a one-dimensional hultigroup pi code for the bm-704

MSTE~ WAPD-TM-135

AEC RESEARCH AND DEVELOPMENT REPORT

'IMG - A ONE-DIMENSIONAL HULTIGROUP P i CODE FOR THE BM-704

JULY 1959

CONTRACT AT-11-1-GEN-14

BETTIS PLANT-PITTSBURGH, PA. OPERATED FOR THE U.S. ATOMIC ENERGY COMMISSION BY BETTIS ATOMIC POWER DIVISION, WESTINGHOUSE ELECTRIC CORPORATION

DISCLAIMER

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency Thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

DISCLAIMER

Portions of this document may be illegible in electronic image products. Images are produced from the best available original document.

UC-34: Physics a n d M a t h e m a t i c s

T ID-4500 (14th Ed.)

PlMG - A ONE-DIMENSIONAL MULTIGROUP PI CODE

FQR THE IBM-704 . .

H. Bohl, Jr. E.M. G e l b a r d . .= G.R. Culpepper ; P.F. Buerger

Contract AT-1 1-1 -GEN-14

July 1959

Price $2.00 Available from the Office of Technical Servieer,

Department of Commerce,

Washinghn 25, D. C.

.N V r t This document i s dn interim memorandum prepared primarily for internal reference and does not represeh a final expression of the opinion of Westinghouse. When this memorandum is distributed externally, i t i s with the express understanding that Westinghouse makes no representation as to completeness, accuracy, or usability of information contained therein.

L.- . BETTIS PLANT PITTSBURGH, PA. OPERATED FOR THE U.S. ATOMIC ENERGY COMMISSION BY

BETTIS ATOMIC POWER DIVISION, WESTINGHOUSE ELECTRIC CORPORATION 1

STANDARD EXTERNAL DISTRIBUTION

UC-34: Physics and Mathematics, TID-4500, 14th Edition

SPECIAL EXTERNAL DISTRIBUTION

Manager, Pittsburgh Naval Reactors Operations Office, AEC Argonne National Laboratory, W. F. Miller Brookhaven National Laboratory, J. Chernick Brookhaven National Laboratory. M. Rose David Taylor Model Basin, H. Polachek Knolls Atomic Power Laboratory, R. Ehrlich Los Alamos. Scientific Laboratory, B. Carlson New York University, .R. Richtmyer Oak Ridge National Laboratory, A. Householder University of California Radiation Laboratory, Livermore, S. Fernbach

,{LEGAL NOTICE

I. Th is r e p o r t was prepared as an account of ~overnment sponsored work. Ne i the r the Uni ted States, nor the Commission, no r any person a c t i n g on beha l f o f the Commission:

A. Makes any war ran ty o r r e p r e s e n t a t i o n . . e x p r e s s e d o r imp l ied , w i t h respec t t o t h e accuracy, completeness, o r use fu lness of t h e i n f o r m a t i o n con ta ined i n t h i s repor t , o r t h a t the use o f any i n f o r m a t i o n , apparatus, method, 6 r process d i s c l o s e d i n t h i s r e p o r t may n o t i n f r i n g e p r i v a t e l y owned r i g h t s ; or

B. Assumes any l l a b l l l t l e s w l t h respec t t o t h e us8 o t , o r t o r damages r e s u l t l n g t rom the use o f any in format ion, apparatus, method, or process d isc losed i n t h i s repor t .

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CONTENTS

PART ONE: PHYSICS AND NUMERICAL ANALYSIS O F CODE

Page No.

1

I. INTRODUCTION

11. P1 EQUATIONS

III. MULTIGROUP EQUATIONS

IV. T W S V E R S E BUCKLING

V. SPATIAL DIFFERENCE EQUATIONS

VI. BOUNDARY CONDITIONS

Cartesian Geometry Other Geometries Right-Hand Boundary Conditions

VII. METHOD O F SOLUTION

VIII. THERMA~L GROUP

IX. DISCUSSION

X. EDIT O F FEW-GROUP AVERAGES

PART TWO: . PROGRAMMING AND OPERATION O F CODE

I. INTRODUCTION

11. GLOSSARY

Indices-Superscripts and Subscripts Quantities

III. EQUATIONS USED IN P l MG2

Coefficient Routine Iteration Routine Edit Routine

IV. PREPARATION 'OF INPUT

Fo rm I Form 11 Fo rm I11

V. OUTPUT

On-Line Output Off -Line &tput

VI. CARD PUNCHING

Furm I F o r m I1 F o r m 111

VII. OPERATOR'S NOTES

704 Requirements Material Needed to Run One Problem Running Instructions Progress of Program Restar t Force Edit Printing Off -Line One Iteration Option E r r o r Stops

VLII. LIBRARY TAPE ROUTINES

IX. GENERAL INFORMATION

PART THREE: APPENDICES

APPENDIX A: INPUT FORMS FOR SAMPLE PROBLEM, FORMS I, 11, AND I11

APPENDIX B: CHOMP CARDS

APPENDIX C: FLOATING POINT NUMBERS

Input Fo rm Output F o r m

AFFENDIX D: DLAMIC CAllDD IN INPUT DBCIZ.

APPENDIX E: CODE NUMBERS FOR ISOTOPES

List by Code Number List by Isotope

APPENDM F: SAMPLE PROBLEM

REFERENCES

The PI m u l t i g r o u p code d e s c r i b e d i n ? .h is r e p o r t was w r i t t e n f o r t h e ISM-704 i n o r d e r t o de te rm ine t h e accuracy o f the few- g r o u p d i f f u s i o n scheme w i t h v a r i o u s imposed c o n d i t i o n s and a l s o t o p r o v i d e an a l t e r n a t e c o m p u t a t i o n a l method when t h i s scheme f a i l s t o be s u f f i c i e n t l y a c c u r a t e . The code s o l v e s f o r t h e s p a t i a l l y dependent m u l t i g r o u p f l u x , t a k i n g i n t o accoun t such n u c l e a r phenomena as s l o w i n g down o f n e u t r o n s r e s u l t i n g f rom e 1ast i .c and i n e l a s t i c s c a t t e r i n g , t h e removal o f neu t rons r e s u l t . i ng f rom e p i therma I c a p t u r e and f i s s ion resonances, and t h e r e g e n e r a t i o n o f f a s t n e u t r o ~ s r e s u l t i n g f rom f i s s i o n i n g w h i c h may o c c u r i n any o f as many as ' 8 0 f a s t m u l t i g r o u p s o r i n t h e one t h e r m a l g i o u p . The code w i l l a c c e p t as i n p u t a p h y s i c a l . d e s c r i p t i o n . o f t h e r e a c t o r ( t h a t i s : s l a b , c y l i n d r i - ca I , o r s p h e r i c a I geometry , number o f p o i n t s . and regi.ons, com- p o s i t i o n d e s c r i p t i o n , g r o u p dependen t b o u n d a r y c o n d i t i o n s , t r a n s v e r s e b u c k l i n g , and mesh s i z e s ) and a prepared L i b r a r y o f nuc lea r . p r o p e r t i e s o f a 1 1 t h e isotopes i n each compos i t i on . The code w i l l produce as o u t p u t m u l t ~ i g r o u p f l u x e s , c u r r e n t s , and i s o t o p i c s lowing-down dens i $ i e s , i n a d d i t i on t o p o i n t w i s e and reg ionw i s e few-group macroscopic c ross s e c t i ons .

PlMG-A ONE-DIMENSIONAL MULTIGROUP P1 CODE FOR THE IBM-704

.H. Bohl, Jr., E. M. Gelbard, G. R. Culpepper, and P. F. Buerger

PART ONE: PHYSICS AND NUMERICAL ANALYSIS OF CODE

I. INTRODUCTION

Few-group diffusion theory provides the reactor designer with a very convenient computing tool.

Two-, three-, and four-group diffusion codes, progra&e'd for various machines, have been in wide-

spread use fo r some time; It is important, therefore, to understand the range of validity of the few-

group model.

In preparing input parameters fo r a few-group calculation, it is necessary to approximate the

flux spectrum in the different regions of the l;eactor, This cannot always b e done satisfactorily since

the spectrum may change rapidly with position in the neighborhood of an interface. Insofar a s the

flux spectrum is in doubt, the accuracy of the few-group appr.oximation is open to question.

To assess the accuracy of the few-group scheme under different conditions, and to provide an

alternative computational device when this scheme fails, a P1 rnultigroup code, the PlMG code, has

been written for the IBM-704. It should be s t ressed that PlMG was not designed to t reat transport

effects, and that e r ro r s , resulting from the limitations of a P approximation, occur in the PlMG 1 equations a s they do in some forms of the few-group diffusion equations.

IT. PI EQUATIONS

The P1 equations, in a Greuling~Goertzel a&roximation (Ref l ) , may be written in the form

where" - j and cp are the current and the scalar flux, respectively

i is an index denoting various isotopes

q. is the isotropic slowing-down ,density resulting from the ith isotope 1 -

pi i s the anisotropic slowing-down density resulting from the ith isotope

S is the fission source Sf plus the inelastic scattering into lethargy m

yi, ti, ci, and qi a r e parameters whose values may be deduced from the slowing-down

properties of each isotope

Za, Cs, and Cin.are the macroscopic absorption, scattering, and inelastic scattering cross

sections, respectively . .

111. MULTIGROUP EQUATIONS

After a group structure has been established, Eqs (1.1) and (i. 3) may be integrated over each

non-thermal group (Ref 2), yielding

th for the xn group. In Eqs (1. 5) and (1. 6 ) , the absorption cross section has been split into a smooth

absorption term zS and a contribution resulting from resonances. The resonance escape probabil- a ity (pa)m is treated a s in MUFT-4 (Ref 2), and will not be discussed in detail in this report.

In a central difference approximation, Eqs (1. 2) and (1. 4) become

and

Equations ( 1.7) and ( 1.8) may be solved for q? and 5"s follows:

" A detailed discussion of Eqs (1.1) through (1.4) will be found in Ref 1.

"" The contribution of inelastic scattering processes, which simply transfer neutrons from one part of the mth roup to another, should be subtracted from (Ein)m. However, inelastic scattering f from the m h group to the mth group should be a small effect if m is small, and this effect has been neglected.

t In the PlMG code, Eq (1.7) is replaced by the more general expression:

1 but only the values fA = f = - are commonly used. B 2

Eliminating qm andpm from Eqs (1. 5) and (1. 6) resul ts in: 1

and

IV. TRANSVERSE BUCKLING

It will be assumed that the flux i s separable in the x, y, and z directions for slabs, and in the

r and z directions for cylinders. More precisely, let

cp(x, y, z) = @(z)(Cos Bxx) Cos B YY (1. 13)

in the slab case; and

o r

in cylinder problems. Conventional physical approximations a r e implied by the assumption of separa-

bility.

For convenience, the argument of.@ will be denoted by p in all cases , and the slab will be treated

first . Again, assuming separability:

and

- h

j,(x, y, z) = [ Jx(z)(Sin Bxx) Cos B ] x , YY - A .

j (x, y, z) = [.S (%)((?OR SXx) Sin B y] y , Y Y Y

h A h where x, y, and z a re unit vectors. Separated expressions for q and 5 resemble thdse for cp and.%

respectively.. To abbreviate notation in the work which follows, let r .

I 1 - (pa) m r (p)(Cos BXx) Cos B y = sm t C qF-l - - 1

Y 1 am. m A m m 1 * (1. 19) 7+ Yi

and

Then, f rom Eq (1. l l ) ,

Equation (1.12) yields three scalar ' equations. Upon introducing the definition

3 C (pp);l-l i tm =

A m 9

m 2 +, G i

these sca lar equations may be written in-the form:

and

3 x ( ~ ~ 1 F - l i

am m 2+ G i

Eliminating (Jx)" and (J )m from Eq (1. 22) results in Y

a ( J )"' m sum Bx 1 (px)F-' 3~" ' B (py)Ym1 w

~ + [ C Y ~ + D ~ B ~ ] @ ~ = ~ - i - Y i (1. 27) 4 a P A m m A m m 7- + G i 7+ Gi I-

v Here ,

i s , in effect, a corrected diffusion constant. With further abbreiriatinn, of the nbtation. Eq (1. 27) may be .rewritten in the form:

In summary, the quantities am and (J )m satisfy the relationships P

and

under the auxiliary conditions

In other geometries, the following modifications a r e required in the basic equations:

The expression

in Eq (1. 29) i s replaced by the expression

where G = 1 if Eq (1. 14) i s valid, G = 0 if Eq (1. 15) is valid, and G = 2 in spherical geometry.

There can be only one transverse buckling. The various special cases will be subsumed in the fol-

lowing work if Eq (1. 29) is replaced by

V. SPATIAL DIFFERENCE EQUATIONS

Let the subscript n denote the nth mesh point., Multiply Eq (1. 34) by pG and integrate the rekult-

ing equation from the midpoint of the mesh interval, preceding this point to the midpoint of the inter-

val following it. To leading order in the mesh width h,

1 G m =, (P,) [ ( s hIn+ + (smhIn-1 . (1. 35).

The n+ and n- subscripts indicate parametric values to the right and left of point n, respectively. .

Equation (1. 24) can also be written in difference form:

and

The ( J p I m t e rms may now be eliminated f rom Eq (1. 35), with the aid of Eq (1. 36) and Eq (1. 37); thus

1 G m m m 1 G m + 7 ( P n ) [ ( a h),+ + ( a W n - I an = z ( p n ) [ ( s hIn+ + (smhIn-]

G G - [ ( P ~ - ~ / ~ ) (Dnt tntl/2)m - ( P , . . ~ / ~ ) (4- tn-l/2)ml . (1.38)

Equation (1. 38) is the basic three-point difference equation which will be solved in each group m.

VI. BOUNDARY CONDITIONS

The left- and right-hand boundary conditions available in PlMG have the foqm . . n

m Jlfl. = -(c@): and J: = -(C@)R . (1.39)

F o r cylinders and spheres. ~ l f l . must be zero. The left-hand boundpry condition will be discussed .i ' 1 .' .. . . . .,

separately for Cartesian and non-Cartesian geometries. . . Cartesian Geometry

Integrating Eq (1. 34) from the origin to the midpoint of the f i rs t mesh interval (to leading order

in h) : . .

1 m 1 m (J~): = ( ~ ~ ) ; j ~ t p ( a h ) O t ~ y - T(S blot = -(cLa61m . (1.40)

F rom Eq (1. 35),

m m When Eq (1..41) is used to eliminate (J )m from Eq (1. 40), a linear relation between a1 a.nd aO P 112

results. This relation supplements the three-point difference equation which i s valid at i n t e r h r mesh

points. , .

It should be noted that a vanishing flux condition is not explicitly provided. .However, the flux ' . m may be made to vanish, approximately, by inserting, for CL, a very large positive number. The:

20 . number 4x10 1s used fo r this purpose in PlMG when a vanishing flux i s requested at the left-hand

boundary. This device has proved very effective. . o the r Geometries

Fit the ori.gi.n,. .Kq (1. 34) becomes

by ~ ' ~ o s p i t a l ' s Hule. Now, if (J )m vanishes in all groups, tf;" must also vanish, and it is clear P 0

f+om Eq (1. 30) that

~ i f f e r e n t i a t i n ~ Eq (1.. 30) a t the origin resul ts in

if om is constant in the f i r s t region. This restriction could be removed, without difficulty, froni the

difference equations. However, to simplify the programming, Pt has been assumed in the PlMG code

that the composition of all materials is uniform over regions (Pa r t Two, Section IV).

It has been shown that am is symmetric at the origin. Similarly, it can be shown that tm i s

antisymmetric. Therefore, in a central difference approximation,

and Eq (1.43) 'becomes r

m Inserting this expression into Eq (1.42), a linear relation between and 9; is again obtained.

Right -Hand Boundary Conditions

At the outer boundary, in all permitted geometries.

G m l G m G 1 m G - m (pR) (Jp)R = z ( p R ) ( S h)R- [ P ( J ~ ) ~ ] ~ - ~ / ~ - r ( a hlR- ( P r )R (1.46)

and

With the aid of Eq (1. 39) and Eq (1. 46). ( J ~ ) F - ~ l2 may be eliminated f r o m E q (1. 47). m m which then becomes a linear difference equation in aR and @R-l .

VII. METHOD O F SOLUTION

In order to facilitate discussion of the procedure used to solve the PlMG equations, i t will be

helpful to write out explicitly the te rm sm appearing iri Eq (1. 38): ,

where

and

(sin)m = I Z K;"(z~,'~ A) . .

I < m

th ( x A ) ~ is that fraction of t h e f i s s i o n spectrum feeding into the m group.

1 . (p,) is the fission resonance escape probability in the lth group ( a s in MUFT 4, Ref 2).

(C . )P is the macroscopic inelastic scattering c ross section in the Ith group, in m . 1 .

KI A is the probability that a neutron, inelastically scattered in the Ith group, will be scat- th tered into the m group.

The PlMG equations a r e solved by an iterative process, which s ta r t s from a guessed source 0 - 0 function (gf)(0). Now, Qi = 0 and P . = 0 if no fission neutrons a re produced with lethargies Smaller

1

than uo. Therefore, it is possible to construct the function s1 in Eq (1. 38), while t1 = 0. With the

inhomogeneous t e rm in the f i r s t group given, the difference equations in the first group a r e solved 1 1 (Ref 3) for @ . Equation (1. 36) o r Eq (1. 37) then determines (J ) at midpoints of mesh intervals,

P and Eq (1. 31) may be used to evaluate the transverse current (o r currents) at mesh points. Equations - (1. 32) and (1. 33) fix the values of Q and P in the f i rs t group. Having computed all the relevant f i r s t

J 2 , group quantities, s2 can be constructed at mesh points and t a t mesh interval midpoints. The second

2 group equation is then solved for Q , etc. After all the group equations have been solved, an im-

proved fission source function (gf)( l) is constructed from the i? and Q values. As in the WANDA code

(Ref 3), the volume integral of gf is normalized to 1, i. e . . the eigenvalue estimate i, is given by the

expression

. . . . . , '... , . . , * . . . . . . Extrapolation on gf is available, a s in the WANDA code. ~ x ~ e r i E n c 6 indie~tes . that ari extrapo-

lation factor which works effectively in a given WANDA problem will also be effectlve'in the' cor re- '

spending Pl MG problem.

VIII. THERMAL GROUP

It should be noted that the thermal group is treated somewhat-differently from the fast and epi-

thermal groups because of the slightly artificial character of the thermal group, a d because there

is no slowing down from the thermal group. The thermal group equations a re :

and

o r , in separated notation.

and

The spatial difference equation in the thermal group is formally identical with Eq (1. 38), with

parameters redefined as follows:

where

Because of the difficulties inherent in a one-velocity model of the ther'mal group, there i s no ~

M clear-cut procedure for determining (Za) and (zJM. Therefore, macroscopic constants for the

thermal group a r e precomputed by any procedure considered appropriate and inserted into the code

a s input.

IX. DISCUSSION

In order to facilitate checkout of the code, and to permit a meaningful comparison between,

few-group and multigroup results, the PlMG equations have been forced to conform closely to the

equations in MUFT 4. .It.will be noted that the buckling appears in the MUFT 4 expression for the

resonance escape probability (Ref 2). Exactly the same expression, Eq (2. 20), i s used to compute

resonance escape probabilities in PlMG. The effect of the buckling te rm on p-resonance is, gener- . , ' ' * I .. .

ally, very small, but a value for this "resonance buckling" is required a s input to the PlMG code.

It will be seen that the PlMG treatment of resonances implies that slowing-down predominates over

leakage. If the flux in a region i s determined primarily by the leakage, rather than by the slowing-

down density, the PlMG resonance model will be inadequate.

In all, four input bucklings must be supplied to PlMG, namely, the "resonance buckling" already 2

discussed, Bx, B and B . yD

If there i s only one transverse buckling, this can be entered a s B .with B = 0, o r vice versa. 2 x ' Y 2 Of course Bx, By. and B should satisfy the relation B2 = B: t B:, but Bx. Bv, and B a r e taken to - -- --

be independent &antities here. It is possible; for example, to sGecify Bx = B> = 0 and B' # 0. In 2 - this case the transverse buckling term in the group equations is simply D ~ B .

Anisotropic slowing down into the thermal group is explicitly taken into account in the PlMG

code, while it is neglected in few-group codes.* It may be that such a refinement i s superfluous a t

present, because of the crudity of the one-group thermal model. At any rate, the effect appears to

be quite small.

X. EDIT OF FEW-GROUP AVERAGES

In a few-group approximation, the non-thermal neutrons a r e assigned to a small number of

groups which will be referred to, for convenience, a s "macro-groups. " These a r e to be distinguished

from the PlMG "micro-groups. 'I In order to facilitate comparisons between few-group and multi-

group results, a few-group edit has been provided a s a PlMG output option. This routine computes

and prints m a ~ r o - ~ r o u ~ parameters, a s follows:

and

* For example, this effect is neglected in the MUFT-WANDA system.

Here K and KU a r e the lowest and highest lethargy micro-groups, respectively,:.~nmacro-group k. I Cut-points for the macro-groups may be specified a s desired, provided':thaf the Chole non-thermal

e n e r b range is divided into three such groups, a t most. . . :I. :;,:. ;..> f v : . , :!'

. . . I ' :. .:., . ..

If the few-group edit is requested, region checks for each ~ a c ~ o - ~ l ; b ; u p ' ~ i l l ' b k . . . Printed . out, a s

in the WANDA code. It should be noted, however, that the tran'sverie bbu&ling.:is not tkeated rigor- . . . . .

ously in the region-check calculation. F o r this reason, apparent imdalindei .in.the region check may

occur when the t ransverse buckling is very high. However, no such difficulty'has a s yet been ob-

served.

PART TWO: PROGRAMMING AND OPERATION OF CODE

I. INTRODUCTION

The equations used in programming PlMG a r e listed in Par t Two, Section I11 in approximately

the order in which they a r e used. In this part of the report, the authors have taken the liberty of

passing on information in the form of warning signs, by underlining descriptive phrases, which indi-

cate the places where e r r o r s a r e most apt to occur in preparing input. Wherever possible, the pro-

gram stop which might result from a particular piece of incorrect data is indicated after the descrip-

tion of that data.

The PlMGl version required that microscopic data for the thermal group also be supplied in the

library. The second version, PlMG2, requires that the problem requester supply the necessary

thermal macroscopic c ross sections for each problem. However, the library used by PlMG2 st i l l

contains a set of dummy thermal microscopic c ross sections which should not be overlooked when

data a r e prepared for the library a s described in Section VIII of this part of the report.

Par t Two is a description of PlMG2, since this is the more practical of the two versions and

the only version available for distribution.

11. GLOSSARY

I ~ ~ ~ c ~ s - S U D ~ ~ S C ~ ~ D ~ S and S u b s c r i ~ t s

a absorption [Eqs (2. 14). (2. 20), (2. 251, and (2. 71)]

A denotes the f i rs t of a set of two numbers [Eq (2. 31)]

B denotes the second of a se t of two numbers [Eq (2. 31)]

B P ~ Breakpoint No. 1 [ Footnote ( *) p 19;' Eq (2.6811

Bpt2 Breakpoint No. 2 [ Footnote ( *) p 19; Eq (2. 6811

c capture [Eq (2.13)] o r

card number (Pa r t Two, Section IV)

f fisai,on [Eqs (2.11) and ( 2 . 30a)]

G geometry [Eq (2. 37)]

i isolope [Eqs (2. 1) and (2. 2))

in inelastic scattering [Eq (2. 16)]

j region [Eq (2. l ) ]

J region farthest from origin [Eq (2.48)]

k resonance within a group [Eq (2.20)] o r

few-group scheme [Eq (2. 64)]

KP lowest value of m in few-group1 of scheme k [ E q (2. 64)]

highest value of m in fcw-group I of scherne k [Eq (L.64)]

P lowest value [Eq (2 . 64), see Kp]

L lower bound of the resonances (Pa r t Two, Section VIII) o r

left [ see (cLlmS Eq (1.4411

m group [Eq (2.111

group number of the highest l e t h a r h group o r

thermal group [Eq (2. 57)]

Quantities

,r* m i

point [Eq (1. 35)]

interface point at right end of region j [ E q (2.76)]

point farthest from the origin (n = 0) [Eq (2.48)]

group from which scattering i s occurring [ Eq (2.29)] o r

control parameter (Pa r t Two, Section IV, Form 11)

removal [ E q (2.65)] o r

right [ see ( c ~ ) ~ , Eq (2.48)]

smooih [Eqs (2. l l ) , (2. l3) , and (2.14)]

iteratcon [ E q (2. 36)]

totai [ E ~ (2. 80)] o r

conv&rged iteration number. [Ey ( 2 . 30L)]

upper [ E q (2.64), s ee KU]

upper bound of the inelastic scattering matFix [Eq (2. 68); Par t Twd; Section VIII]

few;gfoup [Eq (2.64)]

one of the three Cartesiah coordinates [Eqs (2.41) and (2. 52). see y and p]

one of the three C a r t e s i h coordinates [Eqs (2.41) and (2.54), see x and p]

the coordinate corresponding to the direction in which the flux shape is being computed

"interval to the right" o r "interval to the left"

an element in the ine1astic.sc'attering matrix-probability of scattering from multigroup r tb multigroup m for isotope i [Eq (2.29)']

as defined hy b:q ( 2 . IY)

a s defined by Eq (1.29)

a s defined by Eqs (2.45) and (2.47)

total buckling (Pa r t Two, Section IV)

resonance bbckling [ P a r t Two, Section IV; Eq (2.19)]

component of buckling in the transverse x-direction [Eqs (2.41) and (2. 52)]

component of buckling.in the transverse y-direction [Eqs (2.41) and (2.54)j


a parameter dependent upon the geometry [Eqs (2.83) and (2.84)]

macroscopic symmetric scattering cross section of hydrogen a s defined by Eq (2.1)

parameter which controls the left-hand boundary condition a s defined by Eq (1. 39)

parameter which controls the right-hand boundary condition a s def. 'ed by Eq (1. 39)

a s defined by Eq (2.9) 7

as defined by Eqs (2. 78) and (2. 79)

diffusion coefficient a s defined by Eq (2. 30)

f ~ .

f~

(t)

hj

Hn j

.m, (t) J n t v k Jn!

J 1,"

Lml k j, i

(ma):*

N. . J , 1

m (pa) j

average diffusion coefficient for few-group v of scheme k at midpoint nt1/2 [Eq (2.7311

factor A [Eq (2. 31)]

factor B [Eq (2.41)]

a s defined by Eq (2. 38)

mesh size [Eq (2. 32)]

a s defined by Eqs (2.76) and (2.77)

current [Eqs (2. 50), (2. 52), (2. 54), (2. 59), and (2. 60)]

total current [Eqs (2. 83) and (2. 84)]


self -shielding factor [ Eq (2. 20)]

absorption resonance parameter [Eq (2.20)]

number density [Eq (2. I)]

absorption resonance escape probability [Eq (2.25)]

fission resonance escape probability [Eq (2.23)]

anisotropic slowing-down density [Eqs (2.51), (2. 53), and (2. 55)]

isotropic slowing-down density [Eq (2. 56)]

absorption resonance parameter [Eq (2. 20)]

absorption resonance integral [Eq (2. 20)]

fission resonance integral [Eq (2. 22)]







a s defined by Eq (2 . 6)

fission to absorption ratio [Kq (2.22)]



age number [Eq (2.27)]

a s 'defined by Eqs (2.44) and (2.46)

convergence parameter (Pa r t Two, Section IV)

lethargy increment [Eq (2. 28)]

e r r o r criterion [Eqs (2. 61) ,and (2. 63)]

anisotropic slowing-down coefficient [Eq (2. 28)]

isotropio olowing-down coefficienl [Eq (2.4)]

extrapolation. factor [ Eq ( 2 . 3%)] . .



as defined by' Eq ( 2 . 4 ) .

a s defined by Eq ( 2 . 27)

a s defined by Eq ( 2 . 5)

a s defined by'Eq ( 2 . 2 6 )

eigenvalue [ Eq ( 2 . 37)]

maximum pointwise eigenvalue [Eq (2 . 62a)I

minimum pointwise eigenvalue [Eq ( 2 . 62b) l

no definod by Eq ( 2 . 34)

py average cosine of the Elcartering rulgle [Eq (2 . C)] m

vi average number of neutrons produced per fission [Eqs (2.12) and ( 2 . 2 6 ) ]

E: average logarithmic energy decrement per collision [Eq ( 2 . 5 ) ]

m . . as defined hy Eq (2. 10)

s j TT 3.141592654 [Eq (2 . 20)]

Pn . radius from origin [Eq ( 2 . 32)]

s m ("f)i microscopic smooth fission cross section [Eq ( 2 . 1 l ) ]

m ( rii) microscopic inelastic scattering cross section [Eq ( 2 . 1 6 ) ]

(Q;" microscopic smooth capture cross section [Eq ( 2 . 13 ) ]

microscopic symmetric scattering cross section [Eq (2. l ) ]

macroscopic total cross section as defined by Eq ( 2 . 17 )

macroscogic total cross section as defined by Eq (2. 80)

macroscopic smooth absorpli61l cross sect lo^^ [Eq ( 2 . 14 ) ]

macroscopic smooth fission cross section [Eq (2 . l l ) ]

macroscopic inelastic scattering cross section [Eq ( 2 . 1 6 ) ]

macroscogic transport cross section [ Eq (L.15) ]

one iteration parameter (Part Two, Section IV)

multigroup flux [Eqs ( 2 . 36). ( 2 . 40 ) , ( 2 . 4 8 ) , and ( 2 . 49 ) ]

few group flux [Eq ( 2 . 6 4 ) ]

normalized source distribution spectrum component [Eq ( 2 . 39 ) ]

number of neutrons inelastically scattered into lethargy group m per unit lethargy

111. EQUATIONS USED IN P l M G 2

Coefficient Routine "

" The number at the left of each equation refers to the equation in Part One where the quantity is f i rs t introduced o r derived.

or, for i = 01 in' Eq (2. l ) ,

where the summation [ in Eq (2.2)] includes only the nonhydrogenous moderators.

where the summation [ in Eq (2.811 includes only the nonhydrogenous moderators.

. . . . . ,

(RI )fn! = a J S ~

where k = 1, 2, 3 ,..., K L 8 .

where B' = Total Buckling; (see Pa r t One. Section IX and Par t Two, Section IV).

(1.35) Pn=Pn-1 + h - , Po = O

Iteration Routine r 1

w h e r e

dVo = dp,

dV1 = 2npdp8

and 2 dV2 = 4np dp.

F o r ( g f ) r ) and A ( ~ ) ~ s e e Part Two, Sect ion IV.

* All i n t eg ra l s a r e computed us ing Simpson 's .Rule .

where (P~)::!: = 0.

(1 . 33) 111-1, (t) (p x ( ) n+, i = [ ( K l ) i - A] " (Px)nt, + [ ( ~ 2 ) + , ~ ( j x n t ) ( t ) ~ ~ n l j , ( 2 . 5 3 )

where, (P~):.!:) . 0. ( 1 . 2 6 ) ' ( 2 , 5 4 )

(1. 33) ( 2 . 5 5 )

where, (P,):'+!:) 0. '

(1. 32) 1 m' [ ( K j ? - rBAm] <?l*(t) + [ ( K ~ ) + , iq!)~]m ( 2 . 56)

( K ~ ) ~ t f Am A.

where, Q''!~) = 0. ns 1

(1 .59 )

= max { s:~)] max n

(gf)n

(t) = min[X!-] 'min n

(gf)n

where k = l , 2, or 3. v = 1; 1, 2; or 1, 2, 3.'

1 Rpt, 1 ' 3

Bptl+l BptZ 2. 3

BptZtl M-1 3 3

NOTE: Kp and KU are the lowest and highest lethargy microgroups, respectively, which a re included

in macrogroup v of scheme k. Also, see Part One, Section X.

"" U i~ u ~ e d if U i s less t11a.11 Dpt2.

For each region and for each macrogroup,.

For each region,

where c(0) = 1, c(1) = 2n, c(2) = 4a.

IV. PREPARATION O F INPUT

Form I?

Problem Identif~~arlon: Any 8 digit, fixed-point, decimal integer. . .

Total Groups: Number of lethargy groups including the thermal.group. The corresponding

library of data must be used in running the problem .(fixed point integer, M 180) .

Total Points: Total number of mesh pdints in entire problem, excluding the origin which is des-

ignated a s 'point 0 (zero) (fixed point even integer, .N 5 200).

Total Regions: ..A region is defined by the information specified on Form 11. Therefore, in pro-

ceeding along the redctor from the origin, whenever it is necessary to specify a change i n

Form 11, a new region of the reactor is defined (fixed point integer, J 15). . .

Geometry: Specify one type of geometry a s indicated under the space provided for this parameter

(fixed point integer,' G = 0, 1, o r 2). . .

Source Distribution Spectrum: Source spectra for different types of sources can be stored in the

library (Pa r t Two, Section VIII). The number assigned to the source spectrum to be used is

specified here (fixed point integer).

Breakpoints: Fo r edits 3, 4, 5, and 6, it is nece$sary to indicate the number of the last multi-

group included in few-group 1 and the last multigroup included in group 2 of a three-fast group

scheme. The numbers of these two multigroups a r e Breakpoint No. 1 and Breakpoint No. 2,

respectively.

" See Appendix A.

6: A programming constant which selects the type of convergence desired (fixed point integer, - 0 or 1).

Normal Convergence (0):

Pointwise Convergence (I).: Normal convergence

'max .- 'min < 'max

Edit: Call number of the type of edit desired. see description of output (fixed.ii6int integer 1,

2, 3, 4, 5, or, b) . .

convergence Criterion: (Floating point; rnax 8 places; 0 <.E < 1.) .,

Extrapolwti~p Factor: (Floating point*; rnax 4 places) [See Eq (2.'38b)]

fA and fB: Both of these factors should be..the floating point number uue-l id, i. e. , 505. ' (Scc

Part One, Section 111. ) . . , .

Use Tape: (Fixed point integer) (See Part Two, Section IX. )

Boundary Conditions: jm t c:, = 0 (See Part One, Secliurr V1. )

m: Group number corresponding to the first set of parameters in that row (fixed point inte- - ger). If m of the f irst row i s equal'to zero, the first set of parameters in that row will be

used in all groups and this will constitute a coitiplete~specificaliuli of the Doundary Conditions.

If m of'the first row is not equal to zero,. a pair of parameters must be specified for all the

4 groups to a row.

CL: Left-hand boundary condition (floating point; rnax 4 placcs). .~ -

CR: Right-hand boundary condition (floating point; max 4 places). . . .. - . . At either boundary CL or CRfor a zero flux derivative condition, C =. 000; and for a zero flux

condition, C! = 704. CLmwst be 000 for'problems in cylindrical and sPherical geometries but

can take on any value in slab geometry. CR can take on any value in any geometry independ-

ent of CL. . .

Form I1 .

Mesh Point Number at Right-Hand ~ n d of Region: (Fixed point even integer, n. < N) J -

Total Elements: Total number of isotopes 4 the region. (Fixed point integer, 1 < I. '< 10) J -. .. . .

Mesh Size hj: Distance between mesh points in this region. , (Floating point; h. > 0) J -

Total Buckling B': (Floating point; max 8 places; B' 2 0) .. . :

Transverse Buckling : .. .

x-direction Bx: (Floating point; rnax 8 places; Rx 2 0)

y-direcliurl B;: (Floating point; mar 8 ploee's; B . 0) Y.'

2 2 If either Bx o r B i s not zero, .then B mis t equal Bx plus B' (See Part One, Section 1X. ) . Y Y'

* See Appendix C.

Macroscopic Thermal c ros s ' Sections: ' " - D: Thermal diffusion constant (floating'point; max 8 places).

Za: M a c r o s d c thermal absorption c ross section (floating point; rnax 8 places). - vZf: Macroscopic thermal nu-fission c ros s section (floating point; rnax 8 places). - j: Number of this region counting sequentially from the origin which is the left-,hand point of - region number one (fixed point integer).

itr: i is the code number for the isotope ( see Appendix E); r = 100, if the isotope is to be - treated i s a nonhydrbgenous moderator in this region, btherwise r = 0. If hydrogen is not ...

present in a region, at least one nonhydrogenous moderator must be specified (fixed point

integer).

Ni: Number density of isotope i in this region (floating point; rnax 5 places; Ni > 0). - k: Total number of absorption r e s o n k c e s in a group (fixed point integer, 0 5 k 8). - If k = 9 in the first . row for any isotope, all the,resonances will have the same self-shielding

factor, equal to the f i rs t entry in that row; and this then constitutes a complete specification

of the self-shielding factors of isotope i.

If k # 9 &I the f i r s t row fo r an isotope, self-shielding factors must be specified for every

group from the lower bound of the resonance groups"" up to and including group M. In this

case, each row will be sufficient for one group. The k for a particular row must correspond

to the number of resonances in that group for that isotope a s found in the PlMG2 library.

L: Resonance self-shielding factor (floating point; rnax 4 places). - For every isotope in this' region which has resonance data in the PlMG2 library, an L-factor,

o r L-factors, must be specified.

To insure proper card punching, the Forms I1 should follow Form I in ascending order according

to region numbers.

Farm LII

If a set of floating binary source cards which a r e punched from a special WANDA prbgrtimt a r e

not available a s input to PlMG, then a pointwise source guess and an estimate of the initial eigenvalue

must be specified on this form.

Initial Eigenvalue Estimate: (Floating point; rnax 8 places)

c: card number, c = 1, 2, 3, . . . . (fixed point integer). - 7 : A control parameter punched only on the f i rs t decimal source card. If r = 000, iterate - to convergence. If r = 001, one iteration; i. e., the multigroup fluxes a r e completed only

once, with no renormalization of the source o r computation of an eigenvalue.

S: Source (floating point; rnax 8 places). If c = 0 in the f i r s t row, the source distribution - will be assumed constant over all regions and equal in magnitude to the f i r s t source in that

row. The f i rs t space in the f i r s t row is not to be used, a s indicated. If c # 0 in the f i r s t

row, a pointwise sowcc! distribution must be specified starting with the origin. At points

which lie on interfaces between regions, an extra value of the source must be specified and

is entered in the next space in the row ( o r the f i r s t space in the next row).

" See Par t One, section VIII.

" See Ref 2, Library Tape Preparation, p 17. . . t See Appendix B.

Groups to Be Edited: If it i s desired to edit the flux, current, and slowing down densities in

certain groups only, enter in ascending order the group numbers of the multigFoups to be edited.

If none a r e indicated, all will be edited. If M + 1 is entered, none of the multigroups will be

edited (fixed point biteyer).

It is not necessary to. include a Form 111 in a problem, if there is no decimal source to be speci-

fied, and if all the fluxes are to be edited.

V. OUTPUT

On-Line Output

As the problem is being run, the following information will be printed on the orizline printer

during the coefficient tape preparation routine:

1) PROLOG: .This is a form printed at the beginning of any normal run or of any restart. ,It

should be filled out completely by the 704 operator in the event of trouble wliich may arise

during the running of a problem. Tape reel numbers and the tape mil: lellers are filled ~ I I fur . . those tapes which have been saved to make it possible to duplicate the particular machine sit-

uation existing at.the time the trouble occurred or to provide the necessary information for

a future restart.

2) Edit of all the input: An edit of the entire input is impossible when restarting a problem;

therefore, this is the only record of the input data used in the problem.

As the problem is being run during the iteration routine:

1) Initial eigenvalue: This will either be the converged eigenvalue from a WANDA problem, the

estimated eigenvalue from Form 111, or the latest eigenvalue in the case of a restart using

'cards from a Restart-Dump.

2) Initial sources: These will be either the converged sources from a WANDA problem, the

source distribution as specified on Form 111, o r the latest source in the case of a restart

using cards from a Restart-Dump;

3) Eigenvalues: At the end of each iteration the normal eigenvalue or the minimum, normal, and

maximum eigenvalues will be printed for supervisory inspection. On the same line with the ~igenvalu~s will appear t h e "n~arness to rnnver~encc" quantity (NTC) which is useful to the operator in determining how much longer the problem might run. If pointwise convergence

is requested, then NTC will be the left half of Inequality (2. 61). After Inequality (2. 61) i s

satisfied, then NTC will be the left half of Inequality (2. 63).

Off -Line Output

All the information which was printed on-line during the iteration routine will appear on the off-

line printout. The following information will be written on tape during the final edit routine:

1) Final Edit No. 1: (This edit will also be 'performed a s part of each of the other final edits. )

a) Converged eigenvalue:* For one iteration problem, this is identical with the initial, eigen-

value.

b) Normalized source: This is the source which would have been used in the'next iteration

had there been a next iteration. In the case of one iteration problem this is.identica1 with

the initial source.

" If any edit other than Final Edit No. 1 i s requested, the problem will have converged according to the prescribed criterion; however, one more iteration beyond this converged iteration is required in order to accumulate the necessary information required to produce these edits. This converged 'eigenvalue i s , then that eigenvalue computed after the extra iteration.

C) Regional source averages: These a r e the source averages averaged over the volume of

each of the regions defined by Form 11 [Eq (2.86)].

d) Flux: his' is the flux which corresponds to the converged eigenvalue and which was used

in computing the new normalized source. Depending on how the selection of groups was

specified at the bottom of Form 111, the flux for each group at each point is edited.

2) Final Edit No. 2: If Edit No. 2 has been requested, the following information will be printed:

a ) Slowing down densities: Fo r every isotope i of each region of the same groups m a s were

printed in Final Edit No. 1, there will be printed a v

a t each mesh point n, including the double value at interfaces.

m b) Current: For the same groups a s mentioned i n ( a ) , ( jz)n+l/2 will be printed (n = 0, 1.

2,. . . , N-1).

3) Final Edit No. 3: If Edit No. 3 has been requested, the following set of pointwise average,

fast few-group quantities will be printed:

a) Diffusion: This is the diffusion coefficient a t each midpoint averaged over groups m,

where m = 1, 2 ,..., M-1 [Eq (2.73)].

b) Removal: At each point, including the double value at interfaces, there will be printed a

removal c ross section averaged over multigroups m ( m = 1, 2,. . . , M-1) [Eqs (2.65)

through (2. 7011.

Absorption: An absorptidn c ross section will be a s for removal [ E q (2.71)].

Nu-fission: A nu-fission c ross section will be printed a s for removal [ E q (2.72)].

Flux: ,Average fast few-group flux will be printed a s for removal [Eq (2.64)].

c) Fast regionwise absorption:

r

where ( j = 1, 2,. . . j), an is defined in Eq (2. 64), and the surnnlation is defined in

Eq (2. 74).

M ' d) Thermal regionwise absorption: Same a s in fast regionwise absorption for cP ody.

4) Final Edit No. 4: If Edit No. 4 has been requested, there will be two se t s of average,point-

wise c ross sections, a s in (a) and (b) of Final Edif No. 3. Here, the f i r s t set will be averages

over multigroups 1 through Breakpoint No. 2, and the second se t will be averages over the

multigroups from Breakpoint No. 2 through M-1.

5) Final Edit No. 5: If edit number 5 has.been requested, there will be three se t s of average

pointwise c ross sections, a s in (a) and (b) of Final Edit No. 3. Here, the f i r s t set will be

averages over multigroups 1 through Breakpoint No. 1; the second se t will be averages over

. multigroups from ' ~ r e a k ~ o i n t No. 1 through.Breakpoinf No. 2; and the third set will be aver -

ages over the multigroups fromBreakpoint No, 2 through M-1. .

6) Final Edit No. 6: If Edit No. 6 has been requested, Final Edits No. 5 and No. 3 will be per-

formed.

Region checks will be edited after each few-group, except for Final Edit No. 3'when performed

a s a part of 'Final Edit No. 6.

All input which is in a floating point form (-see Appendix C) will be edited in a floating point form,

except for the convergence criteria, extrapolation factor, L-factors, and the initial eigenvalue.

Quantities computed by the code a re edited in a floating point form with.the exception of the eigen-

values printed after each iteration.

All printing both on-line and off-line is done so that the paper can be cut to 8-112 in. x 11 in.

size.

VI. CARD PUNCHING

All numbers on the cards are positive and are punched with their sign in the preceding column.

There must be one and only one punch in every column of each car'd; columns 1-72 are the only col-

umns under consideration. If the information specified for a particular card does not fill all the

columns to 72, then a word of t000.. should be punched to fill out that card. Every card should

have the positive eight-place Problem Identification found at the top of Form I punched in columns

1-9. All floating point fields must be at least 3 columns. I

The last card, which is punched from the infdrmation found at the bottom of Form 111, or which

is blank if Form I l l is not included in the problem, i s an exception to'everything stated in the pre- ~ e d i n g ' ~ a r a g r a ~ h .

Before a problem is punched, a check of the forms should be made such that: (1) the Problem

Identification is the same on Forms I1 and I11 as that found on Form I, (2) the Forms I1 are arranged

so that the mesh point numbers a re in ascending order and a re a11 even numbers, and (3) the Form 111

is present, o r that a set of binary cards has been included with the Forms I and II. (See Appendix A. )

Form I

Card No. 1: The data should be punched as found in normal reading order. The four numbers

( E , 0, fA, fg) should be in x-s 50 floathg point form. The units position of the tape number is

punched in column 72.

Cards No. 2: Each row becomes one card. Punch only as many cards a s there a r e rows with ..

information filled in. CL and CR should be x-s 50 floating point form.

Form 11

Card No. 3: The data should be punched as found .in normal reading order. All four bucklings

should be in x-s 50 floating point form.

Card No. 4: ,Las t three numbers a r e in x-s 50 floating point form, i. e., Dl Za, and vZf.

Cards NO. 5: Each row becomes one card. Punch only as many cards as there a r e rows with

information filled in. Ni should be in x-s 50 floating.point form.

Cards IUu. 6: E a c l ~ ruw becu~l~ebi U I I ~ card. Pul lc l~ u l ~ l y a s I J ~ ~ I I ~ cards as 1ller.e w.e ~ u w s w i l l ,

information filled in. Each card must have 8 L-numbers. L should be in x-s 50 floating point

form.

If a set of binary cards has been submitted with the problem, place this deck immediately after

the last Card No. 6 of the last . ~ o r m 11. These binary cards will take the place of Cards No. 7 so

that the only other card nee.ded is the "last card." The binary cards should have their Problem

Identification punched in columns 73-80. The top card must be blank in columns 1-72.

Form 111"

Cards'No. 7: Each row becomes one card. The first floating point number of the first card, i. e. ,

the box which is "x-ed out, should be the initial eigenvalue estimate. The field preceding the

" See Appendix D.

eigenvalue estimate may o r may not be zero. Punch only a s many cards a s there a re rows with

information filled in. The initial eigenvalue estimate and S should be in X-s 50 floating point

form.

Last Card: This is punched according to the information found at the bottom of the form under

"Groups to be edited. 'I If there a r e no entries, the card is blank. A 9 is, punched in the column,

o r columns, indicated by the entries. If Form 111 is not'included in this problem, the Last Card

is a blank.

Two additional blank cards should be piaced after the Last Card.

VII. OPERATOR'S NOTES

704 Requirements

Magnetic core storage

Magnetic tapes

Physical magnetic drums,

High speed card reader

Punch

Printer

Sense lights

Sense switches

Peripheral equipment

Tape -to-printer

Card-to-tape

Floating point arithmetic unit

Additional instructions

STZ

CAD

1

1 (optional)

Material.Needed to Run One Problem

P I MGZ Library-Program tape. (See column 72 of 1 s t input card for L - P tape number. )

Nke biank tapes, eight at least 100 feet long, and one which is a full reel;

One problem deck.

Restart-Dump deck.

Restart-Positioning card (for all restar ts) .

R.iinning Instructions

1) Mount PlMG2 Library-Program tape a s logical tape 1 .

2) Mount nine blank tapes a s logical tapes 2-0. Logical tape 5 must be a full tape.

3) Insert GL OUT-2 printer board.

4) Insert standard SHARE punch board.

5) Place problem deck in card reader.

L) Push CLEAR.

7) Push LOAD TAPE.

Progress of Program

Coefficient Tape Writing Program

The following steps should be observed by the operator during the coefficient tape writing program:

1) The PROLOG is printed. This form i s to be filled out in the event that a problem must

be removed before i t is completed or in the event that it has been requested that certain

tapes be saved.

2) A complete statement of the problem to be solved is next printed. From this, an esti-

. mate of the running time of the problem can be made.

3) Next, a region by regiof;.printoit of the input will follow. For each region:

a) The efitire library on tape 1 is read. . .

b) Tapes 3, 4, and 5 a r e written with one record for each point.

C) Tapes 2, 6-0 a r e written with one record each.

d) Drums 1-4 are written with one record each.

4) After the last region has been all tapes are rewound:

a) Tapes 3-0 a re individually sorted and rewound.

b) Drums 1 . 4 arc individually sorted.

C) Tape 2 is read into the core and rewound.

5) Tapes 3-0, the data in core froin tape 2, and drums 1-4 a re merged onto tape.2, .one

'record at a time.

6) Tapes 2-0'are rewound.

'In the event of a computer e r ro r before.s;tep 6, restarting is impossible. All time is'waste time.

Step 6 is the f irst plateau. At this point, tapes 8 and 9 are no longer needed and may be replaced by

any other tapes.

Iteration Program'

The following steps should be observed by the operator during the iteration program:

1) More input will be read from the cards..

2) This input wig be prhted on-line and off-line on tape 5 (initial eigenvalue and initial

source).

3) During each iteration, tape 2 will be read completely and tape 3 will be written with a

full set of fluxes. Both tapes will be rewound.,

4) The eigenvalue will be printed for each iteration. The nearness to convergence (NTC)

. of the problem wi l l also be p~.ir~led. The problem is convcrged when NTC is less than

the e r ro r criterion which is found in the right side of the inequality printed on the first

page of the input printout.

5) Upon convergence, the paper will be restored on-line.

6 ) U ally ollier edit than Edit No. 1 io rcqucotod, another iteration will he ma.de after con-

vergence (there will be a line printed indicating convergence) during which tapes 3-7 are

written, after which tapes 2-7 a re rewound, another eigenvalue printed, .and the paper

restored. I-Iowever, if the critcrion for convergence is not met on this extra iteration,

another iteration i s performed. If the criterion is still not met, then the program will

print CONVERGENCE CRITERION WAS NOT SATISFIED ON THE E X T M ITEMTION.

Save tapes 0, 1, 2, 3, 4, 5, 6, 7.

Edit Program

The following steps should be observed by the operator during the edit program:

1) The BCD tape to be printed off-line is written on tape 5.

2) The type of edit, as.determined by the Edit Number indicated on the f i rs t page of the on-

line printout in Part One, is performed.

Upon completion of the edit routine, the computer indicates to the operator that it is finished.

The following tapes must be taken off:

Tape 1: save.

T'ape 5: print off-line with carriage control set to PROGRAM.

Tapes 2 and 0, the coefficient tapes, may be saved if the requester so indicates.

WARNING

Successive P l MG problems cannot

be run without changing tape 5.

NOTE

If sense switch 1 is thrown while the edit routine is running, then an auto-

matic Restart Dump is performed

after the edit is completed.

Restart

In the event of machine failure after reaching the iteration part, a definite procedure should be

followed:

1) A Restart-Dump should be performed.

a) Place Restart-Dump deck in hopper.

b) Push CLEAR.

C) At punch unit: (1) The operator may pi-ecede blank cards with a binary card in whose

label field (columns 73-80) the problem identification has been punched and is blank in

columns 1-72, and then (2) push START.

d) Push LOAD CARDS. Stop at 00172.

e) Run out punch unit. The binary source cards which have been punched a r e sequentially

numbered in'binary in the 9LD. The last card, the one without a sequence number, be-

coines the top card a d inust be blank in columns 1-72.

2) Place the Restart-Positioning card in front of the- binary source cards and place the last three

cards of the original'input deck after the binary source cards; then place this combined deck

in the card reader hopper.

3) Rewind tapes 1, 2, 3, 4, 6, 7, and 0. ,

4) Place sense switch 2 down.

5) Push CLEAR.

6) Push LOAD CARDS

A new PROLOG will be printed and control will be transferred to the iteration part.

Force Edit

If a running-time limit has been specified for a problem, the problem can'be stopped by ,throwing

sense switch 1. Upon completion of the iteration which is being processed at the time the switch is

thrown, the program will priht FORCED EDIT on-line and then proceed with the editing a s specified

by the input. At the end.of the edit, a set of floating binary cards which have the latest source distri-:

bution and eigentralue phched on them will be punched. It would be desirable, for kaentification pur-

poses, to have a card in the punch hopper with the problem identification punched in holumns 73-80.

These CHOMP cards from PlMG should be returned to the.requester along with all the on-line and

off -line printing.

Printing Off -Li.tie .:;'

Tape 5 will.contain one file.of output for the problem. Set printer carri>gf, conti-ol to PROGRAM; . .. ..* .

There will be a clear indication of the end of the output for a problem.

One Iteration ,Option :. . .

. . . The program will ,proceed a s before except that, during the iteration part, only 'what would amount

to the extra' iteration after convergence will be performed. The coefficient and edit parts will r e -

main the same.. ,There will be no eiggnvalues printed on-lhe. See the explaii$tion of 7 in Part Twoi

Section I V .

Error Stops

' In the Coefficient P r o s a m :

An asterisk (*) indicates some sort of e r ro r in the input. Do not run the problem any further;

Mark the stop number and the card being read.

Machine e r ro r occurred in .GL OUT2.

Machine e r r o r occurred in WH 001.

Machine e r ro r occurred in WH 001.

Double punch, blank column, or 150th. * Range e r r o r in input number. Check card order. * Blank card. * Machine error.

Wrong Library -Program Tape. * Blank card. * Problem identification error. . .

Type 2 cards out of order, too high; * Type 2 cards out of order, too low. * .

~ l & k card. * ~ a c h i n e error. .. . Problem identification error. * Duplicate interface number. * Interface numbers out of or'der. * Bad tape 1.

Total number of elements equals zero. * Total number of elements greater .+haxi. 10. * Zero mesh size. * ,Blank card. * Machine erfor.

.Blank card. * Machine error.

Problem identification error. * Wrong region number on thermal cross-sectjnn car@. *.. Blank card. * Machine error.

Problem identification e r ror . * Wrong region on number density card. " Illegitimate element number. " Elements out of order. " Zero number density. " ,Unwanted end of file indication from tape 1.

Bad tape 1.

Wrong group structure on tape 1 library. " Source spectrum not on library. " Element not in library. " Element not in library. " Unwanted end of file indication from tape 1.

Bad tape 1.

Unwanted end of file indication from tape 1.

Bad tape 1.

(Divide-Check indicator shduld be on. ) Hydrogen not present in region, therefore,

nonhydrogenous moderator,,must be specified.*

Blank card. * Problem identification error . " Wrong element number on L-factor cards. " Blank cards. " Machine error .


Bad tape 1. ..I ..


Bad tape' 1.

k from tape disagrees with k from resohance L-factor card. * . . Exponential of the isotopic resonance integral is out of range. * k from tape disagrees with k from resonance L-factor card. * Square root radicand was negative. * Exponential of the total resonance integral is out of range. " Unwanted end .of file indication from tape 1.

Bad tape 1.


Bad tapc 1.


Bad tape 2.


Bad tape 3.


Bad tapc 4. . .

'unwanted end of file indication from tape 5.

Bad tape 5.

Bad drum 1.

Bad drum 2.

Bad drum 3.

Bad drum 4.

Unwanted end of file indication from ta.pe 6. :

Bad tape 6.


Bad tape 7.


Bad tape 8.

unwanted end of file indication from tape ,9.

Bad tape 9.


Bad tape 10.

False end of record skip from tape 1.

Unwanted end of file indication while readirig tape. Display storage location 06360 . to determine tape number. If 223, possible code error. . If 224 or 225, machine

error. Start over from beginning.

Bad tape. See 06364 e r r o r stop.

Unwanted end of f i le indication. Display storage location 06405.' to determine tape

number. . .

Pe.d tope: . See Oh41 1 e r r o r stop.

'unwanted end of file indication. Display storage location 06467 to determine tape

number.

Bad tape. See 06473 e r ro r stop. . .

Unwanted end of file .hidication. Display storage location 06527 to determine tape

number.

Bad tape. See 06533 e r ro r stop.


Bad tape 10.


Bad tape 10.

Bad drum. Display storage location 101 36 to determine drum number.

Bad drum. See 06667 error stop.

Bad, drum :4. . .

Unwarlled end of file mdicatiOn from tape 2.

Bad tape 2. .. 3


Bad tape 2.

Bad drum 2.

Bad drum 3.


Rad tape 3.


Bad tape 4.

' -Unwanted end of file indication from tape 5.

Bad tape 5.


Bad tape 6.

Unwanted end of file. indication from tape 7.

Bad tape 7.


Bad tape 8.


Bad tape 9.

Unwanted end of file indicationfrom tape 10.

Bad tape 10.

Bad drum 4.


Bad tape 2.

Bad drum 1 .

Unwanted end of file indication f rom tape 10.

Bad tape 10.

In the Iteration Program:

00 26 1 Machine or code error. G L OUT2.

00340 Machine or code error. G L OUT2.

02274 Machine error. End-of -file return. Writing tape 3.

03042 Machine error. End-of-file return. Writing tape 4.

03050 Machine error. End-of-file return. Writing tape 6.

03053 Could not write tape 6.


03076 Machine error. End-of-file return. Writing tape 7 .


03126 Failed three times to write sources on drum.

031 27 Machine error. End-of -file return. Reading tape 2.

03130 Could not read tape 2. Bad coefficient tape.

031 32 Could not write tape 3. Error f rom RTT or calling sequence.

03133 Could not write tape 3. Error f rom check sum.

15341 Count end-of -file. Machine error.

16007 Machine error. End-of-file return. Reading tape 2 for first time.

16010 Bad tape 2. Error return when reading.

1601 1 Check sums on binary source cards do not check. t 16012 Source cards numbered wrong. t 1601 3 Identification words from tape and cards do not check. t 1631 5 Machine error. WII 001.

16350 Machine error. WH 001.

16433 Double punch, blank column. t 16646 Range error. Floating decimal number out-of -range.

-In the Edit Program:

For all indicated stops except 02124, restart dump and restart.

00574 Machine error.

00653 .Machine error.


01 457 Will not read tape 2.

02124 Reads sources f rom drum incorrectly. Dump drum 1 and save tapes 2 and 0.

1 3376 Machine a15t.ur.

03377 Will not read tape 2.

03431 'Machineerror.




t Save program tape and tapes 2 and 0.

04267 Machine e r ror .


04545 Machine e r ro r .


04630 Machine e r ro r .


Restar t Dump:

00172 Normal stop. If any other stop, dump drum 1 and save tapes 2 and 0.

VIII. LIBRARY TAPE ROUTINES

There a r e three l ibrary tape routines: LTP4,. LTP5. and LTP6. T h e s e a r e essentially the

same a s the l ibrary tape routines LTP1, LTP2, and LTP3, respectively, for MUFT-4 (Ref 2,

pp 16-22); the operating instructibns ' a re identical, with the exception of the e r r o r stops.

L'l'P4

A l ibrary program tape consists of the same data files a s a MUFT-4 l ibrary tape, with the fol-

iowing changes:

Fi le 1: Coefficient program replaces the MUE"l'-4 program.

Fi le 2: aM = 1. '

File 3: The additional microscopic quantities, and 5, a r e parame'ters which determine the

anisotropic slowing-down density for each element ( P a r t One, Section 11). At present, i t is a s - '

sumed ( a s in MUFT) that all anisotropic slowing down is the result of hydrogen. Correspondingly,

I) and 5 a r e set equal to zero for all other.elements. Values for hydrogen a r e selected so a s to

make the slowing-down model consistent with MUFT-3 and -4. These two values a r e put on a

second card in the same format a s the' other eight microscopic quantities, filling in the r e s t of

the card with zeros. This card is placed after the other data card for that group.

Fi le 4 and 5: L, the lower bound of resonances,. must be greater than U, the upper bound of

inelastic matrix.

File 7: Iteration PI-ogram.

Fi le 8: Edit program.

There a r e two options available in writing the l ibrary program .tape: (1) taking the library data

from tape o r (2) reading the data from cards.

In the f i r s t option, all the blank cards a r e removed from the assembled l ibrary decks and the

data a r e then written onto tape via 'a 714 card-to-tape cdnverter. This tape is then used a s logiCal

tape 8 by the input routine WH 001 B in writing the l ibrary program tape.

In the second option, the assembly of the l ibrary decks is the same a s in MUFT-4, and the decks

. a r e inserted in LTP4 between cards ~ ~ ~ 4 0 2 8 3 and LTP40284. Cards LTP40261 through LTP40282

(WH 001 B) must be removed.

The end-of-program stop is 00533.

E r r o r Stops

00204 Machine e r ro r . WH 001 B. BCD conversion.

00334 Range er ror . WH 001 B.

01021 Tape-read failure. Tape 8.

01045 Double punch, blank column, o r both.

02145 Blank card return. Reading data for table of contents.

02146

02260

02273

02274

02304

02305

02326

02327

02354

02355

02421

02422

02571

02572

02720

02721

02744

02751

02752

061 23

061 24

061 25,

061 27

061 30

061 31

061 32

061 33

061 34

061 35

061 36

061 37

06140

06141

06142

06143

06144

06146

06147

06150

061 52

LTP5

End of r

Card count end-of-file return. Machine e r r o r o r number of elements wrong.

Wrong format o r order of element numbers on second card(s).

Machine e r ror . End of file return when writing tape 1.

Machine e r ror . RWT2 e r r o r return when writing tape 1.

Blank card return. Read data for lethargy increments.

Machine e r r o r o r number of groups wrong.

Same a s 02273.

Same a s 02274.

Blank card return. Reading data for file 4, 5, o r 6.

Count end of file return. Machine e r ror .

Same a s 02273. Writing record in file 3.

Same a s 02274.


Same a s 02274.


Same a s 02274.

File number wrong on card in a source spectrum deck.


Same a s 02274.

Input e r ror . File number wrong in deck 1,. file 2.

Input e r ror . File number wrong, should be 3.

Input e r ror . Element number wrong o r deck misplaced, file 3.

Input e r ror .

Input e r ror .

Input e r ro r .

Input e r ro r .

Input e r ror .

Input e r ror .

Illput erl'or.

Input e r ror .

Input e r ror .

Input e r ror .

Input e r ror .

Input e r ror .

Input e r ror .

Input e r ror .

Input e r ror .

Input e r ror .

Input e r ror .

Input error .

Group number wrong in deck for file 3.

Element number wrong o r deck misplaced, file 4:

File number wrong on resonance R cards, file. 4.

Too many resonances specified on deck 1 card.

File number wrong on resonance M. cards, file 4.

Element number wrong on iesonance M cards, file 4.

' Null& el, uf resonarlees wl'ollg 011 resonance M card.

Element number wrong on second deck, file 4.

File number wrong on second deck, file 4.

Too many parameters (fission ratios) a r e specified.

Element number wrong in set 1, file 5.

File number wrong 'in set 1, file 5.

File number wrong in set 2, file 5.

Element nu.mber wrong in s e t 2. file 5.

Group number wrong in set 2, file 5.

Group number wrong in se t 1, file 5.

Source spectrum number wrong.

File number wrong in deck 2, file 2.

un programmed stop is 1401 1.

E r r o r Stops

0021 3 Machine e r ror , WH 001.

00246 Machine e r ro r , WH 001.

00331 Double punch, blank column, o r both.

00544 Range cr ror . Floating dccimal numbcr out-of-range;

02156 E r r o r in reading program from tape 2.

E r r o r in writing program on tape 1.

Same a s 02156..

Same a s 02201. . .

E r r o r in reading tape 2.

Blank card return from. WH 001.

Count end of file return. Machine e r ro r .

Machine e r ro r . End of file return from RWTZ.

Machine e r ro r . RWTZ e r r o r return. . .


Same a s 03103.

Same a s 03104.

Same a s 03103.

Same a s 03104.

Same as 03103.

Same a s 03104.

111pu.L ei.rur: Fllt: Nu. wrul~g ill deck .l, 610 4 (R card). Input error . Too many resonances (absorption) on one card.

Input error . File No. wrong in deck 1, file 5 (M card).

Input e r ror . Machine o r code e r ror .

.Input e r ror . File No. wrong.

Input e r ror . Element No. wrongin new deck.

Input error . Group No. wrong.

Input e r ror . File No.. wrong.

Input e r ror . ;Group No. wrong in se t 1, file 5.

Input error . File No. wrong in set 1, file 5.

Input e r ror . File No. wrong in se t 2, file 5. .

Input e r ro r . Group No.' wrong in se t 2, file 5.

Input e r ror . Element not on tape.

Input e f ror . Group No. wrong on card with two cross section value@.

Input e r ror . Too many resonances (fission) on one card.

Input e r ror . Element No. wrong in se t 2, file 5.

Input e r ro r . Element No. wrong in se t 1, file 5.

Input e r ror . Source spectrum No. wrong.

LTB6

End of run programmed stop is 03361.

Error Gtopu

Machine o r code e r ro r . GL OUTZ.

Machine o r code e r r o r . GL OUTZ.

Machine e r ro r . Heading tape 1. End of file.return from HWrl'Z.


Same aE 02225.

Same a s 02226.

Same as 02225.

E r r o r on tape ' l . Table of contents does not check.

Same a s 02225.

Same a s 02460.

Same a s 02225.

Same a s 02460.

03126 Same a s 02225.

03127 Same a s 02460. ,

03243 Same a s 02225.

03244 Same a s 02460.

06507 Machine o r code e r ro r .

IX. GENERAL INFORMATION

Librar ies may be numbered if desired. This number is punched into 8LA of binary card

LTP40196 before writing the L - P tape. The check-sum on this binary card must be corrected. The

program will interrogate the last field of the f i rs t input card.of each PlMG2 problem in order to

determine i f the proper l ibrary is being used. This field should contain the number specified on

Form I. (See Par t Two, Section IV. )

PART THREE: APPENDICES . . . . . . . . . . . . I

APPENDIX A: INPUT FORMS FOR SAMPLE PROBLEM, FORMS I, 11, AND 111 , . . . : . .

i ._: . . . I . .

. . - , . . . . .. Fom, I

P11K2 . . . . . . . . I . ' . . . , ..

Problem Ident t i fca t ion ( 7 jC2(?4l1 ; . . , .. . . .

8- ' d ig i t s . ' . .

, , % . . . . . , . . . . . . . Tota l groups L f Total po in t s . . Total regions 3 , ' , ,

. . 1.1 N . ' 'J '

. . #la , Gecnetry Sour& Dis t r ibut ion s p e c t r m ' 1 ' , ' ~ r e a k ~ o i n t s # 2 '3 . . %k . .. .

6, Slab 1, Cyl indr ica l 6 - Edi t 5

Convnr~enac , Fktrapolation C r i t e r i oc Factor Use E A e cmJ fA ?U> I ' 505 Tape 0

Eoundary Conditions

m L c~ C~ CR C~ C~ CL c~

N ' % lrl

"CI

& :

. .

CL = Left hand boundary condition . CR = Right hand boundary condition, C = 000, f o r 4'= 0. C = 704, fax- = 0

m = Group number of f i r s t s e t of conditions in t h a t fow, . m = C A l l groups have same conditions a s f i ~ s t s e t i n the row.

Form I1

P r n 2 Problem Ident i f ica t ion 3 5020041

(8 d i g i t s ) pl\

kr &sh point number a t r i g h t hand end of region 10 ( n ) Total elements 6 (I )

a lvbsh s i ze 5076 j

2 ToUl bucklhg 484032 Resonance Buckling 485 .I

8 Ranaverse bucklings : X-direction 49635 y-directign 000

< Macroscopic The& Cross Sections for Region 2 1 D cd 502897 4977505 vE

j

o 5% f 50134594

r = 0, normal Ni, number density, f o r element i of region j. r = 100, nonhydrogenous moderator

V\

%a

4 5

L, resonance self-shielding fac to r

G

li

- --- -

k =

1

20

-

9, one

k

009

factor

51

L

1

f o r a l l

00

L

0

resonances

00

L

0 00

L

0 00

d

L

0 00

T.

0 00

1.

0 30

1.

0

. . . .. . . . . . . ".

Form I11

. . PlMG2

Problem Identification 35°20C41 (8 digi ts ) ' . . . -

I n i t i a l . eigenvalue estimate 5110144253

Source distribution c , card number

000 converge 7- I

c 3 , f o r f l a t source guess 001 one iteration

. .

E-

3k (0

2 '3

. . ~ r o u ~ s to be edited 10 25 54 55 . . .

.- - - ----------- ' --- _ I _ - - - -

CCJ . %.

'2 To completely eliminate flux editing enter group number H+l. a

a c=>

APPENDIX B: CHOMP CARDS

Since the running time of a PlMG problem using a flat source guess i s prohibitively long, an

option has been included in WANDA-3 (Ref 3) such that the converged eigenvalue and source a r e

punched out in floating binary in a form which is acceptable a s input to PlMG. Sense switch 6 must

be down during the running of the WANDA problem. The CHOMP cards a r e then used a s input to the

PlMG problem in place of the decimal source guess which would have been specified on Form 111.

A CHOMP deck which i s to be inserted in a PlMG problem consists of the following cards:

1) A card which is blank in columns 1-72. All of the CHOMP cards which a r e punched by

WANDA will have the problem number automatically punched into columns 73-80. This

"blank" is used by the program to signal that binary cards and not decimal cards a r e to fol-

low.

2) A set of cards with a sequence number punched in 9LD and a card check sum in 9R. The

f i rs t card will have the converged (or latest) eigenvalue in 8L followed by So in 8R, S1 in 7L,

etc., in the same order a s the information is placed on the decimal input source cards for

P1 MG.

The "last card" (which is read in by the edit routine) and two blank cards should follow the last card

of a CHOMP deck within a PlMG input deck.

CHOMP cards a r e punched out by the PlMG code in two different instances:

1) Throughout the entife iteration and edit routines of PlMG the latest values of the eigenvalue

and source a re stored on drum 1 such that if there is a power failure o r any program stop

which requires a restar t , this latest eigenvalue and source can be punched out in the CHOMP

format via the Restart-Dump deck of PlMG which should be available at the console. Then,

to res ta r t the PlMG problem, the last section of the PlMG input deck-the source guess, the

"last card," and two blanks-should be removed, the source guess replaced by the CHOMP

deck just 'punched, and the Restart-Positioning card placed on top of the CHOMP cards. The

res t of the instructions a re found in Par t Two, Section VII.

2) If a problem must be manually stopped by forcing it to proceed to the editing routine (sense

switch 1 down), at the end of the edit a CHOMP deck is automatically punched so that the

problem can be continued at a la te r time. (See Par t Two, Section VII for tape saving.)

In summary, any CHOMP deck for a given PlMG problem is in the form whereby it can be read

into the problem from the beginning o r via restart .

In order that a CHOMP deck, .which has been punched out by WANDA, be accepted a s input to a

PlMG problem, the total number of points and regions must be the same in the problems run on both

codes.

APPENDIX C: ,FLOATING POINT NUMBERS

Input Form

In order to convert a fixed point number of the form

XX. XXXX

to a floating .point.number of the form

(which in this code is called the excess-50. floating point form), write the fixed point number a s a

fr$ction "

, ,

t imes the corresponding power of ten. Fifty plus this power of ten becomes the xas 50 exponent part,

23 < EE < 88, and the fraction is the x-s 50 fraction part, ffff. . f. Some examples of converting a r e

fixed - x-s 50

An x-s '50 floating point ze ro i.s entered a s 000.

Output Fo rm

All floa'ting point numbers a r e of the form

which .is easily interpreted a s

*(0. fff. . . f). 10 *PP

APPENDIX D: BLANK CARDS IN INPUT DECK

An input deck to PlMG2 consists of the following:

F rom Forms I and I1 - May o r may not be a blank

Source Cards 1 Blank 1- Edit Card

Blank

1) A set of cards which is punched in the mariner described in Pa r t Two, Section VI from

information supplied on Fo rm I and'one o r more Forms 11. There must be no blanks in this

portion.

2) A set of cards which will be either:

a) Decimal Cards punched f rom information supplied on Form(s) 111, o r

b) ~ i n a r y Cards (CHOMP cards)" which a r e obtained from one of two places:

WANDA-In which case columns 73-80 will contain the WANDA Problem Number in

decimal.

PlMG2-Restart -Dump, in which case columns 73-80 will most likely be blank.

En order for the P l l M t i L code to know whether decimal cards o r binary cards a r e to be ex-

pected for source cards, a blank card should be placed ahead of the binary source cards only.

never ahead of the decimal source cards. The program input routine reads only columns . 1-72 of any card and, thereby, determines if a card is a blank o r not; thus, there may be

punches in columns 73-80 and stil l the card would bc considered as a blank. There should

be no blank cards within the binary o r decimal source decks themselves. Some of the binary

cards may look like blanks except for a few 9-punches in columns 1-72; however, this is the

card number (in binary) of that source card, and these cards must be included a s part of the

binary source deck.

' The upper limit on the number of significant places in any x-s 50 fraction part is eight. However, the maximum number of places permitted in the fraction part of each piece of data, a s indicated after the explanation of each piece of data in Par t Two, Section IV, should be adhered to in order to insure that all the data will fit on their respective punchcard.

" See Appendix B.

3) An edit card (referred to previously a s the "last card") which i s punched from information

supplied on Form 111. There is only one card of this type for any PlMG2 problem. If no fo rm

is supplied, this card is a blank. If Form I11 i s supplied and the lines labeled "Groups to be

edited" a r e blank, this card is blank; If there a r e any entries in these lines, a 9 i s punched

in the columns indicated by the numbers entered.

4) Two blank cards which function solely to get the last card into the 704 card reader .

APPENDIX E: CODE NUMBERS FOR ISOTOPES

List by Code Number

Code Number Element Code Number

H-1

0-1 6

Z r

C

Mo

Fe

Ni

Nb

A1

Sn

Cr

C 0

C d

H f

Mn-55

Li

U-235

a-7.36

U-238

h-L3Y

Pu - 240

Pu-241

Pm- 149

1-1 35

Sm-149

Xe-135

Fission Products

B-10

Deuterium

Element

Be-7

Be -9

F

C 1

Eu-151

P

Na

S

Pb

Y '

U-233

U-234

* g Hf -1 77

Si

Au

Th-227

Th-228

Th-229

Th-230

Th-231

Th-232

Th-233

Th-234

Pa-233

Hf-174

Hf-178

Hf-179

Hf-180 .

List by Isotope .

Element '

C r . Ueuterium

' Eu-191

I?

Fe

Fission Products

W-1 H f

Hf-174

Hf-177

.Hf-178

Hf-179

~ f - 1 8 0

1-1 35

In

L i

Mn-55

.Ma

Na

Nb '

. . Code Number : Element ' ' .

0'53 Ni' ' . . .-. .

009 ' ' '0-16 "

056 ' ' P .'

0.29. . . .Pa-233 . ;;

0 39 Pb . . ' 0 . . 040 Pm-149

004 Pu-239.

013 Pu-240

042 Pu-241 :

012 S

Code Number

007

002

045

APPENDIX F: ; SAMPLE PROBLEM

The sample prpblem is constructed from the data a s specified on th,e input forms of Appendix A.

The Forms I1 for the second and third region are not included kAppendix A, but the information

which is entered on them can be deterinined from this appendix. , .

The first two pages of the print'outs in this appendix are IBM-7.O;Q listings of the input cards. The f irst page is the l i s thg of the input deck with the decimal source cards (cards numbeked.15 through

24) a s specified by Form 111. The second page is a card-hiage listing of the CHOMP-type source

cards which a re punched'out by WANDA-3. (See Appendix B.)

The rest of the printouts in this appendix a re those which wffl be: created on the on-line printer

and the off-line ,when the .psmple problem is run,.

*** *** *** *** *** *** *** *** *** *** *** *** *** *I* *** **I *** *I* I** *I*. .** *** *** .** u*+ ++* +** +++ +++ **+ +++ +*+ * I * +*+ +++ +** **+ ++* +I* +++ *a+ +*C *I* a** .*Q ++* **+ +++ **- --* -*- -** -*- --- --- *-- --* --- *-- --- **- --* -*- -it* *-* -*- -** --a t-- **- **- --- ++o ,-,o* ""0 0'9 a*,) 2.0 g r * g j r ~ n * rrlr x.20 ;*a; +*a i;oa 3!+3' i i + j eri; add O C j .ij.l* ;Ou.(i(;a *(iO *a+

* 1 1 1 a I > * 111 1 * 1 1 1 I * I * "1 11" 1'1 .ll" **l **a *l* 1.11 "l* **a. 111 *11 ++2 221 2'2 2 2 2 42' 22.k ' 2 2 2 x 2 "2 2"s 2Zr 22a *a2 222 2'2 222 ear *i2 *2* a22 '"2s ar* 2+*'2** ++3 33" 3 ~ 3 34tr 3"' 34' 33* **a 33a 9x2 ar3 3gr *a 3 33a 333 3** 3** u:* 3 ~ 3 j*3 **a 3*+ 3** *3* aa4 4 4 9 444 41r 4a4 4 4 ~ w&r 4*4 ar4 4rr4 #a+ +44 ++4 44r 444 'I*+ 4a4 %*.a 444. 4 1 4 *a* *** 4+4 44* +c5 55* 535 51+ 555 '"5 gra cr5 jcr r+5 a55 rxr +rj 55a 555 5rx 551 5X* H a "55 *** 5x5 55" * 5 + +r6 6 6 0 666 6 u 6 +xu *6+ ah* 6*6 he6 +6+ re6 b*6 ""6 65' 6 6 5 6** 6 6 6 t6r 'ha 666 66% =a* **a *66 *r7 77+ 777 7*7 +++ 777 *a+ a77 7xu 777 i++ tan 4*7 77c 777 7r7 **a 747 *7* a = 7 * r + **4 7 7 ~ . 7*7 .agx rar K.UU gag 683 gas * a * +*a "8 +*a 868 uax crg 6a* 338 e*a *a? fsg 6aS aqa a** a*% *nu 8*U *+r ++ i t * * i , c+r +r* sxg .+rc *+a rcl+ rrw u+r rnr *so 933 9+r nry 9x9 n c ; ~ 97.7 959 9s* 9 ~ 9 "$7 *Kg *** *** **u *a* u** *** *9* .+* It* **C C * * **I U*X *** +** *** **u T i * ur* *** a** * a * uu* **a

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r*3 3 3 r *33 33+ ;)x 33u 3 3 s a+: rr* 5x3 *a'+ na+ raa uaa .#*a cra +ur +a* x+* aua aua a44 as* ax* *+4 44+ +44 4a4 44s *4* u44 *44 44s a.44 44c 444 **4 4 4 s *44 4*4 i 4 x * z ; aaa 4ra 444 u*4 uau 4*e "rg 55, +55 55s 55' 5+a jag rgj 55a "jj 555 "55 wj 55u ujj 5jr ""5 t,:,j j 3j a95 cr5 r5u a5r e5a ++6 66+ 6X.U bU* +6* ""6 "96 "66 a6a '66 669 * * b 66" "66 666 6Cb 6'6 (,** * & b Xu5 XU* 664 +r7. j7+, 7 ~ s 7*7 "7" "77 77u 77u 7a+ 7+'1 7ar Q K . ~ *+7 77u 7ra 'I++ 77u r;+7 4:*7 a*+ aatl 777 771, 77, r+8 dg+ 8*r 6b* **a a + ~ *nd *+r 688 888 **a U Q ~ 68u g * u a + j ,535 P + Y aaa ~ U J 30" 283 a ~ + 18t I *r+ rr+ a + * +.a* **a a9r a*+ +4s urr aa* K.++ +++.a urjg 9y9 99:: ++9 itys 99,; I???; - 9 9 * a*;? 993 $a3 999 *rr cc* u.u+ +*'* **+ a** *a+ +++ +rr *a* a** *a+ c+u +s;i +a* arra rra.2 a ~ a raa raa <;a+ ++a aua *it*

i

I** i t * , *a* **I W * X t * *,u * Q * at* a*, .*a a*.% **P at* tc.2 *an *%a .>*a *+a at3 *40 Pf-I I** **?I *+* I** UO* *QC ut+ +*t ZIIQ ut* )*a *(I* + X C *XU CO* U*U *u;( u*0 aua +au +r+ u ~ r ur* a** *** +i*t *I* +It *UI UaC t*U **I. +QI UXX FIQ CCI It+* CIC *UE 4EU + + a +?CC US* +%a St+ 41s * t i +tU t * l ++I1 *t* I** ,Sli I+* .Xtt tl4 11+ X U * It* **U *+Q * X U 4 X E S O X X C +** 4Xt * * I * i C t**

*x+ *tit *.XI) ,XI <.+&it C * C ICII \ + + + *u* iTa s 1 ) ~ *+.I t i t * a** *!AX. .L;tn +h9) + i B a *+!a liU* **a a*+ * * i t

*+* t'*+ *at i t * + Q U * !+a* r+n ura twv uua ilux a*+ +.ax ++Y rar ax,> .+*+ a%* auu ;irs xnu aar *a+ *rc *+a x i l r +*a .*a+ uaa ua+ *,?a ;a* a:;* .a+* QUI *a+ U++B **.x a*+ XC.Y +:.c uiie ax* +:+a ae* ++a n+t +** **+ **t +** *x+ **t *t* 441 C*.X nwu G I + .WE* *a* *ta *ax U ~ X sxa c;.* xha ~ * n RCI ax* naa *it* cr+ **a e a r *a* +a* car rar *.*, *+a u*r aau *xu +4x iru .X.XB &ax x q * i a ~ ::a* *** .xtr *a+ + ~ 4 *I+ . ... t*t t * ~ a** **+ U X + !+it* uu* I U W (I*<- a.wa 'i*u uiii t ~ u *xa u** *OK. 81: ( i x f xxr nwa rt:: +nu err er+ t+* I** st+ +*t t * ~ wuu ut * * Q C r i ~ X U ? .at* it** *XI t.2~ .n.xs a** ~ . x . Y ii: - a * CUE ~ t t CC* e+n t** ++r a*+ cxr +r+ *a* a99 # r + *rr r,*x rar c i * as*. +rr rc* #ar **a I = + c g q sra aaa i+c* a+* a** a** *** .** *** *** K*U * * * *,* *u* u** a*, *a* *I* *** *** a.+* a** *** *a* *XU to* *a* at* * I * I**

. . I .. . . . * . * * * PlMGZ • . . • . . . .

PROELEM I D E N T I F I C 4 T I O N 35020041 • . . a ..*I.. ......

ON OFF ... . . YES . ... OPERATOR --------

RESTART . . . ON OFF * .

NO .X. . . . LOG1 CAL PHYSICAL

TAPE TAPE U N I T REEL NUMBER LETTER NUMBER

1 . . . --- , , ', ----- 2 .. . . ---- , . , ----- ..

3 . . ---- . . . ----- 4 1 . . --- , a ----- 5 , -- - , , , - - - - - 6 . m . - - * , ----- 7 . . . --- , , , ----- E . . . ---- , ----- a . . . ---- . . ----- 0 . ---- a a , -----

. .

-

P l M 2 . Z 3 5 0 2 0 0 4 1

5 5 SROIJPS c:, P O I ' T S 3 R E G I O N S

- . . ... - . < ?

S L A B GEOMETRY SJ'JRCE SPECTRUM NUMBER 1

CONVERGEqCE T.ZITEREOk

L A C 3 D A - LAMBDC T T - 1

ABSOLUTE V P L J E O F ---------- t * 0 0 0 5 0 0 0 O LAWBDA

T

AFI3

-AMRDA, - L.8MBD.S - --- - ----------. - ---- $ @ 0 0 C ~ 5 0 C 0 0 ------

LAMBDP

E X ; T R A P O L A T l C q F A I l O R O F .O,COOO.

F = , 5 1 0 F = e.00 A 8'

> .

EDIT 5 . H P j BEIP REOUE$.TEC . '

FEW' GROIJP E R E A K P O I Q T B I S S 1 GROUP 10 FEV GROUP E.R?AKPOINT i I S 4 1 GROUP 2 5

. . GROUPWISE BOUNDAFY ~ V G I T I O N J + cm = o ;

GROUP ST L E F T B C J N ~ A ~ Y AT F ' IGHT BOUNDARY C = C '.

ALL. o o o c ~ o n o 2 0 ~ O O O C O O O

. .

. . *

REGICN 1 3 5 0 2 0 0 4 1

EhlDS 4.1 P O I N T 1 0 MESH S I Z E 7 6 2 0 0 0 0 0

TOTAL NUMBER OF E-EMENTS 6

TOTAL BUCKLING -2 4 0 3 2 0 0 0 0 RESOqANCE BUCKLING -2 5 0 0 0 0 0 0 0

TRANSVERSE R U I K L I M G X-DIRECTION -1 5 3 4 9 9 9 9 9 Y-DIRECTION 3 0 0 0 0 0 0 0

YLCROSCOPIC THERMAL TROSS.SECTIONS

D I F F l l S l O N ABSORPTIOU N11-FISSION 2 8 9 7 0 0 0 0 -1 7 1 5 0 4 9 9 3 1 3 4 5 9 4 0 0

ELEMENT NUMRE? DENSITY

1 -1 3 8 5 6 4 0 0 0 . 2 -1 1 6 9 8 3 0 0 0 3 -1 l a 5 4 7 0 0 0 4 -2 2 2 9 9 6 0 0 0

1 8 - 3 1 6 5 9 0 0 0 0 20 - 4 1 2 0 8 0 0 0 0

RESONANCE SELF S H I E L D I N G FACTORS

ELEMENT K L

2 0 9 1.0007 . n a o o ,0000 . n o o n .oooo .oooa .noon .oooo

. .

- -. ' 1.. '

PlWG2 35020041

I K I T I 4 L EIGEF!VALDF: 1.0:.4(.2529

IN! TI1.L SOURCES

RIGION 1 POINT

3 -1 82834319 -1 92S93P39 -1 82276599 -1 81594190 4 -1 806h8219 -1 7$572;89. -1. 38239360 '-1 76864270 9 -1 75520430 -1 7437>P79 -1 736763'50

RFSION 2 'OINT

10 -1 29602520 -1 1823?130 - 1 76270080 -1 24062590 14 . -1 21807370 -1 L961i560. - 1 15544840 -1 1562685C. 18 -1 13970380 -1 122'75530. -1 10836530 -2 9540769E 2 2 -2 83779399 -2 73375i00 -2 64111199 -2 5595120C 2 6 -2 48942799 -2 5328,,)700 -2 39417900 -2 3826090C 30 ' -2415C8399

RE.310N 3 'OINT

3 0 r l 0 b 0 ~ 0 0 0 ,?)0001?Q00 00000006 OOCOOOOO 3 4 00000000 ~~)0000C00 00000000 :00000000 38 00000d00 ' 0 0 0 0 0 ~ 0 0 onoooooo 00(100000 42 rlOOOO~IO0 60OC70nOO onoorlooo

EZGEVVALUES

ITERATION MIN WJ?MAL MAX NTC 1 ,99452356 :. 0.1~74217 1.04742564 .@lo14

. .

Z 1.00152108 1.00323835 1e01914945 .00100 3 1.00171649 1.00771297. 1-01105395 e00052

- - ~. - -- -.-...A* . .. - - - . - - __ _ 4 1.0019?€70 BeOOZ43683 1-00684005 ,0,00488 5 1 .0020?~11 1.00Zi.3236 1.00459945 e00256

6 1.00207E49 E.OOiZL689 1.00342239 a09134

7 1.00210530 1.00217748 ., 1.00280689 .00070

. .

CONVERMD EIGENVALUE I

8 1.0021?921 1 .00215690 1 e00248'548.- . ..000',7

35020041 PAGE' 1 PlMG2

55 GROUPS 44 POINTS 3 2EGIONS

SLAB GE3METRY

CONVERGENCE CRITERION LAMBDA - LAMBOA

T ' 7-1 ABSOLUTE VALUE OF ------------------- f e00050000

LAFBDA T

AN0 --- LAMBDA. - LAMBDA . --- ----------- - f e00050000

LAMBDA

ZXTRAPOLATION FACT,OR OF eOO0OO

F = 0500 F = a500 A B

EDIT 5 HAS BEEb REQUESTED

GROUPWISE BOUNOARY CONtIt lON J + CO =0

GROUP AT LEFT BOUNOARY AT RIGHT BOUNDARY C = C =

1 00000000 20 40000000 2 0'6000000 20 40000000 3 00000000 20- 4000000.0 4 00000000 20 40000000 5 00000000 - 20 40600000 6 00000000 20 40000000 7 00000000 20 40000000 . 8 00000000~ 20 40000000 9 00000000 20 40000000

10 OOOOOOOQ 20 40000000 11 00000000 20 40000000 12 00000000 20 40000000 13 ,00000000 20 40000000 1 4 00000000 . 20, 40000000 15 OOOOO000 20 40000000 16 00000000 20 40000000 17 00001J000 2 0 . 4 0 0 ~ 0 0 0 0 1'8 00000000 20 40000000 19 00000000 20 40000000 t o ooooopoo 20 40ooonnn 2 1 OOOOOOOO 20 40000000 22 00000000 20 40000000 2 3 00000000 20 4 o o o o n ~ o 2 4 00000000 20 40000000 2 5 00000000 20 40000000 26 00000000 20 40000000 27 00000000 20 40000000 2 8 00000000 20 40000000

. -.. . . . .

35020041 PAGE 3

PlMG2 35020041

I N I T I A L EIGEnVALUE 1.01442529

I N I T I A L SOURCES

REGION- 1 POINT

0 -1 82834319 -1 82693939 -1 82276599 -1 81594190 4 -1 80658219 -1 79532789 -1 78239360 -1 76864270 8 -1 7552C430 -1 74374979 -1 73676350

REGION 2 PO I NT

10 -1 2 9 6 0 i 5 2 0 -1 28232130 -1 26270080 -1 24062590 1 4 -1 21807070 -1 19614560 -1 17544840 -1 15626850 18 -1 13876980 -1 12276530 - 1 1 0 8 3 6 5 3 0 -2 95407698 2 2 -2 83775899 -2 73375300 -1 64111199 -2 55951200 26 -2 4 8 9 4 i 7 9 9 -2 43280700 - 2 39417900 -2 38260900 3 0 -2 4150.5899

REGION 3 POINT

3 0 00000000 3 4 00000000 38 00000000 42 00606000

ITERATION MIN a99452361 a00152116 r00171659 a 00192873 a 00202717 e 0020P858

1400210534

NORMAL 1 r00424223 l a 0 0 3 2 3 9 4 1 1.00271298 l a 0 0 2 4 3 5 8 9 1.00229241 1.00221695 l r 0 0 2 1 7 7 5 4

CONVERGED EIGENVAL 1e002 15696 1e00214621

MAX 1e04742564 1.01914950 l a 0 1 1 0 5 3 9 2 1e00684012 l e 0 0 4 5 9 9 4 8 l e 0 0 3 4 2 2 4 4 1e00280696

.UE l a 0 0 2 4 8 5 5 4 1e00231773

r w a 350200*1 PAGE 1

FlNAL E O i T NO* J

NORMAL1 ZED SOURCE I

REGION 2

REGION 3

REGIONAL SC4JRCE AVER4GE

FLUX

35020041 PAGE 2 -1 62836034 -1 55243795 -1 48457383 . -1 36888639 -1 31903081 -1 27289684 -1 18389545 -1 13410199 -2 88595433. . -2 40696984 -2 28163459 -2 19696420 -3 98387459 -3 69806203 -3 49299333 -3 22991020 -3 14120422 -4 67154256

35020041 PAGE 3

FA- FEY GROUP 1

. . . .

REMOVAL ABSORPTfON .- NU-FISSION FAST FLUX

REGION 1

POINT 0 -3 659022T 1 -3 65899753 2 -1 '65892134 3 -1 65879257 4 -1 65860905 5 -1 658368-9 6 -1 65807145 7 -1 65772044 8 -1 65732708 9 4 65691708

L 0 -a 65654241

1

I 35020041 PAGE 4 26 -1 70138925 -2 44680e15 -2 80375236 -1 55714232 2 7 -1 70025396 -2 44,730423 -2 30449491 -1 47982787 2 8 -1 69770438 -2 44843496 -2 80627897 -1 40523267 29 -1 69199116 -2 45127565 -2 81084452 -1 33160365 3 0 -1 67796396 -2 45911C64 -2 823a3623 -1 25273355

REGION 3

P O I N T 3 0 10735014 -2 13917C05 00000000 -1 25273355 3 1 10359026 - 2 14901638 00000000 -1 17803253 3 2 10035147 -2 15848838 00000000 -1 12659735 3 3 -1 97570052 -2 16762315 00000000 -2 90734184 34 -1 951%7489 -2 17644254 00000000 -2 65454316 3 5 -1 93011799 -2 19494336 00000000 -2 47460595 36 -1 91110824 -2 19309450 ~ O O O O O O O -2 34535869 37 -1 89411711 -2 20032773 OOOCOOOO -2 25165970 3 8 -1 87838910 -2 20804295 00000300 -2 18302062 3 9 -1 86511597 -2 21460430 00000000 -7 13207456 40 -1 85420712 - 2 22034650 00000000 -3 93566863

-1 84525390 -2 22508551 00000000 -3 63675340 41 42 -1 838r8585 -2 22863745 oooooooo -3 39540986 4 3 -1 83432039 -2 23084212 00000000 -3 18933268 44

REGIONWISE FEW GROUP CONSTANTS

REMOVAL ABSORPTION NU-F ISSION D I F F U S I O N

REG1 ON 1 -1 65815360 -3 86216219 -3 61154438 1 25787064 2 -1 70059389 -2 44586603 -2 80280688 1 23140184 3 -1 91209272 - 2 19599735 00000000 1 24360926

FAST REGIONWISE ABSORPTION

REG I ON 1 - 2 37713799 -1 21809700 -3 18319197

REGION CYECKS

REGIOK 1 11148368 11890848 2 -1-98352242 -10357036 3 -1-12345189 -1-11985483

35020041 PAGE 5

EAST FIEW GROUP 2

POINT a5

4 t 5 845

1265 16.5 20.5 2465 28.5 3265 36.5 40.5

REMOVAL ABSORP.~ I ON NU-F I ss I ON FAST 'FLUX

POINT 10 -1 68621906 11 -1 69027929 12 -1 69661802 13 -1 70207335 14 -1 70597863 15 -1 70848282 16 -1 70995009 17 -1 71073245 18 -1 7 l l 09912 19 -1 71122986 20 -1 71122917 21 -1 ~ l l ' r 4 1 0 4 22 -1 71095593 23 -1 71060585 24 -1 70994818 2 5 -1 70874902

35020041 PAGE 6 2 6 -1 70670656 -2 2 2 8 4 6 4 ~ 2 -3 23834701 -1 69668236 27 -1 70364761 -2 22797229 -3 23807880 -1 59101711 28 -1 70031626 -2 22740068 -3 23777264 -1 48921659 29 -1 70120765 -2 22739084 -3 23779492 -1 38745864 3 0 -1 72576848 -2 23083338 -3 23978391 - 1 28188525

REG I ON

P O I N T 3 0 3 1 32 3 3 3 4 35 36 37 38 39 40 41 42 43 44

REGIONWISE FEW CROUP CONSTANTS

REMCWAL ABSORPTION NU-F ISSION


REGION CHECKS

REG I ON 1 -1 34850400 -1 42102013 2 -1-24.963238 -2-58642626 3 -2-74917304 -2-72330232

D I F F U S I O N

REMOVAL

D I F F U S I O N

NU-FI SSION FAST FLUX

35020041 PAGE 7

FAST FEW GROUP -3

R E 6 1 0 n 1

P O I H T 0 -1 82258564 -; 69257177 -1 10273476 55646813 1 -1 82254900 - 2 65257464 -1 10273508 5543E207 2 -1 82251282 -2 69257758 -1 10273519 551048b7 3 -1 82219605 -2 69256276 -1 10273251 54552802 4 -1 82155707 -2 69249844 -1 10272244 53783821 5 -1 82039134 -2 69233628 -1 10269812 52791708 6 -1 81844642 -2 65M0759 -1 10265002 5157E105 -, -1 81548640 - 2 69141809 -1 10256541 50124831 i -1 81146291 -2 65043313 -1 10242595 48412582 9 -1 80696658 -2 6~882898 -1 10219783 46410529

lo , -1 80533852 -2 6E615049 -1 10179842 44083616

REGIOH 2

eorni 10 -1 63975798 -1 15490874 -2 30042498 4408?616 11 -1 63598188 -1 I5542612 -2 29922739 39974967 12 -1 63166791 -1 35568170 -2 29881224 36217207 '

13 -1 62933474 -1 IC%2819 -2 29881094 3-96368 1L -1 63003264 -1 15590996 -2 29903214 2938C864 15 -1 63130029 -1 15595361 -2 29933623 26281368 16 -1 63286894 -1 I5597458 -2 29963376 23417114 17 -1 63436609 -1 15598223 -2 29987983 20799692 18 -1 63553968 -1 15598260 -2 30006045 18428864 1 9 -1 63636169 -1 15597965 -2 30017862 16294374 2 0 -1 63685297 -1 15597574 -2 30024362 14975095 2 1 -1 63705556 -1 I5W.71180 -2 30026438 12662297 22 -1 63701222 -1 15596758 -2 30024679 11121715 2 3 -1 63677509 -1 15596156 -2 30019484 -1 97348814 2a -1 63645512 -1 25595072 -2 30011765 -1 84795152 2 5 -1 63633474 -1 I5593036 -2 30004628 -1 73362478

--

35020041 PAGE 8 26 -1 63707907 -1 15589415 -2 30006725 -.l 62859197 2 7 -1 65007064 -1 15583435 -2 30038125 -1 53160392 2 8 -1 64775217 -1 15575155 -2 30139032 -1 44229909

REG1 ON

POINT 30 3 1 32 33 34 35 36 37 3 8 3 9 40 41 42 43 44

REGIONWISE FEk GROUP CONSTANTS

REiOVAL ABSORPTION ,NU-FISSION DIFFUSION


REGION 1 -1 27309688 . - I 93108524 -3 12783406

REGION CHECKS

REGION 1 -1 21136695 -1 25358908 2 -1-17241223 -1-10891326 3 -2-29049689 -2-28271724

THERMAL REGIONVISE ABSORPTION

I REG 1 ON

REFERENCES . . . . . . . . . . . . . . . . ' . . . . - . . - . . . . . . . . . <. . . . . . . . . . . . . . . . . . . .

1. E. Greuling, F: Clark, and G. Goertzel, "A Multigroup Approximation to the Boltzmann Equation .

f o r Cri t ical Reactors, " NDA 10-96. . .

2. H. B'ohl, E. M. Gelbard, and G. H. Ryan, "MUFT-4, Fast Neutron Spectrum Code for the IBM-

704, Bettis Atomic Power Division Report WAPD-TM-72 (July 1957).

3. 0.' J. Marlowe, C. P. Saalbach. L. M. Culpepper, and D. S. McCarty, "WANDA-A One- !!

Dimensional Few-Group Diffusion ~ ~ u a t i o n Code for the IBM-704, " Bettis At"mik Power ~ i v i s i o n '

Report WAPD-TM-28 (November 195.6).

WND-TM-13 5 ADDENDUM # 1

PIJYG - A ONE-DIMENSIONAL MIILTIGROUP PI CODE FOR THE IBM-704

. : j

, % . . ; : - . , . . . . . I . .

.. . ; : . " . . , . . . . . . . . . .

' . H? ~ b h l , Jr.

CONTRACT AT-11-1-GEN-14

Aqailable fr9m t h e Office of Technical Servfces, - Department of Commerce

Washington 25, D, C,

.. . . . . . . ! '. . ._ , . NOTE ' . . . .. I . . . .. ... /.-. .._. . , ' : . 1 "

This , . :doctynent . . . i s an fnterfm memorandum prepared pr imar i ly f o r ' i n t e r n a l reference and d ~ e s . n o t represent a f i n a l expression of t h e opinfon of Westinghouse, When t$isijemorandum i s d i s t r i b u t e d e x t e r n a l l y , it i s with t h e express understanding that ~ & & , i n g h o u s e makes no representa t ion a s t o completeness, accuracy, o r usa- bi i&ti ' : 'o$> information contained there in . . . . ' , . . I

BETTIS ATOMIC POWER LABORATORY

. . . PITTSBURGH, PENNSYLVANIA 2 .

$ . . . .

OPERaTED FOR THE U,S, ATOMIC ENERGY COB31UIISSION BY WESTINGHOUSE ELECTRIC CORPORATION.

STANDARD EXTERNAL DISTRI'B'TION

UC-34,: Physf c s and Mathematics, TIG-1+530, 15th Edi t ion

Manager, P i t t sburgh Naval Reactors O p e r ~ t i o n s Off ice , AEC Argonne National Laboratory, W. F. M i l l e r ~ r ~ o k h a v e n National Laboratory, J . Chernick Broqkkaven National Laboratory, M. Rose David Taylor Model Basin, H. Polechek ~ n o l i s A tom% c 'Power ' Laboratory, R, EhrIich Los Alamos S c i e n t i f i c Laboratory, B, Carlson New York un ivers i ty , R. Richtmyer Oak Ridge Nationel Laboratory, A , Householder Universi ty ' of ~ a l i f o r n i a ' Radiation Laboratory, Livermore, S. Fernbach

Tota l

No. Copies

615

. . . . . . LEGAL NOTICE

This r epor t was prepared a s an account of Government sponsored work, Nei ther . . . . . . . . . . . . . . .... t h e United S t a t e s , nor t h e Commission, nor any person a c t i n g on behalf of t h e

A , Makes any warranty o r representa t ion, expressed o r implied, with respec t t o t h e accuracy, compl.eteness, o r usefulness of t h e information contained i n t h i s c e ~ o r t , . ' . o r ..... -. ....... t h a t t h e use of any information, apparatus, method, o r process d i sc losed f n ' t h i s . . . . . - . . r e p o r t may not i n f r i n g e p r i v a t e l y owned r i g h t s ; o r

B, Assumes any l i a b i l i t i e s w i t n r e spec t t o t h e use o f , o r f o r damages re- s u l t i n g . . . . . from t h e use of any information, apparatus, method, o r process d isc losed i n t h i s r epor t ,

A s u s e d ' i n t h e above, "person a c t i n g on behalf of t h e Commissionw includes any . '

employe o r con t rac to r of t h e Commission, o r em?loye of such con t rac to r , t o t h e e x t e n t t h a t such employe o r con t rac to r of t h e Commission, o r employe of such cont&ctor prepares, disseminates, o r provides access t o , any information pursuant t o his'employment o r con t rac t with t h e Commission, o r h i s employment with such contrac tor ,

P N G - A ONE-DIMENSIONAL MULTIGROUP , ' Pi CODE .,, FOR; . , THE . I IBH-704

. .

The f9llowing two sentences should beadded t o t he repor t WAPD-T14-135 i n . . . ,.. . . . . . , . . %

; . 4. : . . . . . . . . . , I : . .' . . . . i. , . . . . . . . t h e s 6 c t i o n s . . $*di&A'9do

. . . . : . L . .

nj6 ,; ~ e e % i i i h I V , :Fbi+@ IT $0 t h e paragraph describing + rtt (p. 23) add: . . . . . . t, , .,: '* .

. . : .. , : ,:. . . . . . . . . . . . . . . . . . . . . . . _ & . . . . ( 1 . . ... - l ~ $ p o t o p e s , " ~ $ ~ be entered i d ascending order according t o i . l l . , : : :, <,:,,- , " "' :; ,::

. . , ,:.,;.:~:,::,.,::~~ , , $ " .'

~ * r t . . ~ W O , s ~ ~ ~ ~ ~ ~ ; v I I I ; ~ . L T P L , . . . t o the concerning F i l e 3 (p. 34) add: . . . . . . . . . . . ' . . I .. . . /. : ' , , . . . : . . . i . . , . 8 .

! ~ ~ i n c e ' i s b ~ ~ i b ,:. ., : .. . .. , ,._ .,, . . . . iloiring . ; down due t o hydrogen i s not t r e a t ed separate ly

i n ., . . . this program as it i s i n MUFT-4, y and C. us must be entered i n t h e ! '

$4

~y r lG2 l i b r a r y as equal t o 1 and cs, respectively, i n order t o be consis- . I * , " h t , . .

3. ' . . . . ..." . ,'! : . . . ,

ten<. A:... with ,:! ~ u ~ f - 4 . ~ . , jt

a one-dimensional hultigroup pi code for the bm-704

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