu l006), AAA (trng hp ca carbon 12C s l 012), nn l s ch ca b s liu tit din tng tc sc s dng v X l kiu d liu (v d C tng ng vi d liu tng tc vi nng lng lin tc,D tng ng vi d liu phn ng ri rc,...)1.

Mt s lu khi s dng cc bng d liu tng tc

Ni chung, ngi dng nn s dng cc bng d liu cng mi cng tt. Tuy nhin, trongmt vi trng hp, cc bng d liu mi c phc tp cao hn ng ngha vi vic i hinhiu thi gian x l hn, nu cc bn b gii hn bi kch thc hot ng ca b nh thc th s dng cc d liu c hn.

Lu v ph nng lng ca neutron khi m phng tng tc ca ht ny. i vi cc biton nng lng cao, chng ta c th s dng cc bng tng tc vi nng lng ri rc haycc bng xp x. Trong trng hp nng lng thp hay cc bi ton c s nh hng bitng tc ca neutron cc vng cng hng th li khuyn dnh cho cc bn l nn s dngcc bng nng lng lin tc.

Cc d liu ca cc bng tng tc c xy dng cc nhit c th, chng ta nn kimtra nhit ny trc khi quyt nh s dng chng cho tng bi ton c th, chng hnnh khng th s dng cc b s liu c gin n Doppler nhit 3000K cho bi ton tnh nhit phng (room temperature).

i vi bi ton vn chuyn neutron/photon, cn lu s dng cc b s liu c tnh nqu trnh to photon t neutron.

XSDIR l file lu tr thng tin ca cc bng d liu cng nh v tr ca cc bng . Ni dungca file xsdir gm ba phn

Phn u: dng u tin ca file c dng

DATAPATH =

1Trong trng hp s nguyn t Z c t hn ba ch s, ngi ta thng vit ngn li l Z hoc ZZ, v d 13027.24ythay v 013027.24y

31 CHNG 3. CU TRC CHNG TRNH MCNP

T kha DATAPATH phi bt u trong vng 5 k t u tin ca dng. Khi thc thi, chngtrnh MCNP s tm kim file xsdir v cc th vin d liu tng tc ln lt theo th t cckhai bo sau

Khai bo XSDIR = trong cu lnh thc thi chng trnh.

Khai bo DATAPATH = dng thng tin (message block) cainput file.

Th mc hin hnh.

Khai bo DATAPATH trong file xsdir.

Bin mi trng DATAPATH.

Thng tin ca tng dng khai bo bo bng d liu trong file xsdir.

Th vin c khai bo trong th tc BLOCK_DATA khi bin dch MCNP.

Phn th hai: khi lng tng i ca nguyn t (atomic weight ratio)2, phn ny c btu bng cm t atomic weight ratios trong vng 5 k t u tin ca dng. Cc dngtip theo khai bo khi lng nguyn t theo c php

ZAID AWR

vi ZAID l k hiu ca nguyn t c dng ZZAAA v AWR l khi lng tng i ca nguynt tng ng vi k hiu.

Phn cui: danh sch cc bng d liu tng tc, phn ny c bt u vi t kha direc-tory trong vng 5 k t u tin ca dng. Cc dng tip theo cung cp thng tin ca ccbng thng tc (7-11 thng tin). K hiu ZAID lun l thng tin u tin c cung cp mi dng. Nu bng d liu cn nhiu hn 1 dng m t, ta cn thm k t + cuidng tip tc dng mi. S 0 ch thng tin khng hu dng. Cc thng tin ca bngc cung cp trong xsdir bao gm

Tn ca bng character*10Khi lng tng i nguyn t realTn file3 character*8ng dn truy cp character*70Kiu file4 integera ch5 integer di bng6 integer di bn ghi7 integerS d liu mi bn ghi integerNhit 8 realThng tin flag9 character*6

2y l t s ca khi lng nguyn t chia cho khi lng neutron3L tn ca th vin cha bng d liu.4Mang hai gi tr 1 hoc 2, kiu 1 tng ng vi bng c nh dng chui (ti a 80 k t mi dng), kiu 2 tng

ng vi nh dng nh phn (binary). Kiu 2 thng c s dng hn kiu 1 do gn nh v tc truy cp nhanh,vic chuyn i t kiu 1 sang kiu 2 c thc hin thng qua chng trnh MAKXSF.

5i vi file kiu 1 th a ch l v tr dng trong file th vin m bng d liu bt u, i vi kiu 2 th lrecord number ca bn ghi u tin ca bng.

6Mt bng d liu thng thng cha hai khi thng tin, khi u tin l thng tin c trng ca bng, khi thhai l mt chui cc s. di bng l di (tnh theo k t) ca khi thng tin th hai.

7i vi kiu 1 di ny l 0, i vi kiu 2 th c ph thuc vo c trng ca b x l, n l tng di (tnhtheo bit) ca tt c d liu (entry) ng vi 1 bn ghi (record), thng thng s d liu l 512 cho mi bn ghi.

8Ch s dng cho d liu neutron, tnh theo n v MeV.9T kha ptable dng bo rng y l bng d liu nng lng lin tc cho neutron c vng cng hng gn

(unresolved resonance)

3.2. D liu ht nhn v phn ng ca MCNP 32

Cc bng d liu cho neutron cung cp cc qu trnh tng tc ca neutron vi vt cht. CcID ca bng tit din tng tc cho neutron c dng ZZZAAA.nnC cho tng tc vi nng lnglin tc v ZZZAAA.nnD cho phn ng ri rc (xem Bng G.2, MCNP Manual).

Ngi dng nn ch phn bit s khc nhau gia cc bng c ui .50C v .51C, mc d c haiu xy dng t th vin ENDF/B-V, cc bng .50C l cc bng c xy dng hon ton t dliu thc nghim, cn cc bng .51C c s dng thinned data khi m phng cho cc vng cnghng.

Cc bng d liu cho photon cung cp cc qu trnh tng tc photon vi vt cht, nguynt c Z t 1 n 94 nh tn x kt hp, tn x khng kt hp, hp th quang in vi kh nngpht bc x hunh quang v qu trnh to cp. Cc phn b gc tn x c iu chnh bng cctha s dng nguyn t v cc hm tn x khng n hi.

Cc d liu tng tc cho photon c lu trong cc th vin mcplib[nn] di dng ACE (ACompact ENDF ) v c ID dng ZZZ000.nnP10 vi nn mang cc gi tr 01 (d liu tnh n nm1982), 02 (d liu tnh n nm 1993), 03 (d liu tnh n nm 2002) v 04 (d liu tnh n nm2002 t th vin ENDF/B-VI.8) (xem Bng G.4, MCNP Manual). Cc d liu quang ht nhn(photonucleear data) c lu trong cc bng c ID ZZZAAA.nnU (xem Bng G.5, MCNP Manual).

Cc bng d liu cho electron c s dng cho c m phng vn chuyn electron ln vnchuyn photon c s dng m hnh xp x pht bc x hm (thick-target bremsstrahlung model TTB). Cc bng d liu cho tng tc electron c dng ZZZ000.nnE vi hai th vin el (.01E) vel03 (.03E).

Cc tng tc ca electron vi vt cht c Z t 1 n 94 c xy dng gm c: cc tham s nngsut hm bc x (radiative stopping power parameters), tit din pht bc x hm, ph nng lngbc x hm, nng lng nh K (K-edge), nng lng electron Auger, cc tham s ca m hnhGoudsmit-Saunderson cho xp x tn x nhiu ln (multiple scattering),... Ngoi ra th vin el03cn c b sung thm d liu cho vic tnh hiu ng mt electron (density effect calculation).

Cc bng d liu liu neutron cha cc tit din ca gn 2000 phn ng kch hot v liulng hc cho hn 400 ht nhn bia cc mc kch thch v c bn. Cc tit din ny khng cs dng cho vic m phng vn chuyn ht m c s dng nh cc hm ph thuc nng lngtrong MCNP cho vic tnh ton cc thng s chng hn nh tc phn ng,... Cc bng dliu c xy dng t cc th vin ENDF/B-V dos531 (Dosimetry Tape 531 ), dos532 (ActivationTape 532 ) v ACTL (activation cross-section library), vi ID c dng ZZZAAA.nnY ZZZAAA.nnC(xem Bng G.6, MCNP Manual).

Cc bng d liu nhit neutron cha cc s liu nhit c dng hiu chnh tn x S(, ).Cc s liu ny bao gm lin kt ha hc (phn t) v hiu ng tinh th m chng rt quan trngkhi nng lng ntron thp (t khong 4 eV tr xung). i vi nc nh v nc nng, kimloi berillium, oxit berillium, benzene, graphite, polyethylene, zirconium v hydrogen trong hydridezirconium c cc s liu nhit khc nhau. Cc bng d liu c dng XXXXXX.nnT vi XXXXXXl chui k t (vd: LWTR.01T) (xem Bng G.1, MCNP Manual).

Cc bng d liu multigroup cc d liu ny ch c dng cho cc bi ton m phng vnchuyn nhm hay kt hp (multigroup/adjoint). D cho cc d liu nng lng lin tc c chnhxc cao hn, nhng cc d liu multigroup cng rt hu dng cho cc bi ton m phng phpvn chuyn nhm hiu qu hn phng php Monte Carlo (vd: tc nhanh hn) hay cc bi tonm khng c d liu nng lng ln tc, cc bi ton m phng ht mang in gi neutron vithut ton Boltzmann-Fokker-Planck,... Ngoi ra, cc bng multigroup cng c d liu hiu ng10Tng tc ca photon vi vt cht, ngoi tr cc tng tc quang ht nhn, ch yu l vi electron nguyn t

nn gi tr ca s khi A l khng quan trng.

33 CHNG 3. CU TRC CHNG TRNH MCNP

nhit ring nn ta khng cn dng n cc d liu nhit S(, ). Cc bng ny c dng ZZZAAA.nnMcho neutron v ZZZAAA.nnG cho photon (bao gm c electron) (xem Bng G.3, MCNP Manual).

3.3 Input file

tin hnh m phng bng chng trnh MCNP, trc tin ngi dng cn phi to ra mt inputfile c cha cc thng tin cn thit ca bi ton chng hn nh: m t hnh hc, vt liu, cc ktqu cn ghi nhn, cc qu trnh vt l,... Input file ca MCNP c th hai dng: chy ln u(initiate-run) hoc chy tip tc (continue-run).

3.3.1 Cu trc input file

Initiate-run

Cu trc ca mt file input initiate-run cho MCNP nh sau

Tiu v thng tin v input file (nu cn)Cell Cards (nh ngha cc mng). . .dng trng

Surface Cards (nh ngha cc mt). . .dng trng

Data Cards (Mode Cards,Material Cards,Source Cards,Tally Cards,...). . .

Continue-run

Cu trc ca mt file input continue-run cho MCNP nh sau

Tiu v thng tin v input file (nu cn)CONTINUEData Cards (Mode Cards,Material Cards,Source Cards,Tally Cards,...). . .

Lu : chy c continue-run cn phi c hai file chnh: file khi ng (tn mc nh RUNTPE)v file input (tn mc nh INP).

3.3.2 V d cu trc input file

Hnh 3.1 trnh by v d cu trc mt file input ca MCNP, dng u tin trong input file chnh ldng tiu (c th b trng dng ny), tip theo sau l cc thnh phn chnh ca file input.Trong Hnh 3.1 c 3 khi (block) ln, l cc khi m t cell, surface v data, cc khi ny ccch nhau bi chnh xc 1 dng trng (chng trnh s bo li nu nhiu hn 1 dng trng).

Cell cards Cell l mt vng khng gian c hnh thnh bi cc mt bin (c nh nghatrong phn Surface cards). Khi mt cell c xc nh, vn quan trng l xc nh c gi trca tt c nhng im nm trong cell tng ng vi mt mt bin.

Khi mt (surface) c nh ngha, n chia khng gian thnh hai vng vi cc gi tr dng v mtng ng (xem Phn 4.1.1). Cell c hnh thnh bng cch thc hin cc ton t giao (khongtrng), hi (:) v b (#) cc vng khng gian to bi cc mt. Khi m t mt cell, cn phi chcchn rng cell c bao kn bi cc mt, nu khng chng trnh s bo li sai hnh hc.

3.3. Input file 34

Hnh 3.1: V d cu trc input file

Trong Hnh 3.2, ct u tin l ch s (tn) ca cell ; ct th hai l loi vt liu (material) c lpy trong cell ; ct th ba l mt ca vt liu, trong trng hp vt liu l 0 (chn khng) thkhng cn khai bo mt . Ct th t l nh ngha vng khng gian hnh thnh nn cell thngqua vic kt hp cc vng khng gian to nn bi cc mt, v ct cui cng l khai bo quantrng (importance) ca cell.

Chi tit v Cell cards c th c xem trong Phn 4.2.

Hnh 3.2: V d cell cards

Surface cards c s dng khai bo tt c cc mt c s dng to nn cell. Cch thckhai bo mt c m t trong Hnh 3.3, ct u tin l ch s mt (tng ng vi cc ch s cs dng trong ct th t Cell cards); ct th hai nh ngha loi mt (mt phng, mt cu, tr,ellip,...); ct cui cng l cc tham s khai bo tng ng vi loi mt .

Chi tit v Surface cards c th c xem trong Phn 4.1.

Data cards bao gm nhiu loi khai bo khc nhau (vt liu, ngun pht, chng loi ht, nnglng,...), chi tit v cc khai bo ny s c trnh by trong cc chng sau. Hnh 3.4 trnh bymt v d cho Data cards, trong c khai bo v loi vt liu s dng trong Cell cards (c hailoi vt liu l m1 v m2 tng ng vi cc ch s 1 v 2 trong ct th hai ca Cell cards), v khaibo v ngun pht cng nh phng thc ghi nhn kt qu trong qu trnh m phng.

35 CHNG 3. CU TRC CHNG TRNH MCNP

Hnh 3.3: V d surface cards

Hnh 3.4: V d data cards

3.3.3 Mt s lu khi xy dng input file

Nn dng cc trnh son tho vn bn nh notepad hoc wordpad son tho input file,khng dng cc chng trnh nh Microsoft Word.

Tn ca input file khng c vt qu 8 k t.

Dng u tin trong input file l dng ghi thng tin ca input, nu khng c thng tin th trng dng ny.

Khng c s dng phm tab to khong trng trong khi vit input, ch c s dngphm spacebar.

Trong Cell card hoc Surface card, 5 k t u tin trong mi dng c dng khai boch s ca cell hoc mt.

S k t ti a cho mi dng l 80 k t, nu vt qu th phi xung dng v dng k t& cui dng bo cho MCNP bit l thng tin vn cn tip tc dng di, hoc nukhng th dng tip theo phi trng 5 k t u tin.

K t c c t trong khong 5 k t u tin ca dng c tc dng comment c dng,MCNP s khng thc hin cc dng ny trong khi chy chng trnh.

K t $ c tc dng comment cc thng tin pha sau n.

K t # c t trong vng 5 k t u tin ca dng c cha tn card c tc dng chuynkhai bo dng dng sang khai bo dng ct.

Trong MCNP, cc n v c mc nh nh sau: nng lng (MeV), khi lng (g), khnggian (centimet), thi gian (shake = 108s), nhit (MeV), mt nguyn t (nguynt/barn-cm), mt khi lng (g/cm3), tit din (barn).

Cch vit ngn gn i vi nhng tham s lp li:

nr lp li tham s ng pha trc n ln.V d: 2 3r thay cho 2 2 2 2

3.4. Output file 36

ni thm n tham s ni suy trong khong gia hai tham s cho.V d: 1 3i 5 thay cho 1 2 3 4 5

nm nhn tham s pha trc ln n ln v ghi vo pha sau.V d: 1 3m 3m thay cho 1 3 9

nj b qua n tham s.V d: trong 1 card c 5 tham s cn khai bo, ta ch mun khai bo tham sth 3, cn cc tham s khc mc nh, ta c th vit 2j b qua hai tham su v bt u khai bo tham s th 3.

3.4 Output file

MCNP cung cp nhiu loi file d liu u ra (output) tu thuc vo tng yu cu c th. Mt sfile output c trng ca MCNP

OUTP file d liu u ra chun ca MCNP, file ny cung cp cc thng tin v qu trnh mphng cng nh cc kt qu ca n. Cc thng tin mc nh ca file OUTP gm c

Ni dung input file

Cc bng tm tt cc thng tin v cell, mt, ht ngun, cc tng tc trong qu trnh mphng (iu chnh thng qua lnh PRINT trong input file)

Cc thng tin chu k KCODE (nu c)

Cc kt qu tally

Bng kim nh thng k cc kt qu tally

...

RUNTPE file nh phn cha cc thng tin din bin ca qu trnh m phng, c s dng chy li (hay chy tip) MCNP, c iu khin bi PRDMP card (xem Phn 9.1.2).

MCTAL file ASCII cha cc kt qu tally tng ng vi ln kt xut (dump) cui cng caRUNTPE, n cng c th c c bi MPLOT (xem Phn 9.1.3) v kt qu tally trong MCNP.

Ngoi ra tu vo mc ch ca bi ton, chng ta cng c th xut ra cc file output cha nhngthng tin khc, chng hn nh

MESHTAL file kt qu mesh tally vi nh dng ASCII

RSSA file nh phn cha thng tin ngun mt c

WSSA file nh phn cha thng tin ngun mt c ghi ra

WXXA file nh phn tm (scratch file) cha thng tin ngun mt c ghi

PTRAC file cha thng tin v vt ca ht (particle track)

WWONE file cha thng tin ca s trng s nng lng hay thi gian

WWOUT file cha thng tin ca s trng s c to (file input tng ng l WWINP)

SRCTP file nh phn cha thng tin phn b ngun KCODE

PLOTM.PS file ho postscript

4nh ngha hnh hc

Hnh hc c th hin trong MCNP l hnh hc c cu hnh 3 chiu tu . MCNP x l cchnh hc trong h to Descartes. Hnh hc trong MCNP c m t thng qua cc cell card vsurface card.

S dng cc mt bin c xc nh trn cc cell card v surface card, MCNP theo di s chuynng ca cc ht qua cc hnh hc, tnh ton cc ch giao nhau ca cc qu o vt vi cc mtbin v tm khong cch dng nh nht ca cc ch giao. Nu khong cch ti ln va chm k tipln hn khong cch nh nht, ht s ri khi cell ang . Sau , ti im giao thu c trn bmt, MCNP s xc nh cell k tip theo m ht s vo bng cch kim tra gi tr ca im giao(m hoc dng) i vi mi mt c lit k trong cell. Da vo kt qu , MCNP tm c cellng pha bn kia v tip tc qu trnh vn chuyn.

4.1 Surface Cards

4.1.1 Cc mt c nh ngha bi phng trnh

to ra cc vng khng gian hnh hc phc v cho vic m phng, MCNP cung cp mt s ccdng mt c bn chng hn nh mt phng, mt cu, mt tr, ... (c tt c gn 30 loi mt cbn). Cc khi hnh hc m phng c to thnh bng cch kt hp cc vng khng gian giacc mt vi nhau thng qua cc ton t giao, hi v b.

Cc mt c nh ngha trong Surface card bng cch cung cp cc h s ca cc phng trnhgii tch mt hay cc thng tin v cc im bit trn mt. Cc phng trnh gii tch cho mtc cung cp bi MCNP c trnh by trong Bng 4.1.

C php: j n a list

Trong :j ch s mt.n b qua hoc bng 0 nu khng c dich chuyn to .

> 0, s dng TRn card dch chuyn to .< 0, tun hon theo mt n.

a k hiu loi mt.list cc tham s nh ngha mt.

4.1. Surface Cards 38

Bng

4.1:Mt

sloi

mt

cnh

nghatrong

MCNP

Khiu

Loi

Mt

Hm

Tham

sP

Mt

phngMt

phngthng

Ax

+By

+Cz

D=

0ABCD

PX

Mt

phng

trcX

xD

=0

D

PY

Mt

phng

trcY

yD

=0

D

PZ

Mt

phng

trcZ

zD

=0

D

SO

Mt

cuTm

tigc

to

x2

+y

2+z

2R

2=

0R

SMt

cuMt

cuthng

(xx

)2

+(y

y)2

+(z

z)2

R2

=0

xyzR

SX

Mt

cuTm

trntrc

X(x

x)2

+y

2+z

2R

2=

0xR

SY

Mt

cuTm

trntrc

Yx

2+

(yy)2

+z

2R

2=

0yR

SZ

Mt

cuTm

trntrc

Zx

2+y

2+

(zz)2

R2

=0

zR

C/X

Mt

tr//

trcX

(yy)2

+(z

z)2

R2

=0

yzR

C/Y

Mt

tr//

trcY

(xx

)2

+(z

z)2

R2

=0

xzR

C/Z

Mt

tr//

trcZ

(xx

)2

+(y

y)2

R2

=0

xyR

CX

Mt

trTrn

trcX

y2

+z

2R

2=

0R

CY

Mt

trTrn

trcY

x2

+z

2R

2=

0R

CZ

Mt

trTrn

trcZ

x2

+y

2R

2=

0R

K/X

Mt

nn//

trcX

(y

y)2

+(z

z)2

t(xx

)=

0xyzt 2

1

K/Y

Mt

nn//

trcY

(x

x)2

+(z

z)2

t(yy)

=0

xyzt 2

1

K/Z

Mt

nn//

trcZ

(x

x)2

+(y

y)2

t(zz)

=0

xyzt 2

1

KX

Mt

nnTrn

trcX

y

2+z

2t(x

x)

=0

xt 2

1

KY

Mt

nnTrn

trcY

x

2+z

2t(y

y)

=0

yt 2

1

KZ

Mt

nnTrn

trcZ

x

2+y

2t(z

z)

=0

zt 2

1

SQ

Ellipsoid

//trc

X,Y

,ZA

(xx

)2

+B

(yy)2

+C

(zz)2

ABCDEFG

Hyperboloid

+2D

(xx

)+

2E

(yy)

+2F

(zz)

+G

=0

xyz

Paraboloid

GQ

Hnh

tr,nn

khng//

trcX,Y

,ZAx

2+By

2+Cz

2+Dxy

+Eyz

+Fzx

ABCDEFG

Ellipsoid

+Gx

+Hy

+Jz

+K

=0

HJK

HyperboloidParaboloid

TX

Mt

xuynTrc

//vi

X(x

x)2/B

2+

( (y

y)2

+(z

z)2

A)2/C

21

=0

xyzABC

TY

ellipsehoc

trnTrc

//vi

Y(y

y)2/B

2+

( (x

x)2

+(z

z)2

A)2/C

21

=0

xyzABC

TZ

Trc

//vi

Z(z

z)2/B

2+

( (x

x)2

+(y

y)2

A)2/C

21

=0

xyzABC

PXYZ

Mt

phngto

bicc

im

39 CHNG 4. NH NGHA HNH HC

V d 4.1: Cch vit nh ngha mt

Surface Name Data1 PX 5(Mt phng vung gc vi trc x c phng trnh: x 5 = 0, ct trc x ti x = 5cm)Surface Name Data2 CZ 3.1(Mt tr c phng trnh x2 + y2 3.12 = 0, c tm trn trc z, R = 3.1cm)

V d 4.2: Mt s v d cho nh ngha mt

Mt phng :PX 1.0(Mt phng vung gc vi trc x ti im x = 1.0 cm)PY -10.0(Mt phng vung gc vi trc y ti im y = -10.0 cm)PZ 1.0(Mt phng vung gc vi trc z ti im z = 1.0 cm)

Mt cu:SO 100.1(Mt cu c tm ti gc ta v c bn knh l 100.1 cm)SY 10.0 3.0(Mt cu c tm nm trn trc y ti im y = 10.0 cm v c bn knh 3.0 cm)S 1.0 2.0 4.5 2.0(Mt cu c tm ti im c ta (1.0, 2.0, 4.5) v c bn knh 2.0 cm)

Mt tr:CY 1.0(Mt tr nm trn trc y c bn knh l 1.0 cm)C/Z 3.0 5.0 2.4(Mt tr song song vi trc z c tm nm ti ta (x, y) = (3.0,5.0)cm v c bn knh l

2.4 cm)

Xc nh chiu ca mt mt Nu xt trng hp trong khng gian ch c mt mt, th mtny s chia khng gian thnh 2 vng ring bit. Gi s rng s = f(x, y, z) = 0 l phng trnh camt mt trong bi ton. i vi mt im (x, y, z) m c s = 0 th im trn mt, nu s mim c gi l bn trong mt v c gn du m. Ngc li, nu s dng, im cgi l bn ngoi mt th c gn du dng.

Bn cnh , quy c v chiu ca mt c th c xc nh mt cch n gin hn i vi mts mt c th:

i vi cc mt phng vung gc vi trc to : vng pha chiu dng ca trc to smang du +, ngc li mang du .

i vi cc mt tr, cu, nn, elip, parabolic: vng bn ngoi mt s mang du +, bntrong mang du .

Trong cc hnh bn di, cc con s c khoanh trn l k hiu cho cc cell, cc con s khng khoanhtrn l cc mt. Cell 1 (phn mu xm) l phn khng gian b bao ph bi cc mt bin nh tronghnh, cell 2 l phn khng gian bn ngoi cell 1. Cc trc to c chiu t di ln trn v ttri qua phi.

4.1. Surface Cards 40

Ton t giao:Cell 1 cha vt cht l phn giao ca:

Vng pha trn mt 1 (du +) Vng tri ca mt 2 (du ) Vng di ca mt 3 (du ) Vng phi ca mt 4 (du +)

Khai bo cc mt cho cell 1 l: 1 -2 -3 4

Ton t hp:Khai bo cc mt cho cell 1v 2 ln lt l:cell 1: 1 -2 (-3 : -4) 5cell 2: -5 : -1 : 2 : 3 4

Ton t b :Khai bo cc mt cho cell 1v 2 ln lt l:cell 1: 1 -2 -3 4cell 2: -1 : 2 : 3 : -4hoc #1 (b cell 1)

V d 4.3: M t mt mt phng ct cc trc ta ti cc v tr x = 1cm v y = 2cm

Mt mt phng c phng trnh tng qut Ax + By + Cz D = 0, trc tin chng ta cnxc nh cc h s ABCD m t mt phng ny:

Mt phng ct trc x ti v tr x = 1 cho nn im (1,0,0) thuc mt phng, ta c phngtrnh: AD = 0

Mt phng ct trc y ti v tr y = 2 cho nn im (0,2,0) thuc mt phng, ta c phngtrnh: 2B D = 0

Mt phng khng ct trc z cho nn C = 0

T ta thu c h thc A = 2B = D, nu chn A = 1 ta c th khai bo mt phng nhsau:

1 P 1 0.5 0 1

V d 4.4: M t mt mt elliptic paraboloid

41 CHNG 4. NH NGHA HNH HC

Trong MCNP, cng thc tng qut m t cc mt (ellipsoid, hyperboloid, paraboloid,...) l

Ax2 +By2 + Cz2 +Dxy + Eyz + Fzx+Gx+Hy + Jz +K = 0

Trong cc sch gio khoa, phng trnh elliptic paraboloid c m ta qua cng thc

z

c=x2

a2+y2

b2

Phng trnh trn c th d dng chuyn i sang dng tng ng vi cng thc tng quttrong MCNP

b2c x2 + a2c y2 + 0z2 + 0xy + 0yz + 0zx+ 0x+ 0y a2b2z + 0 = 0

4.1.2 Macrobody

Cc mt c nh ngha thng qua cc khi hnh hc n gin c xy dng sn trong MCNP.

BOX hnh hp vung

C php: BOX Vx Vy Vz A1x A1y A1z A2x A2y A2z A3x A3y A3z

Trong Vx Vy Vz cc ta x,y,z ca 1 gc hp.A1x A1y A1z vector ca mt u tin.A2x A2y A2z vector ca mt th hai.A3x A3y A3z vector ca mt th ba.

RPP hnh hp xin

C php: RPP Xmin Xmax Ymin Ymax Zmin Zmax

Trong Xmin Xmax Ymin Ymax Zmin Zmax cc ta ca cc gc hp.

SPH hnh cu

C php: SPH Vx Vy Vz R

Trong Vx Vy Vz cc ta x,y,z ca tm hnh cu.R bn knh

RCC hnh tr trn

C php: RCC Vx Vy Vz Hx Hy Hz R

Trong Vx Vy Vz cc ta x,y,z ca tm y.Hx Hy Hz vector cao trc hnh tr.R bn knh

RHP/HEX lng tr su phng

C php: RHP V1 V2 V3 H1 H2 H3 R1 R2 R3 S1 S2 S3 T1 T2 T3

Trong V1 V2 V3 cc ta x,y,z ca mt y.

4.1. Surface Cards 42

H1 H2 H3 vector t y ti nh.R1 R2 R3 vector t trc n gia mt th nht.S1 S2 S3 vector t trc n gia mt th hai.T1 T2 T3 vector t trc n gia mt th ba.

REC hnh tr y dng ellip

C php: REC Vx Vy Vz Hx Hy Hz V1x V1y V1z V2x V2y V2z

Trong Vx Vy Vz cc ta x,y,z ca mt phng y.Hx Hy Hz vector cao trc hnh tr.V1x V1y V1z vector trc chnh ca ellip (vung gc vi Hx Hy Hz).V2x V2y V2z vector trc ph ca ellip (trc giao vi H v V1).

TRC hnh nn ct

C php: TRC Vx Vy Vz Hx Hy Hz R1 R2

Trong Vx Vy Vz cc ta x,y,z ca mt y.Hx Hy Hz vector cao trc hnh nn.R1 R2 bn knh nh v bn knh ln ca hnh nn ct.

ELL ellipsoid

C php: ELL V1x V1y V1z V2x V2y V2z Rm

Trong Nu Rm > 0:

V1x V1y V1z ta tiu im th nht.V2x V2y V2z ta tiu im th hai.Rm chiu di trc chnh.

Nu Rm < 0:V1x V1y V1z tm ca ellipsoid.V2x V2y V2z vector trc chnh.Rm chiu di bn knh ph.

WED hnh nm

C php: WED Vx Vy Vz V1x V1y V1z V2x V2y V2z V3x V3y V3z

Trong Vx Vy Vz ta nh.V1x V1y V1z vector ca mt tam gic u tin.V2x V2y V2z vector ca mt tam gic th hai.V3x V3y V3z vector chiu cao.

ARB khi a din

C php: ARB Ax Ay Az Bx By Bz ... Hx Hy Hz N1 N2 N3 N4 N5 N6

Trong Tm b ba u tin (A,B,C,D,E,F,G,H) nh ngha ta cc gc ca a din.Su tham s tip theo mang 4 ch s nh ngha cc mt to thnh t cc gc.

V d 4.5: Cch khai bo macrobody

43 CHNG 4. NH NGHA HNH HC

BOX -1 -1 -1 2 0 0 0 2 0 0 0 2(Khi hp c tm gc ta , kch thc mi cnh l 2cm)RPP -1 1 -1 1 -1 1(Tng ng vi khai bo BOX trn)RCC 0 -5 0 0 10 0 4(Hnh tr cao 10cm song song vi trc y, c mt phng y ti v tr y = 5cm v bn knh 4cm)

4.2 Cell Cards

Mi cell c din t bi s cell (cell number), s vt cht (material number), mt vt cht(material density), mt dy cc mt (surfaces) c du (m hoc dng) kt hp nhau thng quacc ton t giao (khong trng), hi (:), b (#) to thnh cell.

C php: j m d geom paramshoc j LIKE n BUT list

Trong :j ch s cell.m ch s vt cht trong cell, m=0 ch cell trng.d khi lng ring ca cell theo n v [1024 nguyn t/cm3] nu du + hoc

[g/cm3] nu du pha trc.geom phn m t hnh hc ca cell, c gii hn bi cc mt.params cc tham s tu chn: imp, u, trcl, lat, fill, ...n ch s ca mt cell khc.list cc t kho dng nh ngha s khc nhau gia cell n v j.

V d 4.6: Cch nh ngha cell

1 0 -1 Cell s 1 l cell trng nm bn cnh mt 1 (theo chiu m). Khng cn ghi mt trong

trng hp cell trng.2 1 -2.7 1 -2 Cell s 2 l cell lm bng vt liu m1 c mt vt cht l 2.7 g/cm3 nm bn cnh mt

2 (theo chiu m).3 LIKE 2 BUT TRCL=1 Cell s 3 ging nh cell s 2 nhng nm mt v tr khc (TRCL=1).

V d di y th hin r hn s kt hp gia cell card v surface card.

V d 4.7: M t 1 cell hnh hp ch nht c chiu di cc cnh theo trc x, y, z ln lt l 2, 4v 7 cm

Cell hnh hp ch nht c to thnh t 6 mt phng vung gc vi cc trc x, y v z. Nucho tm ca cell nm ti gc ta , cc mt phng vung gc vi cc trc c th c khaibo nh sau:

1 0 (1 -2 3 -4 5 -6)

vi cc mt phng:

1 PX -1 $ Mat phang vuong goc truc x2 PX 1 $ Mat phang vuong goc truc x3 PY -2 $ Mat phang vuong goc truc y4 PY 2 $ Mat phang vuong goc truc y

4.3. Mt s card nh ngha tnh cht ca cell 44

5 PZ -3.5 $ Mat phang vuong goc truc z6 PZ 3.5 $ Mat phang vuong goc truc z

Ngoi ra, thay v khai bo 6 mt, ta cng c th m t hnh hp bng cch s dng macrobody(xem Phn 4.1.2) nh sau:

1 RPP -1 1 -2 2 -3.5 3.5

Khi khai bo cell c mt tham s thng xuyn xut hin, imp (importance), tham s ny c thc xem nh l quan trng (trng s) ca mi cell. quan trng ca cell bng 0 trong trnghp ca cell v tr (universe cell) l cell m t vng khng gian bn ngoi vng m ta m phng.C hai cch khai bo imp:

t ngay sau cc cell trong Cell card2 0 -7:8:-9 imp:p=13 1 -1.0 #2 imp:n=2

a vo trong khi Data cardimp:n 1 2 4 5r 1 0

i lng ny ch thc s c ngha khi ngi dng s dng cc k thut gim phng sai (variancereduction technique). Khi , cc cell c quan trng cao hn s nhn c m phng chi tithn (s lng cc ht c m phng nhiu hn) so vi cc cell c quan trng thp (xemChng 8). Theo quy c, khi ht i vo trong cell c quan trng bng 0, qu trnh m phnght s kt thc. Thng thng cc cell m t vng khng gian bao ngoi khu vc m phng sc gn gi tr ny.

4.3 Mt s card nh ngha tnh cht ca cell

4.3.1 Material Cards

Material card m t loi vt liu c lp y trong cell trong qu trnh m phng. Cc thnhphn trong vt liu c xc nh bng s hiu nguyn t ca nguyn t thnh phn v t l phntrm ca nguyn t trong vt cht.

C php: Mm ZAID1 fraction1 ZAID2 fraction2 ...

Trong :m ch s ca vt liu.ZAID s hiu xc nh ng v, c dng ZZZAAA.nnX vi:

ZZZ l s hiu nguyn tAAA l s khinn l s ch ca b s liu tit din tng tc s c s dngX l kiu d liu (C nng lng lin tc; D phn ng ri rc;...)

fraction t l ng gp ca ng v trong vt liu.

Trong khi khai bo ng v, s hiu nguyn t ZZZ khng nht thit phi vit 3 ch s. i vicc ng v t nhin AAA=000, chng hn nh khi khai bo ng v 16O ta c th vit 8016 hay8000 u c. Trong thc t, i vi trng hp cc ht kho st l photon hoc electron, titdin tng tc khng c s ph thuc r rt vo s khi nn ta c th s dng AAA=000 cho cctrng hp ny. Trong trng hp khng khai bo ui nnX, b d liu tit din mc nh s cs dng.

T l ng gp ca ng v trong vt liu s c tnh theo t l s nguyn t c trong hp chtnu mang gi tr dng, hoc theo t l khi lng nu mang gi tr m.

V d 4.8: nh ngha vt liu kapton

45 CHNG 4. NH NGHA HNH HC

Hp cht kapton (c k hiu l m2) c cng thc C22H10N2O4 c m t nh sau:

m2 6000 0.579 1000 0.263 7000 0.053 8000 0.105

Cc s 0.579, 0.263, 0.053 v 0.105 th hin t l s nguyn t ng gp ca cc nguyn tC (6000), H (1000), N (7000) v O (8000) trong hp cht kapton.

Trong trng hp mun m t t l khi lng, ta s dng du tr t trc t l ng gpca mi nguyn t

m2 6000 -0.731 1000 -0.027 7000 -0.077 8000 -0.175

V d 4.9: nh ngha vt liu uranium t nhin

Trong t nhin U-235 ch chim 0.72%, phn cn li l U-238. Do ta s khai bo vt liuuranium t nhin nh sau

m1 92238 0.9928 92235 0.0072

Ngoi ra, chng ta cn c th xc nh th vin m MCNP cn s dng trong qu trnh mphng. V d nh nu chng ta ang tin hnh bi ton m phng cho vn chuyn neutron,th vin thng c s dng l .66c, ta c th vit

m1 92238.66c 0.9928 92235.66c 0.0072

Lu : nu tng t l ng gp ca cc ng v trong hp cht khc 1, chng trnh MCNP s tng chun li cc t l ny sao cho tng ca chng ng bng 1.

Ngoi ra cc vt liu c nh ngha trong Mm card c th c i km vi mt MTm card xcnh b d liu tng tc S(,) i km (xem Ph lc G, MCNP Manual). Trong trng hp, MCNP s s dng m hnh tn x t do (free-gas treatment) cho n khi nng lng ca htxung ti mc tn x nhit S(,) (thng thng khong di 4eV) v s dng tng tc tn xnhit ny thay th trong m phng1.

C php: MTm X1 X2 ...

Trong :m ch s ca vt liu c nh ngha trong Mm card.Xi ch s ca phn ng S(,) tng ng vi vt liu c nh ngha.

V d 4.10: Khai bo tng tc tn x nhit

Di y l mt s v d cho khai bo tng tc tn x nhit cho vt liu nc nh, polyethylenev graphite

M1 1001 2 8016 1 $ light waterMT1 LWTR .07M14 1001 2 6012 1 $ polyethyleneMT14 POLY .03M8 6012 1 $ graphiteMT8 GRPH .01

4.3.2 Cell Volume Card (VOL)

Card VOL c dng khai bo th tch cho cc cell. Thng thng MCNP s tnh th tch vkhi lng ca mt cell da vo cc thng tin ca cell m ngi dng khai bo. Khi card ny c

1Thng thng hiu ng tn x nhit ch tr nn quan trng khi nng lng xung di 2eV.

4.4. Chuyn trc ta 46

s dng, MCNP s s dng thng tin v th tch c cung cp trong card thay v dng cc thtch tnh ton c.

C php: VOL x1 x2 ... xihay VOL NO x1 x2 ... xi

Trong xi ch s ca cell.NO khng c th tch hay din tch c tnh.

V d 4.11: Khai bo th tch cell

Gi s ta mun khai bo th tch cho 10 cell u l 0.5cm3 v 5 cell sau l 0.3cm3, ta vit nhsau

VOL 0.5 9r 0.3 4r

(K t r dng lp li s ng trc n N ln)

4.3.3 Surface Area Card (AREA)

Card AREA tng t nh VOL nhng dnh cho khai bo din tch b mt.

C php: AREA x1 ... xi ... xn

Trong xi din tch ca mt th i.

V d 4.12: Khai bo din tch b mt cell

Gi s ta mun khai bo din tch b mt cho cc cell ln lt l 0.5, 0.2, 0.2, 1.0, 2.1 v0.3cm2, ta vit nh sau

AREA 0.5 0.2 r 1.0 2.1 0.3

4.4 Chuyn trc ta

4.4.1 Coordinate Transformation Card (TRn)

C php:TRn (*TRn) O1 O2 O3 B1 B2 B3 B4 B5 B6 B7 B8 B9 M

Trong n ch s cho vic chuyn i trc.O1 O2 O3 vector chuyn i (v tr ca to mi so vi to c).B1 n B9 ma trn c trng cho tng quan gc gia cc trc to ca

hai h to c v mi.TRn: Bi l cosin ca gc gia hai trc to c v mi.*TRn: Bi l gc (tnh theo ).

M = 1 ngha l dch chuyn ta vector t v tr gc ca h trc ta ph c xc nhqua h trc ta chnh (c mc nh sn).

M = 1 ngha l dch chuyn ta vector t v tr gc ca h trc ta chnh c xcnh qua h trc ta ph.

Mc nh: TRn 0 0 0 1 0 0 0 1 0 1 0 0 1

47 CHNG 4. NH NGHA HNH HC

V d 4.13: M t 1 cell hnh tr c ng knh 1cm, cao 3cm v nghing 1 gc 30 so vi trc xtrong mt phng xy

m t hnh tr theo yu cu t ra, trc tin ta s m t mt hnh tr song song vi theotrc x c tm nm ti gc ta , ri sau s dng TRn card quay trc i mt gc 30 so vix. Cch m t cell hnh tr song song vi trc x nh sau:

1 0 (1 -2 -3)

1 1 PX -1.5 $ Mat phang vuong goc truc x2 1 PX 1.5 $ Mat phang vuong goc truc x3 1 CX 0.5 $ Mat tru song song truc x

S 1 t sau ch s mt c ngha l cc mt s c chuyn trc toa theo TR1, cch khaibo cc h s trong TRn card c m t trong Phn 4.4.1 v Ph lc D. Trong trng hpny TR1 c dng nh sau:

*TR1 0 0 0 30 60 90 120 30 90 90 90 0

Thc ra chng ta cng khng cn thit phi khai bo ht tt c cc h s Bi, m chng ta cth rt gn nh sau

*TR1 3J 30 60 90

4.4.2 Cell Transformation Card (TRCL)

Card TRCL c chc nng tng t nh TRn nhng c s dng trc tip trn cell card.

C php: TRCL=nhoc TRCL=(O1 O2 O3 B1 B2 B3 B4 B5 B6 B7 B8 B9 M)

Trong n ch s chuyn trc c nh ngha tng t nh trong TRn.

V d 4.14: M t cell 1 c dng hnh tr ng knh 1cm, cao 3cm v cell 2 ging cell 1 nhngnghing 1 gc 30 so vi trc x trong mt phng xy

Tng t nh v d trc ta c cell 1 dng hnh tr song song vi trc x c m t nhsau:

1 0 (1 -2 -3)

1 PX -1.5 $ Mat phang vuong goc truc x2 PX 1.5 $ Mat phang vuong goc truc x3 CX 0.5 $ Mat tru song song truc x

Chng ta thm cell 2 c dng hnh tr ging vi cell 1 nhng c quay mt gc 30 thngqua TR1

1 0 (1 -2 -3)2 LIKE 1 BUT TRCL=1 $ Cell 2 giong cell 1, chuyen truc TR1

1 PX -1.5 $ Mat phang vuong goc truc x2 PX 1.5 $ Mat phang vuong goc truc x3 CX 0.5 $ Mat tru song song truc x

*TR1 10 0 0 30 60 90 $ Chuyen truc

4.5. Lattice 48

4.5 Lattice

i vi cc hnh hc c cu trc lp (repeated structure geometry), bn cnh vic s dng LIKE ...BUT, chng trnh MCNP cn cung cp mt s cc tnh nng gip chng ta trnh vic phi m tnhiu ln cng mt hnh hc. Mt trong nhng tnh nng l mt t hnh hc di dng latticethng qua vic s dng cc card U, FILL v LAT.

4.5.1 Universe & Fill Card (U & FILL)

Khi mt cell hoc mt nhm cell c gn universe (thng qua U), cc cell ny s c lp ymt cell khc khi FILL c gi.

C php: U=nFILL=n

hoc FILL=i:i j:j k:k m1 m2 ... mj ...

Trong n k hiu c gn cho cell c chn lp y.i:i j:j k:k cc tham s ch cc lattice c lp y.mj cc k hiu universe tng ng vi cc lattice.

4.5.2 Lattice Card (LAT)

C php: LAT=n

Trong n=1 lattice dng khi vung.n=2 lattice dng khi lc gic.

V d 4.15: nh ngha lattice hnh hp

1 0 12 -13 14 -15 16 -17 FILL=12 0 27 -28 29 -30 31 -32 U=1 LAT=1

12 PX -113 PX 114 PY -115 PY 116 PZ -117 PZ 127 PX -0.0528 PX 0.0529 PY -0.0530 PY 0.0531 PZ -0.0532 PZ 0.05

Cell 1 c lp y bi cell 2. Cell 2 c dng lattice hnh hp kch thc 1 1 1 mm3. Trongv d trn, cell 1 l mt khi lp phng c kch thc 20 20 20 mm3, vy s c chiathnh 20 20 20 = 8000 lattice nh. Trong , ch s ca cc lattice c cho mt cch ixng. Trong trng hp s lattice c chia theo 1 trc N l s chn, ch s s c nh tN/2 n N/2. Trong trng hp N l, ch s s c nh t (N 1)/2 n (N + 1)/2.Nh trong v d trn, cc ch s s c nh t 10 n 10 theo trc x, 10 n 10 theotrc y v 10 n 10 theo trc z.

5nh ngha ngun

Khi m phng vn chuyn ht, bn cnh vic m t hnh hc ca vng khng gian kho st, chngta cn cn m t cc loi ht cn kho st v cch thc pht cc ht ny. Trong chng ny, chngta s tin hnh tm hiu cch thc khai bo cc ngun pht ht. Chng trnh MCNP cho phpngi dng th nh ngha nhiu loi ngun khc nhau, ph hp vi tng loi bi ton c th.

5.1 Mode Cards

Mode card l phn khai bo loi ht m ta mun xt. Trong MCNP, c tt c 3 loi ht l neutron(n), photon (p) v electron (e).

C php: MODE X

Trong X l loi ht m ta mun xt. X = N trong trng hp ca neutron, X = P trong trnghp ca photon v X = E trong trng hp ca electron.

V d 5.1: Khai bo loi ht cn kho st

MODE P (loi ht kho st l photon)MODE P,E (loi ht kho st l photon v electron)

5.2 Cc kiu nh ngha ngun

MCNP cho php ngi dng m t ngun cc dng khc nhau thng qua cc thng s ngun nhnng lng, thi gian, v tr v hng pht ngun hay cc thng s hnh hc khc nh cell hocsurface. Bn cnh vic m t ngun theo phn b xc sut, ngi dng cn c th s dng cchm dng sn m t ngun. Cc hm ny bao gm cc hm gii tch cho cc ph nng lngphn hch v nhit hch chng hn nh cc ph Watt, Maxwell v cc ph dng Gauss (dng theothi gian, dng ng hng, cosin v dc theo mt hng nht nh).

Mt s loi ngun trong MCNP:

Ngun tng qut (SDEF)

Ngun mt (SSR/SSW)

Ngun ti hn (KCODE)

5.3. Ngun tng qut 50

Ngun im (KSRC)

Cc thng s ca ngun thng bao gm:

Nng lng (energy)

Thi gian (time)

Hng (direction)

V tr (position)

Loi ht (particle ype)

Trng s (weight) (cell/surface nu c)

5.3 Ngun tng qut

5.3.1 nh ngha

Card SDEF c dng nh ngha ngun mt cch tng qut.

C php: SDEF cc bin ngun = gi tr

Mt s bin ngun thng dng:POS to v tr ngun, mc nh: (0,0,0).SUR s hiu mt ca ngun, mc nh: 0 (ngun cell).CEL s hiu cell ca ngun.NRM du ca php tuyn b mt, mc nh: +1.ERG nng lng ca ht pht ra t ngun, mc nh: 14 MeV.WGT trng s ca ht pht ra t ngun, mc nh: 1.PAR loi ht pht ra t ngun, 1:neutron, 2:photon, 3:electron.VEC vector tham chiu cho DIR.DIR cosin ca gc hp bi VEC v hng bay ca ht, mc nh: ng hng.AXS vector tham chiu cho RAD v EXT.RAD bn knh qut t POS hoc t AXS, mc nh: 0.EXT khong cch qut t POS dc theo AXS hoc cosin ca gc qut t AXS, mc nh: 0.X v tr trn trc x.Y v tr trn trc y.Z v tr trn trc z.ARA din tch b mt.

V d 5.2: Ngun photon pht ng hng c ta (0 -4 2.5) nm trong cell 1, ht t ngunpht ra c trng s l 2

Chng ta s s dng cc ty chn POS cho v tr ngun, CEL cho ch s cell cha ngun, WGTcho trng s ca ht pht ra t ngun v PAR cho loi ht pht ra t ngun