Смелов В.В. Лекции по теории переноса нейтронов

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(14.14)

napaJIJIeJIbHbIM

BbIHBJIeHHeM

nopanxa

annpoxcaaauaa.

Tlpeacne

scero

nOJIytIHM

TO:>K,neCTBO

THna

(14.15):

%k+l/2

(Y(k)

(Xk-I/2)

Y(k)(Xk+I/2)]

S x"cD(.)(x)dx==O.

%k-l/2

tOO

(14.87)

rAe B

,cRJIY

(14.76)

)

= 0

= 0).

TO)l{,l(eCTBe

-(14.87)

<PYHKII.HIO

W(k)

(x)"-

aamnnex

no <POp

MyJle

(14.17). Torna

HHTerpaJIbHhIH

qJleH

TO>K,l(eCTBa

npeneraaarcs

BHAe

CHMBOJI

Kpoaexepa, B nocnezmeu

paaeacrae

o6paTBM

BHHMaHHe

OTHomeHHe

CD'(k)

(Xk)!Xk.

113

cooraomeaaa

(14.73), (14.74) it (14.81)

ycTaH81U1HB.aeM, qTO

cD'

(k) (x).-.O npa

x-.O,

noroay

lim

[CD'

(k)

(x)/x]

.¥40

= lim cD"

(k)

(x) H

pasea

KOHetIaOH

BeJIHtBlHe.

TaKHlti

oopasox, ceMeA-

x~o

- -

CTBO

nOCJleAOBaTeJIbHOCTeii

{cD'(k)

(xlz)/xk}~l

paauouepao

orpaaaseao,

TaK qTO nepsoe cnaraessoe B (14.88) .

npeaocxonar

MO,llYJIIO

const·h

•

Ilpa

oueaxe

'BTOPOTO CJI8raeMOro B

(i14.8·8)

ytIHThIBaeTCH

paBHoMepH8H

OrpaHHtIeHHOCTb

cexejicraa

<pyHKII.HH

(J)"(k)

(x),

norouy

Xk+I/2

. const r

d - const hI

)

2hkXk

J x x

X-

5 uY2 •

%k--l/2

peSYJl&T8Te

lai

)

~Blhlk

<:B

•

TOJK,neCTBO

(14.87)

MOJKHO

'Fenepb

nepenacars

BHAe

(14.89)

101

HCnOJIb3yH

paseacraa

(14.19) H (14.21), npeotipaayex TO>K,neCTBO

(14.89) K

aany

{(

~)"

f(k)

(Xk)

'(k)

(ak)

-IF

\ h

~2Xk

(k)

k-l/21

~)Y

[IT

'(k)

(hk)

-'(k)

(Xk)

11'

') h

]}+

2Xk

(k)

k+l/2

It .

"(I+a

2h2k)

()_"[0(1)

)" (2)

X2k <D(k)

+ - 2Xk B

+(1+

::k)

)

npa

1, 2

~)Y

-1

.!!JL+

-1)

2Xk

- - v

2Xk

2'.

2Xk

n09TOMy

TOLKt\eCTBO

MOJRHO

nepenacars

TaK:

(

hi)

v A

'(k)

(Xk)

'(k)

(ak)

-2

Ie h

+!!:!L)"

'(k)

(hk)

'(k)

(Xk)

k 2 k h

"(1+

2 h

)

()+

"{[l+V(V-l)

)Y]

(1)(k)

Xk.

2Xk

[11'

(k)

) -

11'

(k)

)]

;~:

[lJI'

(k)

(Xk-1rJ

lJI'

(k) (X

H 1/

)]

} =

==X"

[0(1)

+(1-

!!:!....)'

o<2)

+(I+~)"a<3)]

(14.90)

k _ k 2Xk k .2Xk k •

epYHKnHSI

W(k)

EC(t)

[0, b], TaK

qTO

lV(~)

) -

W(k)

-2

) =

lV'(k) (e

)

E hk). VIs nOCJIe,l.{HerO pesyasrara H

HepaBeHCTBa

hkl2xk~I

yCTaHaBJIHBaeM,

qTO

nepsoe

cnaraexoe

q>HrYP'HhIX

CKO'6-

xax

npesocxonar

MOJlYJIIO

const

··h

•

JIerKoH

OUeHKe

nroporo

cnaraexoro

·B

3THX

xce cK06'Kax MewaeT

MHO)KHTeJIb

xx.

KOTO'phI:H

aeorpanaseaao

pacrer

Mepe

«H3MeJIbqeHHH»

ceTKH.

B03HHKwee

npensrcrsae

HeCJIOLKHO

npeonoaers,

eCJIH

;BoC'nO~b301BaTbCSI

pasno-

LKeHHeM

KOToporo

cneAyeT

[lJ!

( + (

)]

1.P"(k)

(Xk)

2Xk

(li)

) ·'F(It> X

::k

[lJI"

(1)

lJI"U:1

(~;)l·

108

(14.91)

Bropoe

cnaraexoe

npasoa

qaCTH

orpaaaseao,

TaK

tITO

OCTaJIOCh

ycra-

HOBHTb

OrpaHHtIeHHOCTh

,U.p06H

'I'(k)

(Xk)

!Xk

•

.llJIH

3TOrO

BOCnOJIbsyeMcSI

aSJIOlKeHHeM

m'"

(

....

)-al"

(O)+xm(lV) (ft

)

(O~I1~I).

(k)·'\,

-T

(k)

T(k)

--11

Iloxaacex,

tITO

3TOM

paaJIO}KeHHH

(j)"'(k)

(0)

=0.

CaMOM

.neJIe,

ssnne

yace

nOKaa3HO,

tIro

(!)'(k)

(0)

==0.

aTO

osuasaer,

cOrJIaC'HO

paBeHCTBy

(14.86),

qTO

Y"(k)

(0)

=0.

Haxoaen,

<pOpMyJI

(14.78), (14.79) H

yCJIOBHH

(14.74) nonyxaea

HYlKHbIH

pesynsrar.

TaKHM

otipaaox,

1.I'(k) (Xk) =

DCk)

(Xk)

,'Tf

(k) (Xk)

=_1_

(x)

m(lV)

(Ox)

Xk -

24xk

(II)

T(k)

ecrs

OrpaHHtIeHHa51

BeJIHtIHHa

CJIe,llOBaTeJIbHO,

nee

BbIpa1KeHHe

<pHrypHhIX

cxooxax B (14.90)

npesocxonar

MOAYJlIO

const·h

1l•

0603HaQa51

3TO

aupaaceaae

_8~4),

noayxaea

arore

cnenyroutee

TO>KJleCTBO:

(

X -

!!!..)"

A 'Ck)

(xiJ

.:.....-

CP(k)

(ak) _

!!!..)"

IT fCk)

(hk)

f(k)

(xiJ

k 2 k. hk k 2 k

" ( a,,2

k ) ( ----J"

,X2k «D(k) Xk)= X

ak'

rne

=3(1)+

~.)"

3(2)

..!!lL)"

a(3)

+8(4)" •

k k -

Xk·k

2Xk

k k

BeJIHIIHHbI

3~1)

a~4)

oneneau

TOJIhKO

qTO,

a a

~2)

a~3)

-Ha

85-86.

l1s

Haii,n:eHHhIX

aepaaeucrn

18~i)

I~const.h:

(i=

1, ... , 4)

CJIeAyeT

18kl

~Bhlk~Bh2.

pesynsrare

oT6paCbIBaHHH

B TOJK,lI.eCTBe (14.91)

MaJIOH

npaaoit

qaCTH,

HMelOIlleH

nOpH,lI.OK 0 (h

) ,

npHXO,llHM

KOHetIHO-paSHocTHoA:

cxexe:

(

) "

'k-ft

( h

Cfbk

-ftk

xk-T

s, .hk

Xk+T

Ilk

+X;

(1 + a

: .

=::)

[E(Xk)

fflk

- q (Xk))= 0,

1, 2, ... , N.

,UJI5I

HCKJIIOqeHH5I

<pHKTHBHbIX

aHaqeHHH

nOJIytIeHHOH

ak k

CHCTeMe

CJIe,lI.yeT

Bocn<;>JIb30BaTbCH

paaHOCTHbIMH

YCJIOBHHMH

«CllIHB-

KH»

CTbIKe

coceLLHHX

HHTepBaJIOB

hk+h

Ta:K)Ke

paaaocrasnr

rpaHHQHbIM

yCJIOBH·eM.

3TH

YtCJIOBH5I zraror

epOPMYJIbI

(13.17) H

sropoe

paaencrno

(13.21) .

HCKJIlOqaH

<pHKTHBHbIe

SHatIeHH5I,

npaxonax

K paaaocrnofr cxexe:

Ak(ftt-<Pk-t)-Ak+1(fk+l-<Pk)+-kfk=F

k=l,

2, ..., N, (14.92)

109