LAMS-2 801

(XC-14 REPORT COLLECTION

REFWODLKYTICNd

cow

LOS ALAMOS SCIENTIFIC LABORATORY

OF THE UNIVERSITYOF CALIFORNIAo LOSALAMOS NEW MEXICO

A CODE FOR REDUCING MANY-GROUP

CROSS SECTIONS TO FEW GROUPS

—
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LAMS-2801

UC-32, MATHEMATICS AND

COMPUTERS

TID-4500 (18th Ed. )

LOS ALAMOS SCIENTIFIC LABORATORY

OF THE UNIVERSITYOF CALIFORNIA LOS ALAMOS NEW MEXICO

REPORT WRITTEN December 1962

REPORT DISTRIBUTED: February 11, 1963

A CODE FOR REDUCING MANY-GROUP

CROSS SECTIONS TO FEW

by

Ralph S. Cooper

GROUPS*

*This report supersedes LAMs-2747.

>~m’

cc~ * Contract W-7405 -ENG. 36 with the U. S. Atomic Energy Commission

E~~.

z

All LAMS reports are informal documents, usually prepared for a special purpoee and primarily prepared for use within the Laboratory mther than for

genexal dfetritution. Thte repert has not been edited, reviewed, or verified

for accuracy. All LAMS reports express the views of tbe autbore SE of the

time they were written and do net neceseertiy reflect the opinione of tbe Los

Alamos Scientific Laboratory or the final epinion of the authors on the subject.

—.- -. .’ -1-

ABSTRACT

A code (ZOT) has been written which will produce few-group neutron

cross sections from many-group sets based on a given flux spectrum or

one computed for an infinite medium. The cross-section format is that

of Sn transport theory including the possibility of

energy. The code is written in the Floco II system

IBM 704 or IBM 70%.

upscattering in

for use on the

-3-

co~ms

Page

Abstract . . . . . .

Introduction . . . .

Cross Section Input

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The Equations for Group Collapsing .

General Description of the Code

Code Details . . . . . . . . . .

Input. . . . . . . . . . .

output . . . . ● . . . . .

Operation. . . . . . . . .

Operation on IBM 7090. . .

Results . . . . . . . . . . . .

Appendices . . . . . . . . . . .

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-5-

While many-group cross

INTRODUCTION

sections are necessary for computing a large

variety of problems with a single set of cross section parameters, it is

often desirable to reduce the nuniberof groups used for particular problems. Multidimensional S_ and diffusion codes are beccnningavailable

11

but are time-consuming with many

dimensional problems must be run

or perturbation effects, or when

energy groups. Where many Sn onefor parameter studies, for temperature

coupled to hydrodynamic codes, specially

tailored few-group cross sections would be advantageous.

George Bell.has suggested (internal memo, July 3, 1958) recipes for

collapsing many-group parameters assuming a many-group flux spectrum.

This can be obtained

or approxiwted, for

pendent) equations.

from a single many-group calculation for the system

~le by SOIVing the infinite medium (space indeA code (ZOT) has been written which will collapse groups according

to a given flux spectrum or using a self-generated infinite medium flux.

Code details and the results of several test cases are given.

-7-
CROSS SECTION INPUT

The code is designed

section format. For each

script g and running from

lowest) the neutron cross

aacl

aac2

●

●

●

aaci

‘f

atr

●

●

●

for the standard Los Alamos Sn transport cross

energy group (denoted by subscript or superg = 1 for the highest energy to G for the

sections are entered in the following order:

1

optional activity (at) u’s} eOgO, u

‘J p

J

,

.

\ upscattering from groups of lower energy (higher

v(neutrons/fission) times the fission cross section

the transport cross section (occasionally labeled Ug)

scattering within the group

‘g+l,g J

%? I

‘g-l,g

ag-2,g 1

downscattering

● the group g

●

●

from groups of higher energy to

-8-
The activity a’s are not used in the solution of the transport

equation, but are available for calculation of activities from the

results of criticality calculations. The most commonly appearing one

is aa (absorption).* In the solution of the transport equation the

absorption is accounted for implicitly in the transport cross section

u..> which includes a-. Note that through error or intent, the absorpb.r

tion used by the

appesx as one of

derived from the

a

transport code maybe different from that which may

the activity 6’s. We shall always deal with the Ua

transport and scattering U’S:

L

~%=% “

a ‘tr - ‘K%

all gt

where all gt includes g’ = g. The

downscattering for each group will

position in the table

called ht} hs~ and hj

(1)

number of activity a’s and up- and

be given implicitly by noting the

and the last a t If these are

% )%”

respectively, then:

number of activity U’S = ht - 2

number of upscattering cr’s= hs - ht - 1

number of downscattering Uts = hl ‘ hs.

*

This one is required by the Los XlzunosDTK transport code.

-9-
The ZOT code will take the many-group cross sections for elements

or mixtures and reduce the nuniberof groups to K(K S G) by combining

some of the groups according to equations given latero The new groups

must have energy limits which are a subset of the many-group limits. We

shall use k to denote the few-group energy index (and i for the u position,

analogous to h for the many-group set). Thus each group k will be composed of one or more of the groups g of the input u’s. For example, the

first of the few-group set (k = 1) might be composed of g = 1, 2, and 3

of the input many-group set. Our equations will.use a simple summation

sign to indicate a summation over all g in a particular k group.

THE EQUATIONS FOR (ROUP COIJ.APSING

Fission spectrum (fraction of fission neutrons out in each energy

group)

(2)

gink

Activity and fission cross sections are weighted linearlyby the

(3)

-1o-
Transport cross section

or

Both options (inverse and linear averaging) are available.

Transfer cross sections from group k t to grOUp k

‘k’)k = x

qgt ugt,g

/x

Tgt

gl inkl g’ in k’

For the

from Eq. (1)

=k

a

gink

(4)

(5)

(6)

_-~ouP set> absorption cross sections (Ua:S) are found

and are collapsed with linear averaging

=E,g U:/x,g (7)

These are sufficient to define the new set. The elastic scattering Uw

is determined from the other few-group constants by

(8)

-1.1.-
For conciseness in annotating the code, we define

(9)

Different cross sections may be computed for each region (i.e., core

and reflector) separately, but a single velocity spectrum is used for a

given problem, and this must be weighted by the total fluxes in each

region. The region volumes are used as a measure of the total flux.

(lo)

The infinite medium fluxes (go) canbe generated by

( )

o

‘g +

-=fd%=xg x ~

8+69;8 6

(l-l)

6@+f3

These are solved successively from the highest energy group until

groups with nonzero upscattering are reached, upon which the remaining

equations are solved simultaneously.

-12-
GE’NEML DESCRIPTION OF THE CODE

The code is written for the Floco

and is intended to be fully compatible

routines. The code accepts multigroup

II assembly system* (W-2339)

with the Floco II assembled SNG

cross sections and input data on

atomic composition and computes collapsed group parameters for the mixtures described for each special region. An option allows collapsing

the element microscopic cross sections separately. The code will accept

flux spectra as input, will compute infinite medium fluxes, or can use

the flux used in the previous spatial region (mixture) regardless of its

source. The volumes can be given directly or can be computed from the

coordinates for planesy infinite cylinders or spheres. The code assumes

there has been sufficient size allotted to the up- and duwnscattering in

the output groups and will stop with an on-line comment if this is not

true. The many-group set is divided into a few groups, each containing

one or more of the original groups according to the wishes of the user.

The input and output are printed off-line (on-line if sense switch#6

is down), and the output fission spectrum, velocities, and cross sections

are punched on-line, suitable for direct inclusion in the new Sn codes.

(They may be used in the F1OCO I version of SNG by placing nine punches

in columns 3 and 21.) The code will normally average (utr)‘1 but will

*This will.run on the IBM 704 or IBM 7090 with the appropriate Floco II

assembly program. The standard deck is for the 704; modifications for

7090 operation are discussed in a later section.

-13-
average atr if requested. In either case, a comment will be printed

describing which was done.

CODE DETAILS

Z?l&k

The input is divided into two parts: the parameters which precede

the code and the data which follow it.

The parameters determine the sizes of data storage blocks and are

used in determining exits and loop lengths in the code. They consist of

information on the size of the problem (e.g.} number of mixtures),

options such as the method of transport weighting and the cross section

table size. Parameters are put on Floco cards, following a “load psmmneters”

pseudo-instruction (*OOOOSOO, see W-2339 and exsmple in Appendix 1).

There are three sets labeled FOO, GOO, and KOO, each requiring a load

parameters instruction. All are fixed point numbers. The ccxlewas designed originally to form mixture macroscopic cross sections in a manner

similar to the SNG code. This requires two tables whichwe shaXl label

NO and MO. The NO table contains a fixed point identification number

(I’D#)for each region, followed by the ID numbers of the elements in that

particular region. The elements are numbered implicitly by the order in

which they are input. The MO block contains the atomic densities corresponding to the elements in each region and zeros in the positions

-14-
occupied by the mixture numbers in the

the example (Appendix I). The lengths

quired for input parameter P05.

NO table.

of the NO

One could get a’s for collapsed microscopic

This is illustrated in

and MO blocks are reelements with this

arrangement by placing each element in a separate region with an atom

density of 1.0. However, since this is a common use of the code, an

alternate way to obtain these U’S with simpler input has been built into

the code. This is signaled by letting the mixture specification parameter

P05 (or N) be zero. The number of regions R (P02) is put equal to the

number of elements E, and P03 is input as 2E. There is no need for certain

of the data blocks (NO> MO, FO)j and only one set of weighting fluxes

I

need be entered for all elementso

1. Parameters

Position

Pol

P02

P03

P04

P05

P06

!3!?!EL

PID

R

M

w

N

T

Description

Problem identification number.

Number of regions (or number of elements for

element calculation).

Number of mixtures + number of elements

(or twice rnmiberof elements for element

calculation).

Volume specification, described later.

Number of mixture specifications, i.e., length

of NO and MO tables (N = O for element calculations).

Transport a averaging O for inverse, 1 for

linear average.

-15-
Parameters, continued

Position E

Gol G

G02 ‘t

G03 hs

G04 ‘i

G05 u

KO1

K02

K03

K04

2

3

4

K

‘t

is

‘1 I

Description

Number of input groups.

Position of atr in u table”.

Position of a

gg”

Position of last u in a group (number of a’s

per group).

Number of groups with nonzero upscatteringj

assumed to occur in the lowest energy groups.

Output cross section parameters (similar to

input group parameters, but may have smaller

vslues except for ~). The equivalent of G05.

is not needed.

W, Volume Specification

Meani~

Volumes are supplied inWO data block.

Planar distances of regions are supplied in

WO data block” code will.compute volumes

V = (ri+l- rij and place them in WO data block.

Cylindrical radii supplied inWO; code computes V = (r~+l- r?), etc.

Spherical radii supplied; V = (r~+l-r~)~ etc.

Volumes are not supplied; velocities are

cmnputed separately for each region.

-16-
2. Data

The data follow the code and are on Floco cards preceded by Floco

“load data” pseudo-instructions (*OOOOSO). The order of the data blocks

is immaterial. Binary cards (e.g., flux dumps) maybe

Floco “load data” card if they contain the data in the

loaded behind a

correct number and

order.

Block

co

FO*

-t

NO*

MO*

Wo

so

Vo

Binary card addresses will be ignored.

Number of

Description =

Entries

Group separation, a table giving the fixed K

largest value of g in each output group.

The flux source for each region fixed R

o -- flux supplied

1 -- calculate = medium flux

2 -- use flux from previous region.

The weighting fluxes for each region. floating

The mixture specifications, similar

to the SNG input. For each region

there is an identifying number, followed

by the labels of the elements in that

region.

The atomic densities (x10’24) of the floating

elements in the order given in NO.

Zeros in the positions corresponding

to region numbers in NO serve to delimit the regions.

Volume or radius input. floating

Input fission neutron spectrum. floating

Input group velocities.

*

Can be omitted for microscopic element

t

Only one set (G entries) needed

floating

calculation.

for microscopic

GXR

N

R

G

G

element calculation

-17-
Block Description

Po The input (and mixture) cross section

block. The elements are nuttibered

implicitly by the order in which they

are placed in the input deck. The

regi-ims

nunibers

the DSN

1).

are labeled ~y consecutive

beginning with E + 1, as in

code. See example (Appendix

QQs&

Nutriberof

Type Entries

floating Input = hl x

GxE

Total = hl )(

GxM

The output includes off-line (cm-line if sense switch #6 is down)

listing of all of the input blocks, descriptively labeled and of the

mixture cross sections (in the PO block) and the mixtum absorption cross

sections. This is folluwed by a print of the output fission spectrum,

velocities, absorption cross sections, and titure cross sections.

The fission spectrum, velocities, and mixture cross sections for

each region are punched in that order on separate cards (or blocks of

cards), ready for direct insertim into the DSN code. Cards may SJ.sobe

used in the Floco I SNG code by putting nine punches in columns 3 and 19.

Should trouble arise, one can obtain an input print by transferring manuslly to (1016)8 and pressing start twice.

put pri.ntby setting sense switch #6 duwn

(1017)8 mdpUShing start twice.

When the calculation is finished, an

One can obtain an on-line outand transferring manually to

on-line statement to that

effect will be printed. Push@ start will then result in an cm-line

print of the storage map giving locations of sll code and data blocks.

-18-
@eration

The present deck (10-30-62) has aid.necessary loading and transfer

cards in it. The three parameter cards follow Z(YI’card number 001, and

the data cards follow card number 076.* The Z(YT.deck should be preceded

by an on-line identification card to identify the user on the off-line

listing. ZOT card 00D calls Floco II from the Los Alsmos utility tape 1,

and may be replaced by a Floco II card deck.

Running time -- S 1 minute per case + readin time, unless there are

more than 10 upscattering groups.

Problem size -- for the 8K machine about (4000)10 words are available

for data. The largest block will be the input and mixture cross sections

(PO) which will behl x Gx (E+ R) numbers. Almost &ll problems can thus

be done on an & 704.

stops -- the only programmed stops are for the cases in which

insufficient down- or qpscattering has been allowed in the output groups.

The code will print an on-line comment and stop. One can then transfer

to (1016)8 to obtain an input print. There is an error stop (usually

insufficient space)

divide checks which

Sense switches

in the matrix solver subroutine, and three possible

are described in Appendix II.

-- setting sense switch #% down causes on-line

printing of both input and output. An on-line print of the results can

be obtainedby transferring manually to (1017)8 and pushing start twice

(with sense switch #% down).

*

This is a chsmge from the earlier (9-09-59) deck.

-19-
Operation on IBM 7090

The ZOT deck (001 to 080)

7090. However the appropriate

wilJ work without

Floco II assembly

modificaticm on the

system must be used,

and therefore the ZOT 000 card, which is an XX Floco 2 card for calling

the 704 version frm tape, must be replaced by the equivsJ-entfor the

7090. This is a set of two cards (2-FL2 01 and 2-FL2 02) for celling

Floco from tape, or a master set of cards contiinti Floco for we if

it is not already on the utility tape in the Los Alsmos format. Note

that header or identification cards follow the F1OCO II cards, -Q

the deck arrangement

‘2-FL201

2-FL2 02 }

Floco 11, Cdl

Header Card * in column 1,

ZOT 001 Initialize

Input, etc.,

in from Los Alamos 7090 utility tape.

followed by name, phone, etco

as in 704 version.

RESULTS

A series of DSN transport calculations were

the accuracy of the reduced cross section sets.

made to investigate

Few-group results are

typically within 2% of the many-group results} but each new situation

should be checked, especially where the spectrum changes rapidly in

-20-
space. Some typical.results dbtained in 1959 with S4 SNG trsnsPOfi

calculations are listed in Table 1. Fuz%her calculations are presently

under way to study the extent of application and the effects of varying

the group spacing, the method of averaging the transport cross section,

etc. For example, a 3 group calculation of the C/U = 2hO0 base sphere

with different group aggregations (6, I.1,1) gave only 0.4$$error using

fluxes generated in an18 group ~ transport code, compared to 2.5%

error with the spacing (6, 6, 6) as listed in Table I. However, the

(6, 11, 1) spacing with infinite medium fluxes appears to give a larger

error (7%) slthough this result is difficult to understand and may be

in error.

-21-
Table I

Bare U235 Sphere

fGroups*

6

2

2

1

1

Flux Source

SNG 6 group

00 medi~

SNG 6 group

00 medium

Radius

8.686

8.732

8.742

8*776

8.753

Sign, $ Error

+0.53

+0.65

+1 ● 03

+0.75

Bare Graphite Sphere C/U= 300

# Iterations

22

15

15 .

19

16

# Groups*

18

6

6

3

3

Flux Source k

eff

. 0.9700

18 group SNG o.g6yl

00 medium 0.9778

18 group SNG 009582

cm medium o ● 9883

Sign, ~ Error

-0.7

+0.8

-1.15

+1.9

Bare Graphite Sphere C/U = 24OO

# Groups* Flux Source k

eff

18 0.967

6 18 group SNG 0.934

6 m medium 0.950

3 18 group SNG 0.943

3 00 medium 0.984

# Iterations

13.9

127

126

136

122

Sign,”$ Error I #Iterations

z

-3.4 77

-1.7 75

-2.5 I.ls

+1.7 I I

*

Each of the collapsed groups contained equal nunibers(3 or 6) of groqps of

the 18 group set.

-22-

-1
Appendix I

Consider an H20 reflected, H20 moderated sphere, for which it is

desired to reduce the Hansen-Mi.l.ls18 group cross sections to 3 groups.

There are thus two regions

Atom densityx 10-24

H

o

&35

with the following composition:

core Reflector

0.0663 0.0668

0.0332 0.0334

l.288x 10-4

Assume one wishes to compute the infinite medium fluxes for the core

and reflector compositions

sections and that the core

weighting the velocities.

to use in weighting the 3.8 group cross

and reflector radii wi~ be supplied for

The three output groups are chosen to contain 6, 9, and 3 input groups, respectively, starting from the high

energy end. Parameters and data for the abuve problem follow on F1OCO

ccd.ingforms and are included in the ZOI decks.

-23-
FLOCO 704 77 78 79 80 PROBLEM kU315@f2

PROGRAMMER DATE PAGE

-24-
FLOCO 704 77 78 79 eo PR08LEM I

1 1 1 1

PROGRAMMER OA7E PAGE

IllC OPERATIW AooRESS REMARKS c OPERATION AOORESS REMARKS

I I

1!! PRS]XR

, d 1!! PRs XRSI I

I 2 3 4 !I 6 7 0 9 I 2 3 4 5 6 7 6 9

0 9 * s o 0

1 (a ,A

2

3

4

5

6

7

[

o

I

2

4

s

6

7

1-

2

3

4

5

6

7

—

—0

I

2

3

4

5

6

7

—

0 9

* P 0 0

I I p,

mlis card fc111.Owed bv 18 R~uD 2 m

3 .?a Croas see’i nq n the order, H, ~ a

Ix--fwl “? I I I I I

I 1 1 1 I

i

I I I

I

-25-

Appendix II

ZCICCede Listings and Flow Diagrams

The coding is relatively simple and straightforward except perhaps

where the transfer cross sections u are involved. Flow diagrams are

e’g

given for those cases and for the master or flow code. Annotated listings

are given for all code blocks, as well.as summaries of the data and code

blocks.

Summary of Data and Code Blocks

Data

AO (Al)

A2 (A3)

co

FO

F2 (F3)

F4 (F5)

GO

1{0

m (M2)

NO

Input absorption cross sections by region.

Output absorption cross secticmusby region.

Separation of output groups.

Flux source table.

Many-groqp flux by region.

Few-groqp flux by regim.

Table ,ofthe output groqp corresponding to each

input groqp.

Atomic density table.

Matrix for flux tith upscattering.

Mixture composition table.

-27-
Data (ccmtd.)

Po (Pi, P2)

QO (a, Q2)

Vo

V1

V2 (V3)

Wo

Code

801

803

804

807

806

8Q7

810

811

812

813

814

815

816

817

Many-grouQ cross sectims by element and mixture.

Output cross sections by mixture.

Many-group velocities.

Few-group velocities average over volume.

Few-group velocities for each region.

Volume or radius table.

Flow cede (master code).

Data assignment.

Form mixture 0’S.

CsJ.culatemany-group fluxes} Tge

Set region addresses.

Calculate many-groqp absorption a:.

Cdcdate t~sfer cross sections ‘k!k”

Collapse cross sectims aac$ Vaf$ atr~ aaO

Cslculate few-group self-scatter- ~~”

Generate cde constants.

Calculate fission spectrum Xk.

Cslculate velocities.

Input print.

Output print and punch.

-28-
Code (contd.)

622 Place element a~s in

823 Set flux for element

regim blocks.

calculation.

843- 867 and 871 Print remarks

870 Matrix solver

and headings.

subroutine LA-S885.

TO1-T07

TIO

TSL

T12

T13

T14

T15

T16

T17

T20

T2J.

T22

T23

T24

T25

Use of Temporary Storage Block TOO

Temporary use only.

a:

region base address and region index in decrement.

(pgregion base address.

%

regicm base address.

gk regim base address.

vk region base address.

ua region base address.

aa regicm base address.

Not used.

‘1 - ‘s

# elements

hs-ht-l

hs - ht

ht+l

it+l

-29-
Error Stops

Location

octal

5314

>427

5461

5617

5674

63o4

Region Symbolic

805 x47

805 Y62

805 Z14

810 x46

&l.o x53

815 X50

Type

divide check

belt

divide check

halt

halt

divide check

Cause

o. ‘g - ‘w =

G calculating

14atrixerror.

size.

-

Not allowed

flux.

Stop, check

~k = L

o. Check flux

% =

input●

Too few upscattering cross

sections allowed in output

(on-line print).

Too few downscattering cross

sections allowed in output

(on-line print).

v.

L

Vr v; = 0. Check volume

and velocity inputs.

ZUI Deck

XX Floco 2

or

Zol?000 Floco 11 tape calling card.

Z(YJ?001 Initialize, allow space for parameters.

Input Parameters POO, GOO, KOO cards.

Z(ZC002 Assigns temporary storage TOO, 308 spaces.

003 Assigns formula space 1008 for 801, 15008 for 804~

508 for 803) and 4208 fOr 870.

004 tO 025 Remarks for printing headings.

-30-
026

027, 028

029

030

031- 041

042

043 - 073

074

75, 76

Input

77

78, 79

Z(YIDeck,

Load data assign

Data assign code

continued

code (803).

(symbolic binary).

Execute data assign code.

Load matrti solver (870).

Matrix solver (binary).

Load formulas 804 to 823.

Formulas in synibd.icbinary.

Losd flow code 801.

Flow cede.

Data.

Transfer to flow code.

Blank.

-31-
801 FLOW CODE

Q

Printi.qput and

srkture U:S

,

YEs

Set C1.uxes Cslc. fluxes

822 &15

\ /

I

Cslc. @ 807

I

1“Advanceregion index I

I output 817 I

I

PRINT CONCLUSION m STOMGEw I

-32-
&Fj cflr.lcoLAm FrmEs q)g

~ W, matrixto solve for

+=+===,

*

I*I ER5zl

o

Oet ag,g(h) v

I - I

w

-33-
m.o ag,,g~

1 + g (Ins=?- 2)

I

I

set addresses

I

I

1

Save g

I

+

I

1

set, d.ecnmenta h

I

I I

YES Fiestcme6

‘“ -

A

‘a= I

s

g~G?

NO

Returnto flewcde

I

●

m

1?

I

-3+
Xoo E 8U1

Xol rSX4816

X02 TSX4813

X03 TSX4814

X!34 CLA PL6

X05 T7E Xll

X06 rsx4974

X07 40CO0845

[

Xlo TRA X13

X11 TSX4974 3

Xlz 4ocooe44

X13 CI.A PC5

Xi4 TNZ X17

Xi5 TSX4822

r

X16 TRA X20

XL7 TSX48C4 1

4X20 TSX4974

X21 Oooooabl

x22

X23

4f3fJooPc

LXA24C1

1

X24 SX02T1C

X25 TSX48C6

X26 CLA PC5 %

X27 TNZ X32

X30 TSX4823

E !$2

X36 rsx4811

x37 TSX481O

F’LOWCODE

Linear Utr?

No

Element talc.?

Transfer on “no”.

Print input and

mixture sigmas.

1 -region index.

Save.

Element celc.?

No

Fluxes s~plied?

Transfer on “yes”.

Cdc. flux.

X40 rSX4812

x/,1 LX D211O

X42 10012X43

d

r + 1 + region.

X43 7P022X24 1 All regions dine?

)(44 r~xl+815

x45 TSX4817

X46 FPR Normal program stop.

x47 TSX4$J76 Printstoragemap.

X50 ● 4801 . Transfer to flm code.

-35-
XOO 8 8C4 FORM MIXTURE u’S

Xol LXA14CL l+i

XC2 CLAINC Ni

X03 STA rCl -b Save Ni. 2

X04 CL AIVC 14i atom density.

X05 TNZ X14

X06 LXA2T01 1

Ni-)J

X07 CLA W.)

x 10 SU132P2

)

Set address

Xll STA X26 fnr region sigmas.

X12 STA x27

X13 lRA X31

x 14 STC TC2 J

X15 LX A4TC1 Ni -) index.

X16 CLA Po#

X17 SUB4P2

1

Set address.

X20 $TA X24J

X21 LX A2402

x22 CL A2P2 1

Puthx G

X23 PAX2 in ini ex.

X24 LCC2CC0

X25 F&’P T02 % 1

X26 FA02SCC Form 14ix a.

X27 ST020CC

X30 20012X24 &1

X31 10011X32

d

).dvancei..

X32 7P051X02 2

x33 LXQLi457

X34 TRA4001

-36-
XOO 8 8C5

Xol SUB 4C1

X02 TNZ 221

__ X03 CLA Tll

X04 STA X42

X05 STA X50

X06 CLA GC1

X07 SUB GC5

Xlo. ALS 022 -.

Xll STD X52

X12 LXA1401

X13 CLA TIO

X14 SUBIP1

X15 STA X37

. x16 SUB GC2

X17 STA X23

X20 ACD GC2

X21 SUB GC3

x22 STA x24

X23 CLA OCC

X24 FSR OCC

X25 S10 TG3

X26 CLAISO

x27 S10 T02

X30 SXOITC1

X31 LX02TC1

X32 20012X34

[

x33 TRA X46

x34 LXA4GC3

X35 1C014X36

X36 3G044X46

X37 CLA40CC

X40 TZE X46

X41 LRS 043

X42 FPP2CC0

X43 FAO T02

x44 STO TC2

X45 200L2X35

X46 CLA TC2

x47 FCH TC3

X50 STQ1OOO

x51 10011X52

X52 70C01X13

x53 CLA G05

x54 TZE Z(IL

x55 CLA Tll

(xIcurAm FLUXES

Use flux fram previous region?

YEs

NO, CtiCa.~UX. – . . . .

~~~.%Ips with only downscattering= Gd.

.-— — ----

ar base.

ur(g) base. \ 2

..

‘i3

aim

$

- agg

g hindex 2.

g’= g-l

~t=o

hs+h

h+l-th

h > hf7

No, Ogl ~g 7

1

Pgl Ugt>g

~Qggag*g”

d=l+fy>gt=cn $1

xv.:“gtg/”g - “gg

Pg .. .. .. ..-

g+l+g

g < Gd? No d2

Upscatteringpresent?

YES

X5_@. .SW.Y?5 Set w. .@___ @Ut&_q._. . . . . . . . .

x57 STA Y77

X60 STZ T04

X61 LX01T04

X62 1COL1X63 ~+~’~ j% ‘rm ‘4

.. x 6.3 CLA Yl*__ Set addresee~~___. % 2

X64 SLB1P2

X65 STA Y1O

fromY32

x66 STA Y23

X67 STA Y24

-37-
X70 SUB GC5

X71 SUB 4CI

X72 STA YL2

x73 51A Y36

X74 STA Y37

x75 SXD1T04

X76 LX D2TC4

x77 1000?YCO

Yoo SXO?T05

YO1 3G012Z32

Y02 CLA TIC

Y03 SUH2PL

Y04 51A Y07

Y05 STA Y15

Y06 LXA4GC2

Y07 CLA4CC0

Y 10 S101000

Yll CLA2SC

Y12 S10 CCO

+Y13 1CC14Y14

YL4 3G044X61

Y15 CLA40C0

Y16 S10 TC1

Y17 SX04Y21

Y20 1GC31Y21

Y21 6CO01Y27

Y22 TRA 234

Y23 FAD1OCO

Y24 STOIOCC

i \ Y25 LXOLT04

—Y26 TRA Y13

Y27 LX02TC5

Y30 SX04Y32

Y31 1GC32Y32

Y32 .5CC02X61

Y33 LxnlTc4

Y34 L~Q TC1

Y35 FPP2CC0

Y36 FAO 000

Y37 STO CCO

—Y40 TRA Y13

Y41 bRS 001

Y42 STO Y57

Y43 8!?s C21

Y44 Cl+s

–..?45. AOO Ml*

Y46 STA Y64

Y47 LXA1401

Y50 LX02P2*

j -index 2.

g=j+cd

Save g.

g> G? Exit of matrfi set.

No

Xg +Mn+l,j

h+l+h

h> hif J

1 YRS

No

Index i = j + hs

i=j+h~-h

Patch.

-agsg +Mij -+Mij

Restore j.

g+h8

g+h~- &h=g*<O? 2

NO, rkstore j.

Pgt Cfgl-+g + %+1*J-+%+1,3

From 233

.

‘b .-...-Y52 .\;:;;;. _’_. ~

Y53

Y54 STQIM1 – Store matrix to

Y55 2@O12Y56 with subroutine

. Y-5.6,~OOl~Y5.7-.- . .~:%W.r.~ts*

agree

input

-38-
Y57 70C01Y51 c?1

Y60 LX01457

~lSX*B7Q_.., . Matrti solver.

Y62 OHPR Error stop.

Y63 0G05 001

Y64 4000 CCC

Y65 9GC52Y63

Y66 SXO1457

_Y.&Z ..C~A Y6!t. . .. .. . . . .. . . . .

. Y70 CHS

Y71, ADD G05

Y72 S~13 Y76

Y73 LXALG05

—.Y74. LxD2x52_-.__. ..—...-

Y75 10012Y76

Y 76 CLA1OOO

).

Store upscatteringq

Y77 ST02CC0

in regular qblock.

ZOO 2C011Y75 /

_Jol _CLA, .T.l L No_HEJ_J_ze T*

202 STA ZC7

203 STA 213

20/+ STA 215

205 CLM

206 LXAIGOL

LQZ-.-EAOlCCc J ::+~;+z%

Z1O 20011207

211 STO TCl

212 LXAIGOL

$,.=x

213 CLAICCOe =

216 2ooilz13~

~z17 LX04457

I 220 TRA4CC1 Return to flow code

tl__CLA.-Il.~rom X02.

222 STA 227 Use flux from previous region.

I

223 413D GO1

224 STA Z26

225 LXA2GOI

226 CLA20C0

..Z21..5TO2OOO

J

L

230 20C12Z26~

231 TRA 117

232 CLA M2*

233 TRA Y41

_J3,4. .3GC5lY25

235 CLS TOI

236 TRA Y23

237 80002X11

Z40 Slo X77

_– 2.41—TR-O..-xl?...-

242 fiOO02X60

~g,r-1 + TJg,r

..— .. .

From matrix set.

-1 ~ # upscattering

NO, +g*g

Return to cciie.

Patch.

.———— -—---

Patch. - “ “-”

groups?

243 CLA V2*

244 STA X64

245 TRA X61

-39-
Xoo

Xol

X02

X03

X04

X05

X06

X07

Xlo

Xll

X1.2

X13

X14

X15

.X16

X17

X20

X21

x22

.x23

X24

X25

X26

X27

n 8C6 SIIF REGION ADDRESSES

LX D2TIO r d j.nda 2.

CLA F2* ●% base address.

SUB2F3

STA Tll -’?= base sddress.

PXD2

PCX4

1T214X1C r+E+lndexb.

CLA f’o? -.. -... Ug base address.

SU134P2 Urg base address.

STA TIO

CLA F4*

SUB2F5

%

STA r13 %

CLA 00+ ak

SU82Q2

STA T12

CLA V2*

SUB2V3

STA T14

CLA AO*

SUB2A1

STA T15

CLA A2*

—.—.

ah

‘k

.% ~~

aa(13)

aa(g )

aa(k)

-X30 ..SUB2A3 __

X31 STA T16 “ax(k)

X32 LX D4457

x33 TRA4001

X34 80002X04

x35 CLA T21

x3b ALS 022

\

Patch to

x37 STD X07 get E in

decxement.

X40 TRA XC5

-40-
XOO 8 807 CAIxxm.m Ug

xO1 CLA T15 ., ~: adtiess%ase.

X02 STA X16

—...X03 STA.AL7 .. ——.

X04 STA X33

.X05 STA x34 .

X06 LXA24C1 1:(3

X07 5% D2T01 . . .Save g.

..–.XLO_...CLtI- IJ.C.._-...-._–_–..–-——\ 1 -—

Xll SUB2P1

‘(g,r)

sddress.

X12 STA X31

X13 SUB G02

X14 STA X15

XL5 CLA 000

-- X.6 -. FAD2C!G.O. –-_.~%; –=s%__ —_.._..

X17 S102000

X20 L“XAi T24 ““ - h-t “; “1 “+ ‘h

X21 SXD1X23 i * dec.

X22 1GC32X23 g+h~

2~A9QQ2.X 3 ~ \

X24

E-+++-= g’ 2

PX02

. X25. ARS. 0.22

X26 SUB GOl g#. G

X 27 TZE X3L gt = G?

L

x33 FAD2”OC0 NO-aa - agIg + u~

x34 ST020C0

X35 10011X36 h+l+h

_._~6 ~.G04 1X4.3. . . h .~.hl

x37 LX02TC1 Restore g.

-41-

X40 10012X41 g+l+g

X4L 7G012X07 g~G? d

1

X42 TRA4(IG1 Return to flow cede.

x43 Lx.02T01. . . . .Restore.ge

ti-

.

X44 TRA X21 2
Xoo a 810 CALCULATE u,{, ~ k

Xol LXA2401 l+g

X02 TNO X04 Test accum. overf.lm.

X03 TRA XC4

X04 CLA Tll 9; addr’=ss”

X05 STA X63

X06 STZ TO1

X07 STZ TC2

Xlo

Xll

X12

X13

X14

X15

X16

X17

CLA T13 U$ address.

STA X64

\x02TCl Save g.

CLA TIO

x

CI$ address. ~

Sl,B2Pl

STA X62

CLA2GC

STO TC2

X20 LXA4T02

X21 C.LA T12

x22 SUB4QL

X23 STA X71

X24 STA x73

X25 STA T30

x26 LX A1T24

X27 SXOLX31

- X30 1G032X31

X31 60007X77

X32 3GC12X74

x33 CLA2G0

x34 STO TC3

x35 SUB TC2

X36 TZE x74

x37 CHS

X40 ADD KC3

X41 STO TC4

X42 LXA4TC4

[

x43 3K024X4J .

x44 TSX4975

X45 4COO0847

X46 HTR Y02

X47 3K044X5L

[

X50

)

TRA X54.

X51 TSX4975

X52 40000846

x53 HTR YC2

x54 CLA T04

x55 VCP

., X56 ~op .. . . .

x57 NOP

X60 STO TC4

X61 LXA4T03

X62 LI?QIuOO

X63

1

Fk’P2000 .,

X64 FOH4000

X65 STCI T07

x66 CLA TC7

X67 Vop . . . . . .

o&ad&ss.

i=k- kt + is

i+indexb.

i> it’f

Print.

Too few upscat.

Print.

Too few doiinscat...

-42-
X70

X71

,x72

x73

x74

x75

X 76

x77

Y“oo

Yol

Y02

Y03

LX A4TC4

FAD40C0

‘W!P

ST040C0’ -

LX02TC1

LOOL1X76

7GC41X27

LXD2T01

LX04457

TRA4C01.

Y

e tore i.

Tg’ Ug’ +g/~k’

. .

Uk?+k

Restore g.

h+l~h

h<hl d

1

17e~toreg.

-—-.. ----

g+l+g

g>G7 “2 No 2

Return to flow cOde.

-43-
Xoo e 811

Xol LXA2+C1

X02 LXA1401

X03 CLAICO

X04 aLs 022

X05 STD YC7

X06 CLA T13

%07 STA X42

x 10 STA x43

X11 STA Y24

X12 <TA Y31

XL3 STA Y33

X14 STA ‘f40

X15 CLA T14

X16 STA X50

X17 STA X51

X20 CLA 115

X21 STA X52

x22 CLA T16

X23 STA X54

X24 STA X55

X25 STA Y23

X26 STA Y25

X27 CLA TL1

X30 STA X40

X31 CLA T12

X32 SLB101

X33 STA Y02

X34 ST’A Y03

x35 SUB K02

X36 STA X75

x37 STA X76

X40 CL A20C0

X41 STO TCI

X42 FAOIGCO

x43 Srolooo

x44 CLA TOL

x45 F@P2VC

X46 STQ T07

x47 CLA T07

X50 FAO1OCO

X51 ST O1(IOO

X52 LCQ2UO0

x53 FMP TOL

x54 FAO1OCO

x55 STOIGCO

CALCuLAm (+C, v4> a:,?V& ai$ l+g l-k

#r

&=

9!+!

C+base.

-. Vk .~,g/vg

C&.

~,: U&

X56 CLA TIO_.. .- .__ . . . . . __

x57 SU132P1 u: base.

X60 STA YCO

X61 SUB GC2

X62 STA x67 Ufr base.

X63 STA X12 .——_.— .

X64 CLA PC6 Linear utr?

X65 TZE X71

x66 LOO TO I

.X67 .. FW..QC.. .--.:$r..-.--.--.-.--.--

-44-
[

X70 TRA X75

X71 CLA 101 Inverse Utr.

X72 FPP CCO

x73 $TQ T07

9Ju&

X74 CLA 107

x75 FAo 000

Xi’b ~ ‘g a% ‘r~~g/% STO CCC

X77 LX A44CI l+index~2 i for uac(i).

‘{00 LDQ40G0 R

Yol FMP TC1

Y02 FA040G0

Y03 ST04000

Y04 19014Y05

Y05 7GC24YC0

Y06 10012YO7

Y07 70002X40

Ylo 10011Y11

YIL 7K011X03

Y12 LXA1401

Y13 CLA T12

Y14 SLBIQ1

Y15 STA Y37

YL6 $TA Y41

Y17 SIJ8 K02

Y20 \TA Y30

Y21 STA Y34

Y22 5TA Y35

Y23 CLAICCC

Y24 FCPIGOO

YZ5 STQ1OOO

Y26 CLA P06

Y27 TZE Y33

Y30 CLA OCO

Y31 FDP1OOO

[

Y32 TRA Y35

Y33 CLAICCC

Y34 FCP OCO

Y 35 STQ 00C

Y36 LXA44CI

Y37 CLA4CC0

Y40 F~PIIJOIJ

Y41 STQ40CC

Y42 100L4Y43

Y43 7K024Y37

Y44 10011Y45

., ..Y45_,7KOllY13.

Y46 LX04457

Y47 TRA4L301

Y50 90016YC5

Y51 90016Y43

Linear otr7

l+iudexk (i).

b1

i+l+i

i>ht-l? e

1

k+l+k

..E.K?... &2

Return to flow code.

Dec. - l+dec. of Y05.

OeC. - 1 + dec. of Yb3.

-45-
XOO 8 8L2 a,.,. CALc.

Xol STZ TC1

r~

X02 CLA r16

k

U_ address.

X03 STA X20

a

X04 LX A2+C1 i+k

X05 SXD2TC1 Save k.

X06 CLA r12 \

X07 SUB2Q1

Xlo STA X$2

X11 SUB K02 ‘k

address.

X12 STA X17

X13 hcn K02

Xlfl SUB KC3

X15 STA X21

%

address.

X16 STA X22

XL7 CLA 000 ‘k

X20 FSB20C0 ‘k - ‘a

X21 rAD Oco + Ukk

x22 STO 000

x23. LXA1T25 . . ;’%% .

X24 LX02T01 Restore k.

X25 SX01X27 x

X26 1K032X27 k+is @

X27 6CO02X51 k+i8-i=k’

X.30. 3K012X47.. _ IS k? ~K7

X31 CLM No

X32 PX02

x33 SUB TCL

x34 TZE x47 IS Ic’ = k7

x35 rLA T12 NO,

X36 suB2cl...__ . ..__— —

x37 $UB K03

X40 sTA x44

X41 STA X45

X42 CL SICCO - aklk

x43 QOP

x44

-~di ““

FAD 000 “ +

x45 STO CCC

X46 WOP

x47 100L1X5O i+l+i 4

X50 7K(141X.24 i>il? 6

No 1

X51 LXD2TC1 YES, restore k.

X52 10012X53 k+l+k

x53 7K012X05 k>K? d

No 2

X54 LX04457 YES, return to flow caie.

x55 TRA4CCL

-46-
XOO 8 813 GENERATE CODE CWYCAN!CS

Xol LX A24C1

X02 LXA1401

x03 CLA 4G1 ...._.–—--—---

%04 STO TO1

X05 CLAICC

X 06 ALS 022 % 2

X07 STO X13

.xJQ CI.A. TCl ._. l?o.m a table

X11 ~To2Go

X.12 10012X13

L

of k correvond~

X13 70002X11 1 to each g.

X14 400 .4C1

X15 10011X16

X16._7KOLlX04 d2 ._.._._–-.--_.. _.. -...—

817 CLA G04 –

X20 SUB G03

X21 S10 120

x22 CLA P03 ‘t - %

X23 SCB p!2.?–-——_ —

X24 S10 121 E= M-R

X25 CLA C03

k26 SU8 G02

X27 S10 T23 h= - ht

.&M. _. SU8 401_.. . . . . ... . . . – --- ___

X31 STO T22 h~-ht-l

X32 CLA GC2

x33 AOO 401

x 34 STO T24 ht+l

x35 CLA K02

- X36,,..., AI?O. ,.4C1 . _ . . . . _ . . .

x37 STO 125 i%+l 212, x23

X40 TRA4001

-47-
x 00

)(01

X02

.X03

x 04

X05

X06

X07

Xll

X12

X13

X14

X15

8 814 CALC. ~ (fission spectrum)

LX A2401. . ..3. +index2.

LX A14CI

‘b

1 + index 1.

..::~:z .2-. .Li.rmp—limi ts. ----.—-

STD X12

CLA2SC

FADIS1

%

“~=~xg

1“ “king

Slolsl ____ —.-

‘ioo12x12

d

7CO02X06 1

1001 LX14

0$ 7K011XC3 2 . . . .

TQA4001

-48-
Xoo d 815 CALC. Vk

Xol CLA PC4 Volme specificationW.

X02 sue 4C4

X03 TZE X54 \i= h, co.lc.v for each region.

X04 CLA f)C4

ko5 TZE X24 W . 0 volumes sum lied.

~Ub LXALf Ll Generate volumes, 1 + fid~ 2-.

X07 STZ 1’02

Xlo LXA1P04. . n+kl= i (regim *).

Xll LPC 421 1.0

Xlz F/4P2h’o, ~

X13 LRS 043

XL4 ?O011X12 L

1 8

2

X15 S10 101

:;; .wl:2___.+. %3+:1. -.

x20” CLi TOL “--”- ‘“” ““- “

X21 STO 102 ri + rj.-l

x22 10I312x23 i+l+i

,.X237p022xlo ..- .._. d

2

24 LXAIKUl K+k (indexl).

X25 LXA2P02 R+index 2.

X26 STZ TC1

X27 STZ T02 %

2

%3Q CLA F+*.- q.base address.

X31 SlIB2F5

X32 STA X33

x33 LPQ 10CO 9: &

1

x34 F!4P2W0

x35 FAD TO1 Xvr P:

X36 STO TO1

x37 CLA V2* v base.

X40 SUB2V3

X41 STA X42

X42 LI7Q1OIJO

X43 FMp2hic.... .

x44 FAD T(I2

X45 S10 TC2

X46 20012X30

X47 CLA TO1

Vk

r

..—....-... .

~ V, v;

r-l+r d

1

Regions done.

X.50 FEH TC2,. Vk. .

X51 STQIV1

X52 20011X25 k- l+k J2

x53 TRA4001 Calc. done, r=urn to flow cede.

x54 LOQ KCL v. for each region.

x55 UPY P02 K

X56 . sTQ_ lol__ _....._ .

x57 LXA1101 Rx Kinindexl.

X62 STQLV2

.X63,200.1,1X60 ) .. . . . ...—--

X64 TRA4C01 Return to flow cede.

X65 80002X15 Patch, LRS not reliable.

.36.6SJ.Q .TOJ..

X67 CLA TO1

X70 TRA XL6

-49-
XOO 8 816 IN-PUTPRIIW

XOL .TSX4974 .

X02 00000850

XQ3.CQOO08.51.. _.–——————--

X04 00000852

X05 OO061PC0 Parameters.

X06 00000853

X.07 00051GO0 . . ..

XLQ-9000085.4 .––.—__ —.—

Xll 00051KO0

X12 COOO0855 .. -- ~~~

X13 00000s0 Fission speCtl’IIl&

X14..00Q0OVC Velocities. -

X15 Orloooco Few-group spacing.

2iM..9_OO.OONQ _—--ELementfmfUureses..-.

X17 0000OPO Ataridensities.

X20 00000856 “’

.x21 00C0OFO Flux eotm=.

x22 Oooooklo Volumes or radii.

~zuow!m~

X24 40000F2 .

X25 LX04457

x26 TRA4001 Re&m.

-50-
XOO 8 817 OUTPLECPRINT

Xol TSX4973. .. . . . .. .

X02 60000862

.__XQ3.. CQCQ Qu?L__–_____– . . . . . .

X04 Cf)(loosl Fission spectrum.

X05 Coooovl Velocity iRectrum.

X06 COOO0871

X07 COOOOF2 Fluxes used.

—310 .Q.of30Q8L4_..._& _—.. — ..

Xll 00000F4 Output fluxes. F4

X12 COOO0860

x13 (JOOOOAO Input absorption.

X14 (10000865

X15 00000A2 Output absorption.

..XL6 CCJOOOQ66 ____ ... -.,

X17 4000000 Output sigmas.

X20 CLA P04 Print velocities

x21 SU8 404 for each region?

~ x22 TNZ X26

“1x23 1$X997.4 YES______

X24 COOOG867

L

X25 40000V2

X26 TSX4973 Punch m- line.

X27 COCOOSL

-51-

—.. x3Q.OQCIOQU.––—__ .—— -

X31 40000C0

X32 TSX4975

X33 00000843

X34 4(10020C0

x35 LX04457

._..&36._T.RA.4O(Il., ._ —-— . .-
XOO 8 822 wcE m.mms IN REGION BmcKs

Xol LX A2P02 E+ index 2.

X02 10C12XO3 E+l

X03 ....CPQ*_Q*_. —.—.——— ..—

X04 STA Xll PO blcck address.

X05 SUB2PZ .,

X06 STA X12 Po -hlx GxE

X07 CLA2P2

X.19. .. P/!x L___ JI$X.MSS. m Q@= L = i.

X11 CLALOOO u element.

XL2 STO1OOO

2

a region.

X13 ?OO1l XIL i -l+i 1

X14 TRA4.QC1. Returp$

-52-
X(IO R 823

Xol LXD2TIO

X92 70012X13

x03._CLA TL1. ___

XC14 STA Xll

X05 ATID GC1

X06 STA X1O

X07 LXAIGO1

:E: ~UX FOR ELEMENTCALC.

If yes, fhk supplied>exit.

NO.>— —---.-—----—.

Set P$ address.

X14 ● 801

-53-