Смелов В.В. Лекции по теории переноса нейтронов

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<l>aKT

He.

cnynaea.

,UeACTBHTeJIbHO,

cnynae

HeCTaUHO-

aapnoro

peLKHMa

6eCKOHetIHOe

MHO>KeCTBO

BapH.3HTOB

BbI60pe

<pyHKUHH

p.(r, o,

)

anexer

C060H

TaKoe

LKe MHOLKeCTBO

epyHK-

UHOHaJIOB

(25.1) H

cooTBeTcTBylOIUHx

<pyHKUHH

ueHHOCTH

[perne-

HHH

ypaBHeHHH

(25.5)]. B

cnyxae

CTaUHOHapHoro

peJKHMa

6eCKOHelJ-

Hoe

,MHOLKeCTBO

<pyHKUHOHaJIOB

(25.21)

CHOBa

06eCnelJMBaeTCH

6eCKOHelJHbIM

MHO:>KeCTBOM

BapHaHTOB

BbI60pe

BeCOBoA

<PyHKUHH

p(r,

0).

'3Ta

<PyHKUHH

BXO,llHT

ypasaenae

(25.24), a

nero-

MO:>KeT

caxa

ce6e

<pOpMHpOBaTb

MHO:>KeCTBO

epyHKUHii

ueu-

HOCTH -

3TO

MHO>KeCTBO

epopMHpyeTcH

nOMOIUblO

npOH3BOJIbHOA

nOCTOSlHHOH c.

MOJKHO

nopexoxeanoaa-rs

lJHTaTeJIIO

BbInOJIHHTb

KalJeCTBe

ynpaLKHeHHH

cnenyiouryio

nporpaxwy:

BbIBeCTM

ypaeaenae

JlJISI

ueHHOCTH

HeHTpoHa

paxxax

O,llHO-

CKOpOCTHOH

TeopHH

noxasars

COnpH:>KeHHOCTb

cooTBeTcTBylOIUHx

onepaTopoB

,L H L*;

nOJIytIHTb

,nH<P<PY3HOHHo-Bo3pacTHoe

npH6JIH>KeHHe

.nJISI' ypas-

HeHHH

(25.24).

BOJIee

nonpooaue

pe3YJIbTaTbI

MaTepHaJIaM

aroro

Cne,llYIOIUe-

naparparpon

tIHTaTeJIb

HaH,lleT

patiorax

[44-47].

176

§ 26.•.CDOPMynbl TEOP""

B03MY~EHMA

scex

npezusnymax

naparparpax

npa

H3YlIeHHH

HeHTpOHHO-H,l{ep-

HbIX

npoueccon

BMaTepHaJIbHOH

cpene npennonaranocs,

liTO

CBOHCTBa

3TOH

cpenu

HeH3MeHHbI.

O,l{HaKO

osens

lIaCTO

npaxraxe

H B reope-

TnqeCKHX

sonpocax

MbI

CTaJIKHBaeMCH

YCJIOB~HMH,

xorna

CBOHCTBa

cpenu

MeHHIOTCH

(B03MymaIOTCH).

Xapaxrep

3THX

H3MeHeHHH

M02KeT

6bITb

KaK

eCTeCTBeHHblM

(auropanae

,l{eJIHmerOCH

sentecraa

spe-

MeHeM

paooratourea

peaxrope

HaKOIIJIeHHe

HeM

npozryxros ne-

JIeHHH;

rrorpysceuae

perynapyrourax

CTep2KHeH

aKTHBHylO

30Hy

peaxropa

HJIH

H3BJIelIeHHe

OTTY.lla;·

aBapHHHbIH

pe2KHM

npa

npo-

psrse,

aanpaxep,

KaHaJIa

2KH.llKHM

TenJIOHOCHTeJIeM

peaxrope

n.),

TaK

H UCK,YCCTBeH,H,bL.M, xorna,

aanpaxep,

YTOlIIiHIOTCH

CeqeHHH

HeHTpOHHO-H,l{epHbIX

peaKI.J.HH

OCHOBe

OOJIee

COBepIIIeHHoro

sxcne-

pHMeHTa

3TOM

caysae

06'beKTHBHbIe

CBOHCTBa

BemeCTB

MeHHIOT-

CH, a

MeHHIOTCH

JIHIIIb

HaWH

CBe,l{eHHH

O·

HHX)

HJIH

epHKTHBHO

MeHHIOTCH

napaxerpu

cpensr ,l{JIH

ynpomeaaa

MaTeMaTHlIeCKOH

MO,lle-

JIH

lIaCTHOCTH,

3TO

OTHOCHTCH K

MeTO,l{aM

rOMoreHH3aUHH

rereporea-

HOH

aKTHBHOH

30HbI

peaxropa

[48], K

nOJIYlIeHHIO

MHororpynnQBbIX

KOHCTaHT

npa

TaK

Ha3bIBaeMOM

MHororpynnoBoM

MeTO,l{e

penreaaa

ypaBHeHHH

nepeaoca

[3] H T• n.) .

.llJISI

60JIbIIIeH

CHCTeMaTHlIHOCTH

H3JI02KeHHSI,

KaK

asnue,

ace

paccyscneaaa npoaezteu

caanana

npaaepe

aeonaoponaoro ypasne-

HHH

(21.7),

HJIH,

liTO

2Ke,

(25.12).

nYCTb

Hac

narepecyer

KaKOH-TO

KOHKpeTHbI:H

<pyHKI.J.HOHaJI

C[cp].

OlIeBH,l{HO,

'lITO

H3MeHeHHeM

CBOHCTB cpensr

3TOT

<pyHKUHOHaJI

M02KeT

H3MeHHTbCH

(H,

KaK

npaBHJIO,

.H3MeHHeTCHI).

113MeHeHHe

<pyHKUHoHa-

JIa,

paCClIHTaHHoe

HenOCpe,ll.CTBeHHO

KaK

pa3HOCTb

Me2K,ny

HCXO,ll.HbIM

«B03Mym

HbIM»

epyHKlI,HOHaJIaMH,

M02KeT

OKa3aTbCH

npaKTHqeCKH

nenparonnsnr

npa

MaJIbIX

H3MeHeHHHX

CBOHCTB cpensr,

nOCKOJIbKY

BbI-

QHTaIOTCSI

6JIH3KHe

BeJIHlIHHbI.

060HTH

3TY

Tpy,nHOCTb

M02KHO

no-

MOIUblO

COnpH2KeHHOrO

ypaBHeHHH

- B

3TOM

cnyxae

ynaercs

nOJIyqHTb

q>OpMyJIy

,lI.JIH

BbIlIHCJIeHHH

BapHalI,HH

(B03MymeHHSI)

<pyHKUHOHaJIa

~IC

«6e3

norepa

TOlIHOCTH».

llOJIylIHM

3Ty

epOpMyJIy.

YCJIOBHMCH

see,

lITO

OTHOCHTCH K

B03MymeHHOMY

COCTOSlHHIO *,

OTMellaTb

IIITpHXOM.

JIerKO

aaners,

lITO

H3MeHeHHe

CBOHCTB

cpe,nbI-

3TO

H3MeHeHHe

oneparopa

L B

ypaBHeHHH

(25.12):

L~L'-L+6IL,

orxyaa

cnenyer,

lITO

cp--.cp'

+oep; C...C' ==C

+oC.

Bo3MyrneHHoe

COcTOHHHe

OITHC~BaeTCH

ypaBHeHHeM

L'cp'

- (L

+aL)

cp'

==q.

(26.1)

Hapany

ypaaaeaaeu

(26.1)

paccuorpau

aeeoaxyuieaaoe conps-

JKeHHde

ypaaaeane

(25.13),'

coornercrnyroutee

H3y'lIaeMoMY

<pyHKD:Ho-

* CJIe,ZlYeT

3aMeTHTb,

'liTO

JII060e

'H3

JlBYX

COCTORJtHH cpe,Zl&l MO>KHO

CQHT8Tb

B03·

MyrneuHhlM

OTHOCHTeJIbHO APyroco COCTOSIHHH.

177

HaJIy

YpaBHeHHe

(26.1)

YMH01KHM

CKaJlBpHO

(J)*,

ypasaeaae

(25.13) -

tq>'.

Bsrsaraa

BTOpOH

pe3YJIbTaT

nepsoro

nOJIb3YSlCb

yCJIOBHeM

COnpH}i{eHHOCTH

(25.14), nonynaex

(aLep',

ep*)==(q,

f*)-(P,

f')

BJlH

YIIHTbIB3S1 (25.20),

ac===

-(oL<p',

cp*).

(26.2)

(26.4)

ECJIH

pa3JIHQHH

napaaerpax

vaoaxymeaaca H

HeBo3MymeHHoH

sanas

MaJIhI,

TO B (26.2)

rep'

MOLKHO>

3aMeHHTb

cp,

BHOCH

npa

3TOM

38MeTHOH

norpeumocra

B be.

,lleHcTBHTeJIbHO,

===

(oLep',

ep*)

===

- (aL

(~+

a~),

ep*)

(aLep,

ep*)

(oLaep,

ep*).

TIP'H

M3JIbIX

B03MymeHHSlx

cnaraeaoe

(~L~cp,

(J)*)

SlBJIHeTCH

6eCKOHell-

MaJIOR

BeJIHqHHO'H

60JIee

ssrcoxoro

nopanxa,

qeM

(r6Lcp,

cp*),

TaK

liTO

npH6JIHLKeHHO

noaysaev

- (oL'f, 'f*). (26.3)

<popMyJIaX

(26.2)· H (26.3)

B03MymeHHe

oneparopa

H3Be-

CTHO

HCCJIe,nOB8TeJIIO

«6e3

norepn

TOqHOCTH»,

TaK

liTO

«norepa

TOqHO-

CTH»

6y,neT

H B

BeJIHqHHe

oc.

M01KeT

OKa3aTbCH,

liTO

H3MeHeHHeM

CBOHCTB·

cpenu

MeHBIOTCH

o,nHOBpeMeHHO

npaasre

qaCTH

ypaBHeHHH

(25.

112)

H (25.13). B

3TOM

cay-rae

<popMyJIa

,nJISI

B03M.ymeHHH

<PYHKu,HoHaJIa

HMeeT

BHJJ.

(aLep',

ep*)

(oq,

f*) +

(cp',

ap),

RnH

cnyqae

Ma~~x

B03MyrneHHH

OC==-{oLep,

ep*)+(aq,

ep*)+(~,

op).

3aKJIWlIeHHe

naparpa~a

OCTaHOBHMCSI

KpaTKO

O,nHOPO~HOM

ypaBHeHHH

(21.12).

npe,lU10JIOLKHM,

liTO

naH,lI.eH

KpHTHlJeCKHH

napa-

MeTp

naurea

sanaxa

Ac.

ECJIH"

H3MeHHTb

CBOHCTBa

cpenu,

TO .9T()

.nOJI)KHO

npHBeCTH

H3MeHeHHIO

napaxerpa

A.o.

QToi6bI

nOJIY1JHTb

KOMrr3KTHOM

sane

q>OpMyJIy'

)I.JIH

BbIlIHCtlIeHHSI

B03MymeHHH

6A.<l,

sa-

UlimeM

ypaBHeHHSI

(21.12)

(25.24) B

oneparopaoa

epopMe:

~r.p

===

QJl

;

~*rp*

locf1l,*ep*,

(26.5)

rne

B pOJIM

COOCTBeHHOrO

3HaqeHHH

nucrynaer

KpHTHlJeCKHH

napa-

MeTp

(T.

uaaxeasuree

c06cTBeHHoe

3HalJeHHe).

Haneexca,

xro

qHTaTeJIb

JIerKO

aocnpoasaener

caMOCTOSlTeJIbHO

BH,n

oneparopos

2,.

!1l*.

B03MymeHHoe

yp3BHeHHe

AJISI TIJIOTHOCTH

nOTOKa

HeHTpoHoB

aa-

nHlIIeTCH

B BH,lI.e

(26.6}

~TMEO)KaSl

CKaJISIpHO

ypaaneaae

(26.6)

<p*,

tBTOpoe

ypaeaeaxe

B (26.5)

<p',

'BhIqHTaSl

OJl.HH

pe3YJIbT3Tlf3

npyroro

paapemax

178

nonyseaaoe

paseecrso OTHOCHTeJIbHO

6Ao,

nOJlytlaeM

(all,' - A'oaa,',

,*)

(6t,',

,*)

BJIH

B cnysae

MaJIhlX

BosMymeHHH

81 == ('!/" -

AoaA"

,*)

(26.7)

•

(~"

'f*) •

C!>OpMyJIbI ,nJISI

MaJIbIX

B03MymeHHH(26.3),

(26.4) H

(26.7)

npa-

HHTO

Ha3bIBaTb

<flopMyJlaMH

reopaa

B03MymeHHH.

JlJlH

HJIJIIOCTpaUHH

MaTepHa~a

aroro

naparparpa

paccxorpax

CJIe-

,nYIOIUHH

npaxep.

nYCTb

VI H V

OO'heMhI

aKTHBHOH

30HbI

H orpa-

}KaTeJIH

peaxropa.

BhlJIH

paccnaraasr

KpHTHlleCKHH

napaxerp

"'0

COOTBeTcTByIomHeeMy

epyHKUHH

<p(r,

<p*

(r, v,

0).

HeCKOJIbKO

n03JKe

paCnOpHJKeHHe

HCCJIe,nOBaTeJleH

nocrynana

OOJIee

To-rtHhle

,naHHbIe

ceseaaa

aaxaara

MaTepHaJIa

OTpaJKaTeJlH.KaK

paccnarari,

nonpaaxy B

KpHTHlleCKOM

napaxerpe

iAo?

,llJIH

3TOH

-ueJIH

cnenyer

BOC-

nO~b30BaTbCSI

4>OpMyJIOH

.(26.7),

xoropas

aaurex

qaCTHOM

cnysae

rrpaxer

BH,ZI.

SdV S

aEa

(v) dv S

ep*

(r,

(r, e,

al = VI 0

•

JcivJepoio(r.

o, Q)

d!2

5v (v')

(v')x(v.

Vi) dv' 5'f

(r,

o'; Q)

dQ'