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SCIENTIFIC AND TECHNICAL INFORMATION

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NOTICE: 'Wen goverment or other dravings, speci-fications or other data are used for any purposeother than in connection with a definitely relatedgovernment procurement operation, the U. S.Government thereby incurs no responsibility, nor anyobligation whatsoever; and the fact that the Govern-ment may have formulated, furnished, or in any waysupplied the said drawings, specifications, or otherdata is not to be regarded by implication or other-wise as in any manner licensing the holder or anyother person or corporation, or conveying anW rightsor permission to manufacture, use or sell anypatented invention that may in any way be relatedthereto.

ASD-TDR-63-72

Technique for Calculating Trajectoriesof Singly Charged Particles in a StaticMagnetic Field for Shielding Purposes

"Elmer White

C= TECHNICAL DOCUMENTARY REPORT NO. ASD-TDR-63-72

April 1963

Roam

Propulsion LaboratoryAeronautical Systems DivisionAir Force Systems Command

Wright-Patterson Air Force Base, Ohio

S,, AFSC Project 5350+ , ..,,. +, ...1 ,

NOTICES

When Government drawings, specifications, or other data are used for anypurpose other than in connection with a definitely related Government procure-ment operation, the United States Government thereby incurs no responsibilitynor any obligation whatsoever; and the fact that the Government may haveformulated, furnished, or in any way supplied the said drawings, specifications,or other data, is not to be regarded by implication or otherwise as in anymanner licensing the holder or any other person or corporation, or conveyingany rights or permission to manufacture, use, or sell any patented inventionthat may in any way be related thereto.

ASTIA release to OTS not authorized.

Qualified requesters may obtain copies of this report from the ArmedServices Technical Information Agency, (ASTIA), Arlington Hall Station,Arlington 12, Virginia.

Copies of this report should not be returned to the Aeronautical SystemsDivision unless return is required by security considerations, contractualobligations, or notice on a specific document.

D

ASD-TDR-63-72

FOREWORD

This report was prepared as an in-house effort by the Propulsion Physics Section,Electric and Advanced Concepts Branch, Propulsion Laboratory, Directorate of Aero-mechanics, Aeronautical Systems Division, Wright-Patterson Air Force Base, Ohio.The work upon which this report is based is documented under Project 5350, "AdvancedConcepts for Propulsion," with the author as the chief contributor.

The studies presented began in June 1961 and ended in October 1962.

The author is grateful for the aid and suggestions offered by Mr. T. E. Duvall and otherindividuals of the Digital Computation Division, Directorate of Systems Dynamic Analysis,ASD.

ASD-TDR-63-72

ABSTRACT

The interacdons between a charged particle and an externally applied static magneticfield are reviewed. The elementary effects that involve the introduction of an energeticcharged particle into a magnetic field are discussed. Equations are derived for themagnetic flux density and for calculating the trajectories of singly charged particles.Also discussed are the applications of these equations and the boundary conditions. Theseequations are then adapted to the Fortran program. The use of the Fortran program andthe method of data input are explained. Sample problem data. a printout of the programdeck, and printouts of the solutions to the problems are also presented.

PUBLICATION REVIEW

This technical documentary report has been reviewed and is approved.

FOR THE COMMANDER:

Chief, Electric and Advanced PropulsionBranch

Propulsion Laboratory

ifi

ASD-TDR-63-72

TABLE OF CONTENTS

Pagp

List of Symbols ......................................... . vi

Introduction ............................................ I

Charged Particles in a Static Magnetic Field ....................... I

Derivation of Magnetic Flux Density ............................... 3

Solution of Particle Trajectory ................................ 5

Configuration of Coil ...................................... 5

Program Logic .......................................... 6

Sample Problems ......................................... 8

Example I ......................................... 8

Example 2 ......................................... 10

Examples 3 and 4 ..................................... 12

Relative Error ............................. ............ 16

Conclusions ............................................ 17

List cf References ........................................ 18

Appendix I - Description of Fortran Program... ........................ 19

Appendix II - Data from Example I Problem .......................... 45

Appendix III - Data from Example 2 Problei,........................... 65

Appendix IV - Data from Examples 3 and 4 Problems ..................... 71

iv

ASD-TDR-63-72

LIST OF ILLUSTRATIONS

Figure Page

1 Trajeco,.ry of Particle in Magnetic Field ..................... 2

2 Circular Coil Loop ................................... 3

3 Model of Air Core Coil ................................. 6

4 Particle Trajectory .................................... 7

5 Order of Example I Problem ................................. 9

6 Order of Example 2 Problem ................................ 11

7 Order of Example 3 Problem ............................. .... 13

I-I Composite Flow Diagram of Fortran Program ................. 20

11-1 Deflection Current Versus Particle Incident Angle (E) ............ 63

11-2 Particle Trajectories .................................... 64

111-1 Deflection Current for Six Different Energy Particles Versus IncidentAngle ................................................ 68

111-2 Particle Energy Versus Loop Current ...................... o...69

IV-1 Magnetic Field Strength at 150 Off Coil Axis .............. 79

IV-2 Magnetic Field Strength at 30 Off Coil Axis ................... 80



IV-5 Magnetic Field Strength at 75* Off Coil Axis ................... 83

IV-6 Equipotential Lines p Versus ZS (Bz a 0.018)................... 84

IV-7 Equipotential Lines p Versus ZS (Bz w 50) .................... 85

IV-8 Equlpotent•al Lines p Versus ZS (B = 0.10) ................... 860

ASD-TDR-63-72LIST OF SYMBOLS

SYMBOLS USED IN THEORETICAL EQUATIONS

a a acceleration vector

A - vector potentialb = radius of a circular coil loop

B - magnetic flux density

C a multiplication factor

d - derivative

D = additive factor

e - charge

E(k) = elliptic integral of the second kindF - force

I w current (amperes)

k - constant term of elliptic integral

K(k) a elliptic integral of the first kind

m - mass of particler - scalar distance

R = radius of cyclotron

s - element of length

t a element of time

U - unit vecm:orv = velocity

w n angular momentum

X a co-ordirate

Y a co-ordInate

Z w co-orJlnate

- angle used In change of variables

A = increment or gradient

p - radius in cylindrical co-ordinates

} - angles in spherical co-ordinates

vi

ASD-TDR-63-72SYMBOLS USED IN FORTRAN PROGRAM

A - a trigonometric function

AAA A - multiplication factor

ACOIL - radius of coil

AGMX - maximum configuration of coil (inches)

AHCOIL - radius of coil in zone H (inches)

AHMAX u maximum radius of coil in zone H (inches)

AHMIN - minimum radius of coil in zone H (inches)

B - a trigonometric function

BBBB - an additive term

BN - absolute value of magnetic field strength (webers/meter )

BRIHO - radial component of magnetic field strength

BX - X component of magnetic field strength

BY - Y component of magnetic field strength

BZ - Z component of magnetic field strength

CL - speed of light

CONV a conversion factor

DADDZ - derivative

DR = element of distance (inches)

DTETAO - increment of angle (degrees)

DTHETA - increment of angle

DT - element of time

DZH - pitch of coil in zone H (inches)

EOT - energy of particle

IAT a input signal

I a subscript variable

IH - zone number

IHMAX = maximum zone number

IMAX - maximum number of particles

IOT - initial current value (amperes)

ISMAX = maximum number of steps taken (R j + 1); ISMAX must be aninteger.

IT a time quantum

JAT a input signal

LAT a input signal

vii

ASD-TDR-63-72

SYMBOLS USED IN FORTRAN PROGRAM (Continued)

MMAX u .. aximum number of angular increments

MO = mass of charged particle (kilograms)

RHO - radius in the xy plane

RMAX = maximum three-dimensional distance (inches)

THETAO = angle with respect to Z axis

T - time

UO = permeability of free space

VOT - velocity of particle (meters/second)

VX - X component of velocity

VY - Y component of velocity

VZ - Z component of velocity

WX - X component of angular momentum

WY - Y component of angular momentum

WZ = Z component of angular momentum

XO - initial X co-ordinate of particle

XS - X co-ordinate of particle

YO - initial Y co-ordinate of particle

YS - Y co-ordinate of particle

Z - distance between coil loop and particle

ZHCOIL = location of coil on Z axis

ZHMAX m maximum zone dimension (inches)

ZHMIN a minimum dimension of zone (inches)

ZO = initial Z co-ordinate particle

ZS = Z co-ordinate of particle

viii

ASD-TDR-63-72

INTRODUCTION

With the advent of space flight came the introd-uction and design of manned space vehicles.The realization of the full potential of manned space flight is impaired because of the limi-tations Imposed on the vehicle and its occupants by the dangerous effects of ionizing radia-tion encountered in space. These principal radiation sources are the Van Allen belts thatsurround the earth, solar flares that occur periodically with varying intensities and strength,and intergalactic cosmic radiation. In the past, radiation shielding has been considered fromthe concept of interposing bulk shielding between the occupant of a space vehicle and thesource. Interposing bulk shielding increases secondary radiation on the down-stream sideof the shield. Therefore, the resultant radiation increases and intensifies the detrimentalbiological effects which in turn requires even greater bulk shielding with attendant weightincreases.

Studies have been made to compute the weight penalties imposed by the bulk shielding re-quirements (References 1, 2, and 6). These weight estimates are used in arrivinr at spacepropulsion system performance criteria. The following study has been made to piovidesufficient information to allow the computation of electromagnetic shield weights. Thestweights may be compared with bulk shielding weights to allow further definitization of spacepropulsion system criteria.

Shielding or primary radiation sources (energetic free-charged particles) by magneticfields has been considered by many shielding experts (References 3 and 4). However, shield-ing by magnetic fields appeared unattractive because of large power requiremcnts and therelative massiveness of the power-source equipment. With the advent of superconductors,this picture changed considerably.

Laboratory experiments have demonstrated that superconductors showing no detectableelectrical resistance can generate magnetic fields of 100 to 500 kilogaus3 with very littleexpenditure of power. Corresponding current densities range from 1 to l0` kiloamperesper square centimeter. Large, lightweight, low-power coils will become a reality withina few years, which will make magnetic shielding of charged particles extremely attractive.

Before magnetic shielding can be established, we must be able to compute the magneticfields of large coils and project the method of computation to the calculations of trajectoriesof singly charged particles. First, we define the charged particles in a static magnetic field.Then equations are derived for magnetic flux density and frc calculations of trajectories ofsingly charged particles. From these equations and the geometric configuration of the coil,we use the Fortran Program of the IBM 7090 digital computer as the analytical tool to cal-culate the trajectories. The Fortran code Is described in Appendix I; a flow diagram of theprogram is shown in Figure I-1 of the appendix. To prove the feasibility of our method, wepresent three basic problems and a slight deviation of one of the problems. The same modelwas used for all problems.

CHARGED PARTICLES IN A STATIC MAGNETIC FIELD

When a single particle of charge (e) that traverses a magnetic field of flux density (B)with velocity (v) is considered, the force (F) on the particle can be written in vector nota-tions as T

Manuscript released by author on 10 January 1963 for publication as an ASD TechnicalDocumentary Report.

ASD-TDR-63-72From Newton's second law, the force is equal to the mass, m, times the acceleration, a.By substitution, one can show that

If the vector of the velocity is exactly normal to g. the acceleration is a maximum.Conversely, if the velocity vector is exactly parallel to 9. there is no acceleration.

Suppose a positive ion is moving in a field-free space as shown in Figure 1. If amagnetic field is applied at point A. the acceleration is downward and the particledescribes a circular path in the clockwise direction in the plane of the paper. Theforce on the particle can then be expressed as

F a ma a ev.

A V

0 0

Om (D0D (D( 0 0DI Hout)

Figure 1. Trajectory of Particle in Magnetic Field

The acceleration can be written asv2

R

where R is the radius of curvature of the particle's trajectory.

Therefore,m2

MV eveR

and

R mv. (2)e8

ASD-TDR-63-72

DERIVATION OF MAGNETIC FLUX DENSITY

In the preceding equations, the magnetic flux density (B) (Reference 5) is defined as

B 'O .I f ds X s4B 7r r

By introduction of the vector potential (A), the magnetic flux density may be expressedas

B-AXA.

The circular coil loop is illustrated in Figure 2. From Figure 2, s Is a coil containinga current I. If this current is considered a circular ring charge, the vector potential Afor this configuration may be written In the form

1 f ds

The factor d s is defined as an element of surface and r is defined as the distance fromthe element of surface to a point at which the vector potential is being computed.

zP( IZ)

SI ,r

ziI "\

Figure 2. Circular Coil Lioop

At point s,ds a bd 46

d#S is given as

d S6 x I, sin d 4 + cA2 c0 s4 d

One can see that

A ' I fo (W sin Odo+j7 2 cos Od l6)b

S [(p-b cos *)'+ (b sin )+

3

-. ASD-TDR-63-72where r and A are unit vectors in the radial and tangential direction, respectively. Thefirst component is radially directed and is cancelled by the symmetrical element (-q).The second component is tangential. By a change of variables, one may see thl,

AO z -±'-" [(p +b )'+ ze ][(I- I e) K Ik)- E W] (3)

when cos € - 2 sin' - 1.

The factors K(k) and E(k) are elliptic integrals of the first and second kinds, respectively.In cylindrical coordinates (Reference 7).

aAzOp a aZ

sz, p' +

P aa8p /I2• [z(,p+ b)" + Z" K Wk bP + E zEk) (4)

8a • --Z p+b' + ze]' I K W+ b P 2 z (k)] (5)(b p)e + z"

and

BS = 0 because of axial symmetry.

Also

p [1x' + By z

Bx 8B cos

and

By 2 OSi S.

These equations, which represent the components of the magnetic field (B), will he usedto compute the magnetic flux density of a coil loop at a point in space.

4

ASD-TDR-63-72

SOLUTION OF PARTICLE TRAJECTORY

From the equation of acceleration of a charged particle in a magnetic field, the accelera-

tion vector () can be expanded into its respective components as follows:

Since the angular momentum of the particle can be defined as

W t I

the components of acceleration can be written as

ax a Wz Vy - Wy Vz

oy wx - wz (6)

3z a Wy VX - wx Vy

In considering an approximation to the solution of the three differential equations, assumethat the charged particle is acted upon over a period At. In this element of time, the com-ponents of velocity are shown to be

Vx - ox (At)

Vy a Oy (At)

vz - oz (At)

If the initial location of the particle is (xo, Yo, zo), the location of the particle after timeAt is

X 3 X " + VX

y X Yo + V A (7)

z Zo + Vz AIt

CONFIGURATION OF COIL

Since the computation of the magnetic field is based on cylindrical co-ordinates, anydipoles must show cylindrical symmetry. An air-core coil can, therefore, be described.See Figure 3. The radius of each coil can vary longitudinally as illustrated in Figure 3.The longitudinal profile of the coil may be portions of cylinlers of different radii, orcones, or combinations of these. The variation in the radius of a coil as a function oflongitudinal position (Z) in these geometries may be expressed as

b 2 ( Z M in + Z 1-m-4- bminm

5

ASD-TDR-63-72

where the variable Z Is the location of the coil loop in question. If d is equal to zero,db dz

the coil is a cylinder. If is not zero, but is either negative or positive, b describes the

radius of a single loop in a conical configuration at position Z. The Z can be shown to be

Z a Zmin + (n) dZ (8)

where Zmin is the location of the first coil in the configuration and dz is the pitch of the

coil. The indexing integer, n, varies from 0 to n

Z

mxx

I.) (b)ZONES Three - dlmewsional View

Figure 3. Model of Air Core Coil

PROGRAM LOGIC

In superconductor theory, each coil may exist as a separate entity. In computationof the magnetic field B at a point, each loop contributes to the separate components ofmagnetic field. As shown in Figure 4, the magnetic field B1 , at point I is assumed tooperate on the particle for time At,. After time At,, the particle is at point 2. After B,is computed at point 2, the components of acceleration at that point are computed. Aftertime At 2 , the particle is located at point 3. If the value of the current in the magneticfield computation is of sufficient magnitude, the field will be strong enough to cause thecharged particle to deflect away from the coil.

6

ASD-TDR-63-72

tioP(p,Z)

BI at Point I Z tt.At /B2 at Point 2

B3 ot Point 334 at Point 4

7yt t+,&t2 0, I•t2

3t 3

Figure 4. Particle Trajectory

If the value of the current is not of sufficient magnitude, a charged particle willpenetrate the coil configuration. We consider this penetration a collision. If the com-puter detects two simultaneous collisions, we have programmed the computer to checkthe two points of entry into the coil. If the distance between the two points is greacerthan 10-l meters, the program will automatically compute an increased value of thecurrent using the expression

In * CIn. 1 + 0 (9)

where C is an intuitive multiplication factor for partially determining a new current.The new value of current will be substituted into the magnetic field Equation (5) todetermine a new set of field parameters.

The factor D is an additive parameter in the current selection equation; it increasesthe multiplication factors mentioned in the last two statements. In the program, C isAAA.\ and D is BBBB. From previous computer runs, reasonable values of C and D are7 and 1000, respectively. Smaller changes in the current may be obtained by lowering C.

If the two collision points are identical, the program will not print out more than threetrajectories. In this case, the current changing routine will be bypassed. A capability

7

ASD-TDR-63-72

for changing the incident angle of the particle is built into the program. This routinefollows an identical collision-point event as described in the last statement.

Complete trajectories are not necessarily printed out. Only the significant parametersthat cause a particle to deflect may be printed. To determine an upper and lower limit tothese significant parameters, one must print the parameters of the miss and the lastcollision hit. See Figure I-I of Appendix I. If both sets of parameters are identical, theinformation indicates twin collision points. Of primary interest are the current values.

In a trajectory run, the program computes and prints out approximately 100 lines perminute. A single trajectory constitutes 100 lines of print out.

The program can compute magnetic field strengths about a cylindrical air-core coil.If the axis of the coil corresponds to the Z axis, the value of the magnetic field may bedetermined at any point on the axis or at any point on the trace of a line that makes anangle 9 with the Z axis. If the geometric center of the coil corresponds to the centerof the coordinate system, the magnetic field at any number of points spaced equidistantfrom 0 to Rmax on the trace will be computed. The point 0 is included. The values of

magnetic field will peak at or near the periphery of the coil loop and will decrease as thedistance from the loop to the reference point increases. If the angle 6 is varied from 0 tov radians, enough information on the magnetic field of the coil may he computed to plotequipotential lines around the coil configuration.

SAMPLE PROBLEMS

EXAMPLE 1

As example 1, we will develop a sample problem of computing the trajectory of a chargedparticle in a static magnetic field. A configuration similar tu that sl -wn in Figure 3 wasused. The order and makeup of a sample problem deck are showr- inc igure 5 (Example 1).Figure 5 shows the information that is necessary to compute and printout a trajectory.The printout is given in Appendix II.

The first card must have seven bits of information. If the control word is not applicableto the type of information desired, then zeros must be punched in that position. These bitsof information are used as follows:

1. SMAX is not used in a trajectory run.

2. HMAX indicates the number of zones in which the configuration of the coil isdivided. Each zone must have the same coil pitch and slope. The change of coil-loopradius per unit distance along the coil axis defines the slope. The configuration of thecoil may be divided into any number of zones up to 999.

3. MMAX is not used in a trajectory run.

4. IMAX indicates the number of particles in this problem.

5. IAT is a switching signal, which determines whether this problem is a trajectoryrun. A number equal to or greater than 1 will indicate a trajectory run.

8

ASD-TDR-63-72i • - op -- -o -i - - -

N 0 - 0 0 Nn

- I I -I- - •I

p.- -=-.-,- -I! ! .

** - o - -G- -t 0- -- N 4- - 0---i- -

o + ,'- •---- -- -- ¥ - - - - --/

* o N - - I - • ,- • - - -

"+ +

NN

* - ,. ,- ., a C - _" - - • - -

-+ + I I + I +

tqt

* -. In 0 0 06 - 0e

S0 0

Fn + +_ N

0 D N N

~~ oa • z 9 :

t. 4- 0 0 0 0 0 -N+ + _0+ + + +

ON0 -

* 0 x 0 0 0 0 0a 0

0

09 + + + +N -- x 7F 7T +

0 -w- 4 CO O CS 4 4$

0 0 a cu

0 -X -ZI

N0( 0 0- 0 0 N 0 0 0D

*~ ~ 001f

NY N ) In la r O

-A I I I

t9

ASD-TDR-63-726. JAT can cause different types of information to be printed. For JAT a 0, the entire

particle trajectory will be computed internal to the computer. JAT - 1 indicates the entiretrajectory will not be printed. JAT a 2 is used for other types of problems.

7. LAT can cause different types of information to be printed. For LAT - 0 only para-meters that caused a particle to miss the coil and the parameters of the last hit are printed.If LAT a 1. the hit and miss data will not be printed. LAT - 2 is used for other types ofproblems.

In the remaining cards, the input format is the same. The values are input in fields of13. Only four fields per card are allowed. All information will be stacked continuously asshown in Figure 5.

In the second card, AGMX represents the most distant point from the center of thereference system and is input in inches. The factors AAAA and BBBB cause the coilcurrent to be increased. MO is the rest mass in kilograms of the particle being investi-gated.

In the third card, DTETAO represents the incremental change in the incident anglefrom 0 to a maximum of 180 degrees over which the particles will approach the coil.DTHETA, DR, and RMAX are not used in the trajectory routine.

In cards 4 to 8 there are HMAX values of ZHMAX, AHMIN, the coil pitch DZH, thechange in coil radius per unit length DA/DZ, the maximum radius of the coils in eachzone AHMAX, and the minimum radius of coils in each zone AHMIN, respectively. Cards4 to 8 represent the coil configuration In its entirety.

After the configuration of the coil as defined in cards 4 to 8, there will be IMAX valuesof EOT, the particle energy in million electron vwtw (Mev), followed by the same numberof values of VOT, the velocity of the respective partic.es listed under EOT. Finally, EOTand VOT will be followed by IMAX values of current (IOT). These values are assumed tobe great enough to generate magnetic fields of sufficient strength to cause deflection ofthe particle.

Not shown in the Example 1 sample problem is a card with an asterisk in Column I andthe word DATA punched in columns 7 to 10. This card precedes the problem deck. All ofthe information described will follow the binary program deck.

The printout of the sample problem is shown in Appendix II. The significant parametersresulting from this problem are plotted In Figure 11-1 of Appendix II immediately followingthe printout.

Projections into the X-Y plane of a hit and a miss pair of trajectories are shown inFigure 11-2 of Appendix II.

EXAMPLE 2

In the computation of the trajectory of a charged particle in a static magnetic field, thesame critical parameters that are plotted from trajectory data in Example I may be ob-tained through a hit or miss printout. The Example 2 problem, shown in Figure 6, has theappropriate values to cause a hit or miss printout. When the first card of a problem deckis changed, information of a hit or miss printout may be obtained as listed in Appendix III.

10

ASD-TDR-63-72

a* -000o o I••" " 0 0 0 000

S- -o-- -o - - 0+ +I + + + +

1111 -- o -- -••

N o y o o o o 0 o

,- + + + + +

=., 0 - - 0 0 -- --0

S + ++ + + + +

*-T

3 N

t" O . --- 0 Im 0Y v• i•,

• 0 0 0J' v ' ~ ••N

S 0 o . . • . . . . +

0O O 0 000

+ + + + + + +

0 _ z0 00 0 0

1 01

0 +_ + +4 + + +T

0 -_ - --

Ina0 0 0

0 _ _NO 0 N

0 NO3t- ~___0 0 0 *a

* 00 -0 0000

00

000++;++ +++ + 0

- 0~

o* 0 0 t on . o a P

* 0 u

ASD-TDR-63-72

The information of the Example 2 problem is the same as that of Example 1. except incard I IMAX and JAT now have the value 2. Cards 8 and 9 now have two values of EOTDVOT, and IOT, respectively. These data are plotted in Figure III-1 of Apvendix III. Addi-tional data not tabulated in this report are also plotted in Figure III-I.

The values of IOT and SBN of this printout have no meaning in the hit or miss data. Thecritical current I is significant.

The critical currents necessary for the magnetic field to deflect charged particles ofenergy E are taken from Figure 111-I and plotted in Figure 111-2. From Figure Ill-i, it isapparent that the maximum sensible current is that which causes the field to deflectenergetic particles with an incident angle of 30 degrees. The minimum current is thatwhich causes deflections at an incident angle of 90 degrees with respect to the axis of thecoil. The currents in Figure 111-2 represent upper and lower limits for creating magneticfields of the coil.

EXAMPLES 3 AND 4

Both Examples 3 and 4 problems compute the magnetic field strengths at any point inspace. The Example 3 problem gives the input necessary to obtain from the programthese strengths. The order and makeup of a sample problem deck are shown in Figure 7.The first card must have the following information to produce plot information:

1. SMAX is the number of steps to be taken on a trace.

2. HMAX indicates the number of zones in which the coil configuration is divided.

3. MMAX indicates the number of angular increments over which traces will betaken.

4. IMAX indicates the number of current values of which field plots will be made.

5. IAT is a switching signal, which determines whether this problem is a field plotrun. IAT - 0 indicates a field plot.

6. JAT greater than 0 will determine the type of printout format. JAT = 2 is usedfor more than one current value Input.

7. LAT = I can be used if only I value of current is input. For multiple values ofcurrent, the value of 2 is assigned to LAT.

In the second card, AGMX, AAAA, BBBB, and MO need not be assigned valuesother than 0, but If their values are input, the problem will not be affected.

In the third card, DTETAO need not be input but a value in this position will not affecta field plot problem.

1. DTHETA is the angular increment over which a trace is varied.

. DR represents the incremental step sizes taken along a trace.

3. RMAX represents the greatest distance from the center of the co-ordinate sys-tem where DR will begin to be stepped along a trace.

12

ASD-TDR-63-72

"N 000 0 0

0 + + + + +

SI" v N 0 010

S+ + I + I+ +

0 0 0 0 0

+ o + o 0 v to

++ + 1+ +

I

0 1 l

00

t 0 0 0 0 0 0 .o0 + 1++

0 00 0 010

S0 . . . . . . .62 ol0 0 It

V00

"~o o 0 • ,-

"" V 0 0 00+ + + 0

0 o

0 . 0 m in v I ' 0 .

9 - -ic ;d c 0 , 00, 0

13

ASD-TDR-63-72

Cards 4 to 8 have HMAX values of ZHMAX. ZHMIN, DZH, DA/DZ, AHMAX, and AHMIN.respectively. These cards represent the coil geometry in its entirety.

Immediately following the configuration cards numbered 4 to 8 will be IMAX values ofEOT and VOT, respectively, which will be zeros for the field plot problem. If values otherthan 0 are input, the problem will not be affected. Following values of EOT and VOT will beIMAX values of IOT, the current.

The sample problem printout of Example 3 is shown in Appendix IV. Note that JAT andLAT both have values of 1. It can be seen that one value of current is input in Example 3.In the printout there are six printed columns (Appendix IV) as follows:

1. Theta is the angle in radians over which the magnetic field trace of points wastaken. As can be seen at the top of the printout, the increment of change in THETA isDTHETA equal to 15 degrees. The first column reflects this information.

2. Since the problem model exhibits cylindrical symmetry, 0 represents the radialdistance from the coil axis to the point at which the magnetic field is being computed,where

p * (X' + y, )i

SRmoX- (n -lI) DR Isin

and

n - 1,2,3 .......... k.

The program computes this value.

3. The point of magnetic field computation in the Z direction is ZS, where

ZS [Rmo,,- (n-l,)DR] Cos.

The program computes this value.

4. SBN is the absolute value f the magnetic field at the point (p, ZS),

SeN a ( p + BZ' )

where B and B, are defined in the next two columns.p

5. SBRHO is the radial component of magnetic field. When p - 0, SBRHO will be equalto 0. SBRHO was defined in Equation (4).

6. The SBZ is the Z component of magnetic field and was defined in Equation (4).

In Example 4, slightly different input values were used and the printout is differentfrom that of Example 3. In the input, IMAX - 12. In this printout, IMAX - 12, which indi-cates 12 values of EOT, VOT, and IOT, respectively. The EOT does not enter into any

14

ASD-TDR-63-72computations but acts as a means for identifying the derivation of the current IOT. Theprintout of Example 4 is also shown in Appendix IV.

The currents listed are those which created magnetic fields of sufficient strength aboutthe described coil configuration to cause deflection of charged particles with EOT millionelectron volts.

Since VOT does not enter into the computation, 12 values of 0 are input. It is essentialthat these 12 positions be filled.

There are 7 columns in this printout. The added column is the value of lOT. Withineach value of IOT, traces over all angles are taken. This type of printout results whenthe value of 2 is assigned to JAT and LAT. Field plots for all values of TOT were notcomputed because of the error returned shown at the end of the printout. For example,

VKSQ - 1.000000015 STOP

If, on the trace of the line on which a field plot is being taken, the Z component of coilcorresponds to ZS of the reference point and the radius of a zone AHMAX exists so thatp/DR - AHMAX, VKSQ is printed out, which indicates an error. This error originatesin the elliptic function routine where the elliptic function

(I-E (k) G(X -!( ,in'e )i

wherek VKSO

If k0 is too close to the value of 1. the program writes out the error statement andstops.

If AHMAX/DR is an integer, an error printout will probably result. For example, asshown at the end of Example 4 of Appendix IV, the value of the ratio 48/8 a 6. The pointon which the magnetic field was being computed lay on the periphery of the coil. Werecommend that DR and/or RMAX be changed.

The data from the printout of Example 3 as given in Appendix IV is plotted in FiguresIV-1 through IV-4. Multiple peaks appear on the 15-degree and 30-degree line traces.The meaning of these multiple peaks is not clear until the equipotential plots are con-sidered. As the line traces approach 90 degrees, single peaks are observed. FiguresIV-i through IV-4 represent the radial component of magnetic field. These graphs areplots of the magnetic field that caused a 500 Mev proton to be deflected.

No plots were made of the magnetic field traces because of low current values, butequipotential lines were plotted in Figures IV-5 and IV-6. Equipotentials of B and B%.prespectively, have been plotted. Note that the radial component of magnetic field goes tozero at the ends and is normal to the coil axis at the center of this model. The equipo-tential of the Z component of magnetic field shown in Figure IV-6 reveals dips at the 45-degree and 135-degree line traces. The critical current versus particle incident angleshould have reflected these dips. This information implies that twin peaks should haveappeared at the 45-degree and 135-degree angles in Figures IT-i and III-1. Since traceswere not taken at these angles, this information was not revealed. The coil could be re-designed to eliminate these dips.

15

ASD-TDR-63-72

The equipotentlal of the Z component of magnetic field Is shown in Figure IV-7. Thisequipotential was derived from the current, which caused a 500-Mev particle to be de-flected.

At relatively high values of current, the equipotentials appear smooth. The presentstate of the art leaves considerable doubt as to the ability of superconductors to generatea magnetic field of this strength. Superconductivity is at present in its infancy. Highmagnetic field breakthroughs are promised in the future for superconductors that canfill the range of fields required by this investigation.

RELATIVE ERROR

The technique used in computing a trajectory of a particle is that of defining the newposition of a particle with respect to the magnetic field parameters of the last positionas follows:

X X0 + v, (At)

Y Yo + Vy (At)

Z • + (At

Position co-ordinates x, y, and z are functions of the magnetic field strength at xo, Yo,and z,. The x, y, and z components of velocity are the parameters controlled by thelocal magnetic field. Obviously, some error is introduced into the program when successivesteps are taken into the target area. This occurs when the new position is computed as afunction of the local conditions of the last position. As the distance between the particleand the target approach zero, the time steps were made smaller and smaller.

In the computer program the values of At are approximately

At = 1.5625 x 10-2 seconds

- 1.953125 x 10-3 seconds

a 2.4414063 x 10"4 seconds

- 3.0517578 x 10"5 seconds

- 3.8146973 x 10"6 seconds

= 4.7 x 10"7 seconds

= 6 x 10-8 seconds.

The expression for the position equation is written

x I Xo + v.(nAt) (10)

where n is the number of the step being taken over element of time At. Suppose the particleis made to travel from point 1 to point 2 with the largest time step. When the second At isused, approximately seven steps would be required to go from point 1 to point 2. In otherwords, n would vary from 1 to 7 in the preceding equation.

16

ASD-TDR-63-72When one large step is taken from point 1 to point 2, the magnetic field at point 1 was

assumed to operate on the charged particle over the entire distance. As At is madesmaller, the number of steps n from position 1 to position 2 increases. As the number fsteps increase, the magnetic field influences to a greater degree the trajectory of thecharged particle, that is, the Larmor radius becomes smaller. When the Larmor radius ofthe charged particle is compared by use of small time steps to the Larmor radius byuse of larger time steps, the degree of deviation at point 2 in all cases is negligible. Thepoints 1 and 2 were taken at a large distance from the coil, which may account for thenegligible deflection. Previous computer runs indicate significant deflection takes placeat 5 to 10 meters from the coil model of this problem. The current in the coil creatingthe magnetic field is directly proportional to the particle energy. In all cases, significantdeflections took place within 5 to 10 meters.

CONCLUSIONS

From the investigation, it is apparent that shielding from charged particles by meansof magnetic fields is possible in outer space. When simulated superconductor coil geome-tries are used, preliminary investigations indicate logical system parameters.

Superconductor theory is in its infancy. Future investigations promise to advance thetechnology of superconductivity to the point at which currents and fields as predictedwith this program will be possible. More elaborate tools for analyzing coil designs forspace shielding purposes will be forthcoming.

17

ASD-TDR-63-72

LIST OF REFERENCES

1. Rossi, Bruno, High Energy Particles, Prentice-Hall Inc., New York, N. Y., 1952.

2. Schaefer, H. J., Proton Radiation Hazard in Space, Astronautics, February 1961.

3. Levy, R. H., Radiation Shielding by Superconducting Coils, Research Note 224,AVCO-Everett Research Lab., Everett, Mass., April 1961.

4. Tooper, R. F., Electromagnetic Shielding Feasibility Study. Armour ResearchFoundation, September 1962.

5. Kraus. J. D., Electromagnetics, McGraw-Hill Book Company, New York, N. Y.,1953.

6. Verga, Robert L. and Cooper Richard F., Weight of Radiation Shielding as aFactor in Designing Propulsion Systems for Manned Space Flights. ASD-TDR-62-697, Aeronautical Systems Division, Wright-Patterson Air Force Base, Ohio,April 1963.

7. Weber, Ernst, Electromagnetic Fields, John Wiley & Sons, Inc., New York, N. Y.,1960.

18

ASD-TDR-63-72

APPENDIX I

DESCRIPTION OF FORTRAN PROGRAM

19

ASD-TDR-63-72

[ ~ ~ ~ MINIIL ILS

PROGRAM

I

PROBLEM ENDI POSITION ENDLM

r IAT

FOIELDIOT TRAJECTORY IO

LAST INITIA i RTED PPR BL M TA E I POST IO

EX RA AT O

CHANE -ANEI -RTIA

Figure 1-1. Composite Flow Diagram of Fortran Program

20

ASD-TDR-63-72

The total program is composed of a main program and seven subroutines. The subroutinesand their functions are listed as follows:

1. Input

Readin of formats and writeout of input information

2. SUMB

Computing and summing the components of magnetic field

3. SRS

Elliptic function tables

4. MLH

Miss and last hit printout formats

5. TRAJ

Format for printing particle trajectories

6. TIME

Element of time selection routine

7. INTP

New position interpolation routine

21

ASD-TDR-63-72

0 l

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006 X U *ij-eMI

00 I0)0

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28

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30

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32

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ASD-TDR-63-72

The control statements of the main program and their addresses are listed. Explanationsof the control statements are provided to allow changes in the main program logic, ifthis becomes necessary. If changes are made in the main program, a careful check shouldbe made of the subroutine input to see if it is affected.

398 Start.

404 Call input subroutine.

499 Allot storage space for the energy, velocity, and current.

60 Allot storage space for the geometry.

75 Convert from inches to meters.

1 If the value of the equation of signals is negative, go to 900 tocompute the field plot.

If it is zero, go to 20 to compute the field plot.

If it is positive, go to 21 to make trajectory computations.

FIELD PLOT

900 Write out according to format 901.

20 Write out according to format 996.

700 If JAT is negative, go to 2.

If it is 0 or positive, go to 801.

801 Use a new subscript.

2 Compute angular parameters.

3 Compute cylindrical space coordinates.

4 Call SUMB, the magnetic field subroutine.

Check this zone; if more coil loops are to be computed, go to 5.

If this is the last coil loop, go to 6.

5 Increase the coil index and then go to 4.

6 If this is not the last zone, go to 7.

If this is the last zone, go to 8.-

If this is a trajectory, go to 4.

8 If the computed value is negative (-), write out the Informationrequested at 200.

If it is 0, write out the information requested at 201.

If it is posi:ive, go to 23.

200 If more coordinates are to be computed, go to 9.

If the last coordinates are computed, go to 10.

201 If more coordinates are to be computed, go to 9.

If the last coordinate has been computed, go to 10.

41

ASD-TDR-63-72

9 Step to the next coordinate position and then go to 3.

10 If all angles have not been computed, go to 11.

If all angles have been computed, go to 399 or 403.

11 Increase the angle indexing factor, then go to 2.

TRAJECTORY

21 Check the value of the subscript, then go to 51.

51 Compute the relativity mass.

If the subscript is not a maximum, go to 24.

If it is a maximum, go to 30.

24 Compute the components of velocity and initiate a position of the particle.

31 If the position of the particle is outside of the coil configuration, go to 33.

If the position is inside the coil, go to 597.

33 If KAT , 0, the magnetic field has not been computed; go to 74 and then to 4.

If KAT = 1, the field has been computed. Go to 34.

34 Call Subroutine Intp (interpolate).

Compute the new position of the particle based on local magnetic fieldconditions. Go to 31.

597 Continue.

32 If the Z component of the particle is greater than or equal to the minimumZ component of the zone now being checked, go to 36.

If the Z component of the particle is less than the minimum Z componentof the zone being checked, go to 35.

35 If this zone is not the last zone, go to 600.

Go to 598 if this is the last zone.

600 Increase the zone subscript.

Go to 32 to determine if the particle is in the new zone.

If all zones have been checked and the particle is in none, go to 38.

598 Check to see if the particle is in the first zone.

599 If this zone does not match the first zone checked, go to 32.

If this zone matches the first zone checked, go to 38.

36 If the Z component of the particle is less than or equal to the maximumZ component of the zone being checked, go to 37.

If the Z component of the particle is greater than the Z component of thezone being checked, go to 35.

37 Compare the radius of the particle's position from the center line of thecoil with the maximum radius of the coil.

If the radius of the particle's position is greater, go to 33.

42

ASD-TDR-63-72If the radius of the particle's position is less. go to 42.

42 Determine if the shape of the coil is conical or cylindrical.

If the coil shape of this zone is such that its slope is negative or equal tozero, go to 46.

If the slope of the coil in this zone is positive, go to 47.

46 Choose the maximum radius of the coil and go to 48.

47 Choose the minimum radius of the coil and go to 48.

48 Determine the radius of the coil at the particle Z component of position.

If the radius of the particle's position with respect to the center line ofthe coil is greater than the coil radius at this Z coordinate, go to 39.

If the radius of the particle's position is equal to or less than the radiusof the coil, go to 49.

39 Tol is the difference between time T and the maximum significant timeof flight of the particle.

If Tol is less than or equal to the allowable tolerance, go to 33.

If Tol is greater than the allowable tolerance, go to 139 and then to 57.

49 Compute some spherical radius.

493 ITHAT signifies the number of times this particle has been checked atthis incident angle.

If ITHAT is less than or equal to the maximum allowable number ofcounts, go to 507.

506 An angle sensing signal is set.

107 If JAT is less than or equal to zero, go to 510.

If JAT is greater than zero, go to 509.

510 Call the subroutine TRAJ for plotting the trajectory.

509 Re-initiate all parameters.

If the difference in the spherical radii of the last position and thisposition of the entry of the particle into the coil is equal to or greaterthan an allowable tolerance, go to 491.

If it is less, go to 501.

501 If the number of allowable particle trajectories is less than or equal to1, go to 491.

If the number of allowable trajectories is greater than 1, go to 490.

490 Re-initiate the ITHAT count.

Call the subroutine MLH. This is a tally of the miss and last hit.

Give the current of the coil its initial value and go to 25.

491 Prepare the present coordinates for the past history tabulation andincrease the value of the current for the next trajectory, then go to 24.

23 If JAT is less than or equal to zero, go to 52.

43

ASD-TDR-63-72

If it is greater than zero, go to 53.

52 Call subroutine 11 RAJ in preparation for tabulating trajectory information.

53 Call subroutine TIME to choose an increment of time.

If the time indexing subscript IT is less than or equal to the maximumindexing subscript, go to 54.

If it is greater, go to 55.

57 If the JAT signal is less than or equal to zero, go to 56.


56 Call the subroutine TRAJ.

57 Call the subroutine MLH.

Re-initiate the current, then continue.

555 If the particle incident angle is less than w, go to 502.

If it Is equal to or greater than v, then go to 556.

556 Choose the next particle.

If the subscript of the particle is less than or equal to the maximumsubscript, go to 500.

If it is greater, then go to 30.

25 If the angle sensing signal SIS is less than or equal to zero, go to 502.


502 If the angular increment is less than or greater than zero, go to 26.

If it is equal to zero. go to 27.

26 Change the angle of incidence of the particle.

If the new incident angle is less than or equal to zero, go to 500.


27 If the LAT signal is less than or equal to zero, go to 29.


29 Call the subroutine MLH. Choose a new particle subscript.

If this subscript represents a value less than or equal to the maximumallowed, go to 500.


30 Go to 403.

403 Call exit.

54 Determine the components of magnetic field and the cyclotron frequencies,then go to 34.

44

ASD-TDR-63-72

APPENDIX II

DATA FROM EXAMPLE I PROBLEM

45

ASD-TDR-63-72

&XAMPLE ICHARGED PARTICLE SHIELDINGIATnC INDICATES A FIELD PLOTIAT-I INDICATES A TRAJECTORYJAY-C INDICATES A PLOT OF TRAJECTORYJAI1l INDICATES NO PLOT OF TRAJECTORYJATw2 INDICATES MUTPLE CURNT VALUESLAT-O INDICATES DUMP MISS AND LAST HITLAT-I IV4D1CATES NO DUMP MISS AND LAST HITLAY 2 MUIPLE CURNT FIELD PLOTSNAXu 0 HMAXs 3 MMAX= 0 IMAXm I IATm I JAT= 0 LATu 0AGNX=7.1999999E 01 AAAA=9.000O0OOE 00 686bu.00OOOOOOE 03 Nost.6724300E-21

OTETAO=3.OOOCOOOE 01 UTHETAUQ0. DR-O. RF4AX.0.ZHMAXa -5.ICOOOOOe 01 4.9999999E 01 7,1999999E 01ZHMNIP4 -7.1999999E Cl -4.9999999E 01 5.IOOOOOOE 01DiM. 1.0000000E 00 1.0000000E 00 1.00000001- 00DA/DZm 2.OCOOOLOOE 00 0. -2.OOOOOOOE 00AHMlAXu 4.8COCOOOoE 01 4.8000000E 01 4.800000LOk 0AHMINm 4oCCOOCCOE 00 4.OCOCCCOE 01 4.OOOOOOOE 00EDT= 1.0000C. 00VOT* 1.400CE 01IOT- 1.OOOCE 03TwO. KS. 0. Y5. 0. IS= 1.t4999982t 06

SON- 4,.97416520E-16 THETAOu 0. to 1.00000000E 03T*0.015625C0 XSa 0. YSS-0. IS- 1.53124982E 06

SBNz 5.6047596SE-16 THETAC. 0. Is 1.OCOCOOOOE 03T-0.03125000 XSv-0. YSS--. LS* 1.31249982Ei 06

SbNa 6.63221973E-16 THETAC. 0. In I.000'DL.000E 03T&0.046815C0 XS*-O. YSS-0. IS= 1.09374982E- 06

SBN. 7.95866'448E-16 'THETAO* 0. In 1.GCOGOOOOE 03T-0.06250000 XSw-O. YS.-0. I15 8.74999ditE 05

SON. 9.9'.53304CE-16 THETAOs 0. Is 1.OOOLOOOO( 03Tu.0C7812500 XSw-0. YSU-0. IS= 6.S62498Zte 05

SONx 1.32644424E15-I THETAO. 0. Is I.OCOOOOOOi: 03TwO.C937S000 XS.-0. YSS-0. IS- 4.37'.99u2lE 05

Sb4. 1.98966663L-15 THETAO- 0. 1n L.000C0000tik 03T=0.10937SO0 XS.-0. YS--C. ISs 2.187498271. 05

SON= 3.97933501E-15 THETAC. 0. In 1.000000001 03T=0.11132813 XSm-0. YSU-0. ZSu 1.91406079E 05

SbN. 4..54u781199E-15 rIIETAO. 0. Is 1.0OOOOOOGE 03TmO.11328125 XS.-0. VS*-0. iS. 1.64062329E. 05

SBN- 5.30578136E-15 THEW:O 0. In 1.0C000000a 03Tw0.11523438 XS*-0. 'fSz--. IS= 1.3671851V1B 05

SBNx 6.3669392SE-15 TI'ETAOz 0. Is t.O000000CE 03T-0.11718?50 XSm-0. yss0. ZS- 1.01374829L. OS

SBN- ?.95867658E-15 THE1AOs 0. Is L.CCOOUOOG& 03r=0.11914063 XSm-o. YSS-0. 15. 8.203107951: 04.

SRNu 1.06115745E-14. TtHETAC. 0. In 1.000000001. 03T0O.12109375 XSm-0. YS--o. IS- 5.468~7330iE 04

SONz 1.59173799E-14 THETAOm 0. Is 1.OCOC0OO0L 03Ta0.123046138 XSZ-0. YSM-0. ZSx 2.134358011. 04

SON= 3.1834865SE-14 THETAOm 0. In 1.00000000E 031-0.12329102 XSz--. YSZ--. IS- 2.39256114F 04

SON= 3.63827378E-1'. THETAC- 0. In 1.00000000L 03T-0.12353516 15.-C. ys-0o. IS= 2.05076426L. 04

SON= 4.244658I1E-14 THETAOx 0. In t.OOOOOOC.UE 03Tw0.12377930 XS--C. YvS--. ZS* 1.708967'.0E 04

SONs 5.09359896E-14. THETAO- 0. In 1.0000000C.E 03T-0.12402344 KS--C. YS.-0. iSz 1.367170531. 04

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SON. 1.48855C86E-13 THETAO- 0. 1. 1.0C000000t 03T-0.12451172 XS-C-C vSZ-0. ISs 6.8357676S1E 03

46

ASD-TDR-63-72

SBNs 3.77665019E-13 TIETA0s 0. In 1.00000000t 03TO.1247S586 XS-. VSR-0. ZSw 3.41179912k 03

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S8N" 4.11I94500E-12 THETA0s 0. In 1.O000000OE 031-0.12481689 XS--0. VS--0. ISs 2.56330690E 03

5fiNs 6.57323349E-12 THtTAOs 0. Is 1.00000000t 03T=0.12484741 XS--0. YS--0. ZS- 2.13606080E 03

S8N- 1.1305844CE-11 TIHETAO 0. IZ 1.O000000Ct 01

1-0.12487793 X5"-0. ySa-O. IS- 1.108814731E 03

SBN= 2.20860159E-11 THETAO" 0. Is I.U0000000L 03T-0.12490845 XS-0. YS--O. ZSs 1.28156863E 03

SBNm 5.23919529E-11 THETAOw 0. In 1.00000000E 0.T-0.12493896 XS-0. YS-0. IS= 8.54322541t 02

SBNx 1.75960638E-10 THETAOx 0. 1- 1.00000000E 03

T=0.12496948 XSM-O. YS=-0. ZS" 4.27076447E 02SBN. 1.40506244E-09 THETAU 0. Is 1I.O000000OE 03

T=0.12497330 XS--O. YS=-0. ZS= 3.73670688k 02SON= 2.09152175E-09 THETAO" 0. l= 1.00000006t 03

T=0.12497711 XS--O. VS--O. IS- 3.20264927L 02SBNx 3.33018425E-09 THETAO 0. I 1.00000000Ek 03

1=0.12498093 XS.-0. YSM-0. ISs 2.66859165L 02SBNs 5.7S600576E-09 THETA0 0. I 1.00000000 OJ

t-0.12498474 XSa-0. YSM-U. ISa 2.13453403E 02SBNa 1.12454656E-08 IHETAO= 0. Is 1.OOOCOOOOE 03

T=0.12498856 XSu-0. YSa-0. IS= 1.60047641 02

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T-0.12499237 XSs-0. YS--C. IS= 1.06641880E 02

SIN" 9.01944184E-08 THETAC- 0. In 1.00000000 03

T=0.12499619 XS-C. YSS--. IS= 5.323611566 OtSON- 7.25694305L-07 THETAO- 0. Is 1.00000000L 03

T-0.12499666 XS--O. YS--0. IS= 4.65603983E 01

SBNx 1.085127371-06 THETAC- 0. Im I.0000000GE 03

1.0.12499714 XSa-O. YS-O. ZS1 3.98846781k 01SBN- 1.72721200E-06 THETAO- 0. Is 1.00000000E 03

T-0.12499762 XSt-0. YS--O. ISm 3.32089519E 01

SBN- 2.99484503E-06 THETAO- 0. 1- 1.00000000E 03

T-0.12499809 XSs-0. YSS-0. IS- 2.65332371L O0

SIN- 5.88077688E-06 THETAO0 0. In 1.00000000C 03

t-0.12499857 XSs-O. YSM-0. ISs L.98S7Sl6E 01

SBNw 1.40738671E-05 THETAOs 0. In 1.OOOOOOE 03

T-0.124999C5 XSw--. YSM-0. ZS= 1.31817914E 01

SBN- 4.85342789E-05 THETAOm 0. I 1.OOOOOOOL 03

-=0.12499952 XSa-O. YSM-0. IS- 6.50607735E 00

SBN- 4.22011656E-04 THETAOs 0. In 1.00000000E 03

1=0.12499958 XS--O. VS--O. IS- 5.67161232E 00

SSNs 6.48244804t-04 THETAO- 0. Is 1.00000000L 03

T1O.12499964 XSa-O. YSM-0. IS= 4.83114130E 00

SBN- 1.07267271E-03 1HETAOu 0. I- 1.00000000E 03

T-0.12499970 XSm-0. YSS-0. lSa 4.00268227E 00

SON= 1.97378920E-03 THETAO- 0. I- 1.00000000E 03

To0.12499976 XSa-O. YS-U. IS= 3.16821124E 00

SIN- 4.27874273E-03 THETA0" 0. 1- 1.00000000E 03

T=0.12499982 XSs--. YSS-0. lSz 2.33375221E 00

SON= 1.26322816E-02 THETAOG 0. I 1.O0000000OF 03

1-0.12499988 XS--O. YS--U. ZS- 1.49928719E 00

SINS 0. rHETAO- 0. Is I.OCO00000 03

T-0. XS- 0. VS2 0. 1S- 1.74999982E 06SIN= 4.97416443E-15 THETAO" 0. In 1.00000001E 04

T=0.01562500 XS- 0. YS--0. ZS- 1.53124982t 06

SIN- 5.68476C03E-15 THETAOP 0. 1[ 1.00000000E 04

T-0.031250CO XSx-O- ySM--. IS= L.31249982E 06

47

ASD-TDR-63-72EXAMPLE I (Cont'd)

SBt~u 6.6322204SE-I5 THETAOs 0. Is 1.00000000E 04.To0.04687SC0 XS.-0. YSm-0. IS* 1.09374989E 06

SM.s 7.9586641SE-15 THETAOs 0. Is 1.OCOOOOOO1. 04Tw0.06250000 XS--O. VSM-0. IS= 8.14999dsZlk US

SBNs 9.9'.83314SE-15 THETA0a 0. Is l.OOOCOOOG1. 04.T*0.07612900 XS- SO-0. iSs 6.56249821E 05

SBNU 01.32644'.2?E-1'. THETAO- 0. Is 1.0OCOOOOOL 04TwO.09375000 XS--Oy VSa-0. IS= 4.37499821E. 05

SBNs 1.98966663E-14. THiETAO- 0. Is1- .OOOuOOul 04.r=0.10937500 XS.-o V Sm-0. ISs 2.1874.9827F 05

SbNa 3.9793349SE-14. THETAOx 0. Is 1.00000000t 04ToO.11132813 XSm-0. YSU-0. ISs 1.91406079E 05

SBNm 4.54781199E-14. THETAC- 0. Is13 .0OOOOOUa. 04T=0.11320125 KS--C. VSM-0. IS* t.64062329E C5.

SUNs S.3057816CE-1'. IHkTAC- 0) . Is .L00C0O00L 0'.T-0.11523438 KS--C. VS=--. IS= 1.3671851'Dk 05

SBNu 6.36693931E-14. THiETAOz 0. In 1.00OC00001: 04IaO.11716750 XSU-0. VS-0. 15z 1.09314829E. 05

SBNt 7.95867658k-I'. THETAOs 0. Is 1.0000000(,a. 04.TOC.11914063 KS--C V SZ-0. ZS* 8.2031019SL 04

SBNw I.06115751E-13 liiETAC- 0. I- 1.00000000E 04.t-0.12109375 XSw-C. YSM-0. IS- 5.468733011- 0'.

SONs 1.5917379?E-13 THETAOm 0. Is 1.00000000t: 0'.T=0.12304688 XS--0. VSM-0. iSu 2.734358011. 0'.

SBNs 3.18348652E-13 THETAO& 0. In 1.0OOOOOCCk 04.T-0.123291C2 XS--C. VSM--. ZSs 2.37256114k 04

S8Ns 3.6382736'.E-13 THETACz 0. In 1.00000000L. 04T-0.12353516 XSm-0. YSM-0. ZSs 2.050764261. 04

SBNs 4.2'.46SO23E-13 THETA0u 0. Is l.0OOO0OCLk 04T-0.12377930 XS--C. VS--C. IS= 1.7CU9674'.0r(4

SRNs 5.09359890t-13 THETAO& 0. Is 1.00000000L. 0'.T-0. 124023'.4 XSz-0. ySs-0. I$* I.367170153E 0'.

SON= 6.367015'.8E-13 ThETAOu 0. in 1.00000001O1E 0-tT=0.12'.26758 XS--C. SSU-C. IS& 1.0253736Sk 0'.

SON= 1.48855092E-12 TMETAOs 0. In 1.00000000k 0%.T=0.12451172 xsm-0. VSW-0. ZS* 6.83576781E 0j

SONs 3.17665004.E-12 ThiETAOw 0. Is 1.0006.0000E 04.T-0.12475566 XSs-0. VSS--. IS- 3.41779912L. 03

SON= 2.78938791E-11 THETAC- 0. 1s 1.000(00001. 04T-0. 12478636 XS--0. YSS-0. IS= 2.99OS52991. 03

SBNs 4.11894494E-11 THqETA~w 0. 1n 1.000000001. 0'.T=0.12481689 XSu-0. VS--C. IS= 2.56330690E. 03

SUN* 6.57323307k-11 THLTAOs 0. 1- 1.00000000t 04T-0.124.8474.1 XSZ-0. YSX-0. ZS- 2.L36060b0E 03

SON* 1.130504451-10 THEIAC' 0. 1s 1.0000000Ut 0'.1-0.12467793 XSz-0. VSM--. IS* 1.70881473E. 03

SGN- 2.20860165E-10 THEIAD- 0. 1- 1.000000001. 04.T-0. 12490845 XSs-0. VS=-o. ZS- 1.281566e31 03

SONw 5.23919517E-10 THETAUs 0. 12 1.00000000k 0'.1-0.12493896 XSw-0. YS2-0. ISa 8.54322'541k 02

SONs 1.75960639L-09 THETAOm 0. Is 1.0000000Ul- 0'.T-0.12496948 XSm-0. YSM-G. ZS- '..27U76447E 02

SON- 1.405062SIE-08 TH1.TA0m 0. 1- 1.OOOCOOOUL 0'.1=0.12497330 XS-0. VSS--. IS= 3.136706881. C2

SBN 2.09752175E-08 THETAOu 0. Is 1.0000U00ok 0'.1-0.12497711 xSw-0. VSS-U. ZS- 3.20264927t: 02

SON- 3.33018428k-OS ThETAO- 0. In 1.000000001. 0'.1=0.12498093 XS--C. VS--C. ZSm 2.66859165t 02

SON- 5.75600582L-O8 THETAO- 0. In 1.00000000E 04T-0.12498474 X5M-0. YSM-0. iS- 2.13453403E. 02

SON- 1.12'.54663L-07 IlIETACs 0. 12 1.00000000t 04T-0.12498856 XS5-C. YSS-O. IS- 1.6C047641L 02

48

ASD-TDR-63-72

,A 0

N N

0 0

a 00~~~~~~ ~ ~ ~ 0 000000o

-4~ ~ ~ 00~~~~ ')0 0 0 0 0 O

00 010 0 0o-0f F 0 a0 wo 0N 0O of- 0 0r -0 VIC

00030 3 0 MO0 0lo- ?O f o A o I^ 0N NON.") 110

C t IOOO W 0MOP400004o0U40N60 0N0400 ft.ON

,a *A to ON stm *W0-1 o f s o SO su n 00..O...pr

-- " -4 -- 14 -41P cm Gib

N N1N 0 N N1 N 111 N N Ok lp (P0lfl Ifl fl U01l4 0 v) tA 0 1.6 IA V) fp 0% 0 0

N N N N N N N N N N N N N It 040

0 0

0 0

0 000

. 0 a 0 0 0 0 0 0 0 0 0 0 0 0 30- 0

0at 0 0 0 0 0 0t 0 0 0 0N~~~~~~ gl N~e .0 e0e 0Ne ~ N so N .

000 00 000 00 000 00 000 00 0N W16 WIV ~ ~ 4 ~ E ~ ~ EI g g g I g g

0 d~ in .0 N*,U 0N 0 P. 0% - - - '00

4oco

&A N 4 vi ul AA V, %A 4- %A %A N IAUA

00 0% 0 00 04 00- 0 0 0 0 C w

So, - Ol 0. 0 4t C 04 a% N I 6N NN N I N N N 0 N N N 49 x 0

0 4 4 W p - 4 " N4 .4 N - 1 .4 N 4 N4 6u "0%~~~~~~ W 00 - w

4 C N N 0 4; 0 N 0 0 N N- 00 0000 0000 000 0000 0000 000

.~ N 00N0 00NO %0- 0404 40~i .004~49

ASD-IDR-63-72

EXAMPLE I (Cont'd)TaO. XS= 8.74999881E 05 YSS 0. IS- 1.51554431E 06

SON& 5.99625260k-16 THETAO. 5.235909766E-01 Is 1.00000000E 031.0.01562500 KS. 7.656240887k 05 VS. 1.958600?4t-04 IS= 1.326101.26k 06

SBNs 3.52458900E-16 THETACw 5.23598766E-01 Is 1.00000000E 03T-0.03125000 XS- 6.56249887E 05 VSs 3.77130146E-04 ZS- 1.13665819E 06

SbN. 2.27130863E-L6 JIIETAO. 5.23S98766E-Ot In 1.00000000k 03T=0.04687500 KS. 5.46874887k 05 VSx 6.33789676t-C4 ZS- 9.47215128E 05

SON= 3.81702700k-16 THETAO. 5.23598766k-CL Is 1.00000000E 031.0.06250000 XS. 4.37499893E 05 VS. 9.715411?SE-04 ISm 7.57772076b 05

SON- 6.68944006E-16 THE7AO= 5.23598766E-0I In 1.00000000k 03Ta0.078125C0 KS* 3.28124896E 05 Vs. 1.45705922Er-03 ZSx 5.68329012E 05

SBNs 1.32113637k-1S THETAC. 5.23598766k-0l1 Is .OCOOOOOCE 031=0.09375000 XS- 2.18749902E 05 VSu L.86387115L-03 iSz 3.78885955k 05

SON- 2.15319857k-1S TtHETAO. 5.23598~766E-01 to 1.0000000GE 03Ta0.10937500 KS. 1.09374905t 05 V5. 2.9739996bL-l.3 ISm 1.89442900E 05

SBN- 1.36278419k-I5 THETAO. 5.2359b766k-Ok In L.OOOOOOOGE 03Ta0.11132813 XS. 9.57030308E 04 YSs 3.119720SdE-03 ISs 1.65762517k 05

58Nu 4.76621681k-IS THETROm S.23598766E-O1. In1.00000000k 03To0.1132el25 KSw 8.2C311558E 04 VS. 3.28428090E-03 IS= 1.420821.34E 05

SAN- 8.72181523E-16 THETAOs S.23598766E-Ol I- 1.00000000E 031.0.11523438 Ksw 6.83592808k 04 YS- 3.4518084Sk-03 IS= 1.15401751k 05

SRN. 8*85262752E-15 THETAC. 5.23S98766E-Ol1. Is.OOOOOOOOL 041.0.11718750 XS- 5.46874064t 04 VS. 3.66229165E-03 IS= 9.47213686t 0'.

SBNm 1.01353662E-14 THETAO. 5.23S98766E-Ol In 1.GoOOOOOOOE 031.0.11914063 KS. 4.10155320E 04 'fS- 3.91770560L-03 15= 7.10409862k 04

S6N. 1.00300527k-14 TI-ETA0. 5.23598766E-01 In 1.00000000E 03T.0.12109375 XS- 2.73436576E 04 VS. 4.221342S0E-03 25. 4.73606038E G4

so

ASD-TDR-63-72EXAMPLE 1 (Cont'd)

SBN= 2.13648283E-14 THETAO= S.23598766E-0| Is 1.00000000C OJT=0.12304688 XS= 1.36717832E 04 YS. 4.65365076L-03 LS= 2.J6802217E 04

SBN- S.15632292E-14 THETAC= S.23598766E-01 In 1.00000000E 03=0.123291C2 XS= 1.19627988E 04 VS= 4.712244931-03 1S= 2.07201740E 04

SON. 6.87767619E-14 THLTAO= 5.23598766E-OL Is 1.00000000E 03T=0.12353516 XS= 1.02538145E 04 VS= 4.71632374k-03 ZS= 1.77601261E 04

SBN= 1.10183725E-13 THETAO= 5.23598766E-01 I- 1.00000000k 03I=0.12377930 XSs 8.54483032E 03 YS- 4.84918916E-03 ZS= 1.48000783F 04

SBNw 9.07442772L-14 THETAO= 5.23598766E-01 I= 1.0000000OL 03T=0.12402344 XS= 6.83584607k 03 VSs 4.92870361E-03 ZS1 1.16400304E 04

SBN. 9.31398213E-14 THETAO- 5.23598766E-01 1. 1.00000000E 03T=0.12426758 XSz 5.12686181L 03 YS= 5.01385182k-03 IS= 8.87998259L 03

SON= 1.51193041E-13 THETAO= 5.23598766E-0l I= 1.00000000E 03T=0.12451172 XS. 3.4178775ok 03 VS. 5.10754305E-03 ZS= 5.9199348TE 03

SBN. 3.5287983IL-13 THkTA0= 5.23598766E-01 I- 1.00000000E 03[=0.12475586 XSm 1.7C889340k 03 YS- 5.20850229L-03 IS= 2.95988712k 03

SBN- 2.47041413L-12 THETAO= 5.23598766E-01 I= 1.00000000k 03T=0.12478638 XS. 1.49527037E 03 YSs 5.22060496E-03 ZS= 2.5b988112L 03

SBN= 3.67390141E-12 THETA0- 5.23598766k-Ol In 1.O0000000F 031-0.12481689 XS. 1.28164734E 03 YS. 5.231919LIE-03 ZSs 2.21987516E 03

SON. 5.84804684E-12 THLTAO= 5.23598766E-01 Is 1.00000000t 03T=0.1248474t XS. 1.06802431E 03 YS= 5.24174023E-03 ZS= 1.84986918E 03

SBN& 9.97370625E-12 THETAOa 5.23598766E-01 In 1.00000000E 03T=0.12487793 XS- 8.54401278E 02 YS= 5.24876860k-C3 IS= 1.47986318E 03

SBN= L.97737338k-lL THETAO= 5.2359u766E-01 Is 1.00000000k 03T=0.12490845 XS. 6.40718255E 02 YS. 5.24981248E-03 IS= 1.10985720E 03

SBN- 4.65588874E-I1 THETAOm 5.23598766E-Ol Is 1.000O000E 03T=0.12493896 XS= 4.27155232k 02 YS= 5.23571098E-03 IS- 7.39851230E 02

SON- 1.57646234E-L0 THETAOn 5.23598766k-Ol Is 1.00000006k 031=0.12496948 XS= 2.13532212E 02 VS. 5.16959369E-03 1S 3.69645262E 02

SBNw 1.26541419E-09 THETAO& 5.23598766E-01 Is 1.00000000E 031=0.12497330 XS= L.86829333E 02 YS= 5.15451992E-C3 IS= 3.23594517E 02

SBN= 1.8890475SE-09 THETAO= 5.2359b766E-01 Is 1.0000000of 03T=0.12497711 XS- 1.6012645SE 02 YVS 5.12927151E-03 ZS- 2.77343760E 02

SON- 2.99954161E-09 IHETAOm 5.23598766E-01 Is 1.00000000E 03r=0.12498093 XS= 1.334235?7E 02 YS. 5.00786434E-03 lS= 2.31093019E 02

SON= 5.18538064E-09 THETAO= 5.23598766E-01 In 1.00000000E 03T-0.12498474 XS. 1.06720701E 02 YS= 5.01853817E-03 IS& 1.84042274E 02

SON= 1.01343016E-08 THETAO= S.23598766E-01 In 1.00000000E 03T=0.12498856 XS. 8.00178230E 01 YS= 4.89460450L-C3 IS= 1.38591525E 02

SON- 2.40469122k-08 THETAO. 5.23598766E-01 In 1.00000000k 03TsO. 12499237 XS. 5.33149469E 01 yS= 4.64091760E-03 ZS- 9.23407181E 01

SBN. 8.13111842E-08 THETAOu 5.23598766E-Ol [a 1.00000000E 03T-0.12499619 XS= 2.66120714E 01 YS. 3.94801062E-C3 ZS= 4.60900325E 01

SBN. 6.54346675E-07 THETAOm 5.23598766E-01 Is 1.00000000k 031=0.12499666 XS= 2.32142116E 01 VS= 3.80614763E-03 IS= 4.03086884E 01

SON. 9.78431046E-07 IHETAO= 5.23598766E-01 In 1.00000OOOE 0310.12499714 XS= 1.99363521E 01 YS. 3.58147004E-03 IS= 3.45273459k 01

SBN. 1.55?35581E-06 THETAOs 5.23598766E-01 In 1.00000000E 031-0.12499762 XS= 1.65964924E 01 yS= 3.2249666SE-03 IS= 2.81460023k 01

SBN. 2.70011890E-06 THETAO= 5.23598766E-OL Is 1.00000000E 03T=0.12499809 XS- 1.32606331E 01 YS. 2.63962209E-03 ZS= 2.29646593E 01

SBN. S.300948SOE-06 THtTAO= 5.23598766E-0 Is 1.00000000E 03T-0.12499857 XSm 9.922173864E 00 YS 1.60403715E-03 IS* 1.71833161t 01

SON- 1.267877?OE-05 IHETAO= 5.23598766E-0 I- I.OCOOOOOOE 03T=0.124999C5 XS. 6.58491486E 00 YS=-S.13255537E-04 IS= 1.14019729E 01

SON. 4.36341560E-05 THETAO= 5.23598766E-01 I 1.00000000E 03T=0.12499952 KS= 3.24705833E 00 YSa-6.3990208SE-03 IS= 5.62062965E 00

SBN" 3.74858990E-04 THETAOs 5.23598766E-01 1 1.00000000E 03TO.12499958 XS= 2.82982719E 00 VS-7.67184281E-03 IS= 4.89796191E 00

SON= 5.73186457E-04 THETAOw 5.23598766E-O Is .O1.0000000E 03T10.12499964 XSs 2.41259861E 00 YS=-9.76445196E-03 ZS- 4.17529396E 00

51

ASD-TDR-63-72

EXAMPLE 1 (Contr'd)SbN. 9.42461991E-04 THETACs 5.23590766E-01 I- 1.00000000E 03

T-0.12499970 KS. 1.995377276 00 YS*-1.33229573E-02 ISm 3.45262608E 00SbNs 1.71960224E-03 THETAo- 5.235937666-01 Is 1.00000000E 03

T=0.1,2499976 KS. l.57817908E 00 'VSs-1.9S696231E-02 ZSu 2.729958181: 00SON= 3.69510'159E-03 THETA0- 5.23598766E-01 I- 1.00000000E 03

1-0.12499982 XSs 1.16107517E 00 YS--3.2133374SE-02 ZSu 2.00729030E: 00S8Nv 1.07898226E-02 THETAOs 5.235987666-01 In 1.00000000E: 03

T=0.12499988 XSw 7.445'.69201:-01 'VS=-6.38184482E-02 ZSx 1.28462243E 00SRN- 3.68290862E-02 THETAOm 5.23598766E--01 I- 1.00000000E 03

Tw.0.12499994 KSz 3.230120001:-O1 'VSe-2.96864618E-02 IS= S.61954570k-OlSBN. 0. THETAO- 5.23598766E-01 I- 1.00000000E 03

Tw0. KSs 8.74999881E 0S 'VS. 0. iS. 1.51554431E 06SON& 5.996254036-15 THETAOw 5.235987666-01 In t.0C000000E 04

T-0.01562S00 XS- 7.656248816 05 'VS. 1.95860094E-03 ISm 1.32610126F 06SON. 3.524589036-15 THETAOa 5.235967666-01 Is 1.000000006 04

T0O.03125000 ~s~ 6.562496887 05 'VS- 3.711301856-03 iSa 1.13665819 06SbNs 2.271306696-15 TIIETAO. 5.23598766E-01 I- 1.000000000E 04#

T=0.04687500 KS. 5.468748876 05 'VS. 6.33789736E:-03 IS* 9.47215128k 05SbN. 3.81702703E-15 THETAG. 5.2359b766fi-01 Is t.0OOOOOOOE 04

T=0.06250000 XS- 4.37499893E o5 'VS. 9.77541208E-03 iSu 7.57172076E 05SbNz 6.88944012E-15 THETA0. 5.235967666-01 I- 1.00000000i 04

1-0.07812500 XS- 3.28124696E os 'VS. 1.457059321*-02 15. 5.68329012E 05SgN. 1.321136156-14 THErAOm 5.23598766E-01 Is 1.000000006 04

Tw0.0937SC00 KSs 2.18749902E: 05 'VS. 1.86387186E-02 IS& 3.788859551: 05SON= 4.63346863E-15 THETAOm 5.23598766E-01 1- 1.00000006E: 04

Tz0.10937500 KSu 1.09374911L OS 'VS. 2.4042253ft--02 iSm 1.89442900t: 05SRN- 1.47180682E-14 TIliETAC. 5.23598766E-01 In 1.00000000E: 04

1-0.11132813 KS- 9.57030380t 04 'VS. 2.47928115L-02 IS& 1.657625171. 05S8N. 4.76055920E-14 THETAO. 5.23598766E-01 1- 1.0000000OZ 04

T-0.11328125 XS- 8.20311642E 04 'VS. 2.57190406Ei-02 ZSa I.42u82t34r 05SON= 8.72181463E-15 THETAG. 5.23598766E-01 Is 1.OOOOOOOOF 0'.

Tw0.11523438 XSs 6.8359289Sk 04 'VS. 2.6674944hE-02 ISm 1.18401151k: 05SON. 9.385592346-14 1146140. 5.23598766E-01 I- 1.0OOOUOOUE 04

T=0.11718750 XS- 5.468741661: 04 'VS. 2.80654120k-02 IS* 9.412136u61: 04SON= 8.06765985E-14 THETACz 5.23S98766E-01 In 1.0O0003OLF 04

1-0.11914063 KS. 4.101554271: 04 'VS. 2.98676291&:-C2 iSm 7.1C409862IF 04SBN- 1.4628918SE-13 THETA140 S.2359d6766-01 I- 1.0000000U4. 04

T-0.12109375 XS- 2.734366951: 04 'V5. 3.230?8fl#t:-02 ISa 4.13606038L 04SON. 2.77236626E-13 TO-ETAOs 5.235987661:-Ol Is 1.0OOOOOOGE 04

T=0.12304688 KSm 1.367179656 04 'VS. 3.60570851E-02 IS* 2.368022111: 04SON. 4.5e6C0926E-13 1*46140. 5.23598766E-01 Is 1.00000000E 04

T=0.12329102 XSm 1.19628124E: 04 'VS. 3.65585563L-02 15. 2.07201740E: 04SON. 5.907182166-13 TO-LTA0. 5.2359b7666-01 I- 1.000t.OOOGk 04

F=0.12353516 KS. 1.02538282E 04 'VSs 3.71C503736--C2 15. 1.17601261t: 04SON. 8.585645796-13 THETAO- 5.2359b6166-01 I- 1.00000000t- 04

Ta0.12377930 KS- 8.54484403t: 03 'VS. 3.71164328k-02 ISm 1.48000l63E U4SON= 8.50801504E-13 TIhETA0. 5.23598766E-01 In 1.000000001: 0'e

1-0.12402344 KS. 6.635859956 03 'VS. 3.83913982E-C2 IS* 1.10400304f 04SON. 1.110730S1L-12 1*46140- 5.2359U766E-01 In 1.00000000*: 04

Ta0.12426758 KS- 5.126875881: 03 'VS. 3.91497374E-02 ISu 8.81996259E u3SON. 1.280C79511:-12 1*46140. 5.23598766E-01 I- 1.000000O"E* 04

Tu0.12451172 X~s 3.417891036 03 VS. 3.994459096-C? 15. 5.919934811: 03SON- 3.497671786-12 1*46140- 5.23598766E-01 Is 1.00000000i- 04

Ta0.12475586 KSa 1.100907781: 03 'VS. 4.073110LQ6-02 IS. 2.95988712L: ý3SONw 2.456318266-11 THETAC. 5.235987666-01 Is I.00000000k 04

T=0.12.478638 KS. 1.49528477 03 'VS. 4.082511?2t-C2 £5- 2.8988112E 03SON* 3.625413811:-lI THETA40 5.23598766E-01 Is 1.00O0000oua 04

T&0.12481689 KS. 1.28166175E 03 'VSm 4.09100187C-02 Z5. 2.21981516C 03SON. 5.817619566-11 THETA0z 5.23598766E-01 I- 1.00000C~00k 04

1=0.12484141 XS. 1.068C38?3E 03 VS. 4.098162111:-C2 iS. 1.84986918L 03SON. 9.996215221:-IL THETAOs 5.23598766k-01 In 1.0000000#,L 04

T=0.12487193 KSu 8.54415721E 02 'VS. 4.102480176-02 15. 1.47986318k 03

52

ASD-TDR-63-72

EXAMPLE 1 (Cont'Id)SIN. 1.96053205Ek-b THETAO. S.23!M9766k-01 I- L.OOOOOCOGE 04

ToO.12'.90645 XS. 6.4C792722E 02 VS. '..1006446SL-C2 IS- 1.109857206 03SINw 4.65425569E-IC THEIAOx S.2359b766E-O1 Is 1.OOOCOOOOL 04

Ta0.12493896 KS. 4.2?169116E 02 vs. 4.083?4840E-OZ ISs 7.39851230E 02SON= 1.577981?61k-09 II4ETAOm S.23598766E-01 In 1.00000006t 04

T.0.12496948 KS. 2.13546714E 02 VS. 4.0142369'JE-CZ ISu 3.6984S262E 02SON= 1.26479226k-08 WkhTA~w S.23598766E-01 In 1.O000000001 04

Tw0.12497330 KS. 1.86843841E 02 YS. 3.99873549E-02 IS= 3.23594b17E 02SONa 1.88851875k-08 THETA0w 5.235987661-01 In 1.00000000E 04

1.0.12497711 XSw 1.6CI40966E 02 VSs 3.97301834E-02 IS& 2.71343768E 02SON= 2.9996050O0k-08 THiETAOs 5.23598766E-01 In 1.00000000t 04

T=0.12498093 XS. 1.33438091E 02 YS. 3.931234871-02 iS. 2.31093;jl9E 02SBN= 5.185538231E-00 T14ETAO= 5.23598766E-01 Is 1.OC0O(00001 04

1.0.12498474 KSz 1.06735216E 02 VS. 3.861451451-02 ZS' 1.84b4??74a. 02SONm 1.0131S154L-01 TI4ITAO= 5.23598166E-01 In 1.0000000OE0 4o

T=0.12498856 KS. R.00323415E 01 YS. 3.73706412E-02 ISz 1.3&59eIN251h 02SIN. 2.40415302E-07lIHETAO. 5.23598766E-01 In 1.00000000t 04

T=0.1249923? KSO 5.33294672t 01 VS. 3.48Z890581-02 IS= 9.2340?Y81C 01SIN- 8.12896132E-01 THETAOm S.23598?66E-01 Is 1.000000001 04

T.0.12499619 KS. 2.66265941E 01 '15. 2.78942740E-02 IS. 4.609003251 OtSINu 6.5400771SE-06 THEYAO. 5.23598766E-01 In 1.OCOOOOOOL 04

To0.12499666 XSs 2.32887349L 01 VS. 2.64736414L-02 15m 4.030868894 01SON= 9.77862215k:-06 TWEAO. 5.23598766E-01 In 1.00000000L 04

T-0.12499714 KS. 1.99508764E 01 '15. 2.42250890E-02 ISs 3.45273459E 01SIN. 1.55630989E-05 THETAGn 5.23590766E-01 Is 1.00000000L 04

T=0.12499762 KSm 1.66130104t 01 Y~z 2.06S66024E-02 /Sz 2.81460023i 01SUM. 2.69792882k-OS IHLTAO. 5.2359u766E-01 Is 1.LOOOOOO%&. 04

T=0.1249960j9 XS. 1.32751630E 01 VS* 1.479677081-02 IS* 2.29640~90h 01SON- 5.29556543k-OS THETAO- 5.23598766E-01 I- 1.OCOCOOOOI 04

Ta0.12499657 XS- 9.93131570E 00 VS. 4.427283881-03 IS. 1.118331561: 01SIN. 1.2661S05SE-04 TtIETAO. 5.23598766E-01 I 1. .000u00O.i 04

r*o.12*g99qo KSm 6.59950203E 00 VSs-1.67823896k-02 IS-z 1.14019123F 01SIN. 4.3543S1701-04 THETACu, S.23598766E-01 In 1.OC0000001 04

T-0.12499952 XS- 3.26192659E 00 YS*-7.579434S11-02 ISs 5.62062419i 00SbNm 3.7309075CL-03 TgkTA0m 5.235987661-01 Is 1.uO0uOU~uE 04

Tu0.12499958 KS. 2.844827411 00 YS.-8.S5723615E-02 IS= 4.89796126L 00SIN. 5.699141201-03 THiETAOu 5.2359d7661-01 Is 1.OCOCOOO0i. 04

T=0.12499964 XS- 2.42798504E 00 VS.-1.09798740E-01 IS. 4.1152933)1: 00SON- 9.3S434604fi-03 ThETAO. 5.23598766E-01 Is 1.00000060C

T-0.12499970 XS. 2.01187322E 00 VS2-1.4SJ71147E-CI LS2 3.45262542E 00SON= 1.700IS91SE-02 THEIAO. 5.2359B7661-01 Is 1.OCOCOOOCa. 04

T=0.12499976 XS- 1.598106071 00 YSm-2.06370700E-Ot ISm 2.72995152E 00SINs, 3.610252861-02 TI'ETAO.; S.23596766E-01 In 1.0000000LL 04

T&0.12499982 KS. 1.19390613E 00 YSa-3.34205571E-01 IS= 2.00728965[ 00SBNu 9.976525281-02 THETAOs, 5.23598766k-01 Is 1.OCOCOOO0i. 04

T0O.12499988 KS. 8.48434436E-01 YS~-6.4S6841441-01 IS* 1.204621781: 00SON= 4.341622471-01 THETAO., 5.23598766E-01 In 1.0000u0000E 04

T0O.12499994 XS- 2.32929CU6k-01 YSe-6.66516113E-01 IS2 5.61953914E-01SIN- 0. rHETAO. 5.23598766L-01 Is 1.OCOCOOCGcL 04

Ts0. KS. 8.74999881E 05 VS. 0. j5. 1.515544311 06SON- 5.456590711-14 THiETAOm 5.2359b766E-01 In 9.09999994jE 04

T0O.01562500 XS- 7.656248871 05 '15. 1.78232698k-02 IS. 1.32610126E 06SIN. 3.207376001-14 TIIETACm 5.23598766E-01 Is 9.09999990k 04

T-0.03125000 KS. 6.562496071 0S VS. 3.4373449L1-02 ISs 1.13665819E 06SIN., 2.0668909CE-14 ThETAC. 5.235967661-01 to 9. 999999GE 04

TR0.04687500 XS- 5.466748671 0S VS. 5.76746693E-C2 IS= 9.472151281 05SIN. 3.473494501-14 THETAO. 5.23598766E-01 I- 9.09999990E 04

T.0.06250000 KS. 4.37499693E 05 VS. 8.8956253SE-02 iSs 7.57772016E 0SSON= 6.26939023E-14 TIIETAC- 5.23598766E-01 Is 9.0999999G1 04

T*0.07812500 XS- 3.26124896E 0S VS. 1.32592404k-Cl IS. 5.68129012E 05SIN. 1.2C2234151-13 THETAO. 5.23598766E-01 Is 9*09999990a. 04

Tm0.09375000 KS. 2.16149902t 05 VS. 1.69612345L-01 IS= 3.886595SE OS

53

ASD-TDR-63-72

EXAMPLE 1 (Cont'd)SBN. 4.21645635E-1' TIETA0O 5.23S96766E-01 Is 9.09999990E 04

Ta0.10937500 XS. 1.09374911E 05 VS. 2.18784517E-0C ZSs 1.89442900E 05SBN. 1.33934419E-13 THETAOw $.23598766E-01 1I 9.09999990E 04

TO.11132813 XS. 9.57030380E 04 YS 2.25614601k-01 ZSs 1.657625171 05SBNs 4.33210856E-13 THETA0 5.23598766E-01 1 9.09999990E 04

T-0.11328125 XS. 8.20311642E 0' YSS 2.34043216E-01 ZS- 1.42082134E 05SBN. 7.93685126L-14 THETAO. 5.23598766E-01 In 9.09999990k 04

Ta0.11523438 XSm 6.83592898k 04 YS. 2.42742002E-01 ISw 1.18401751E 05SBN- 8.54088902E-13 ThETAC. 5.23598766E-01 In 9.09999990E 04

Iu0o11718750 XS. 5.46874166E 04 VSm 2.55395254E-01 ZSz 9.47213686t 04SBNw 7.34156996E-13 THETAO& 5.235987661-01 In 9.09999990E 04

To0.11914063 XSw 4.10155427E 04 YS. 2.71795431E-01 ZS. 7.10409862E 04SBNs 1.33123183E-12 THETA0. 5.23598766E-01 Is 9.09999990E 04

T.0.12109375 XSu 2.73436695 04 YSm Z 94001642E-01 1Sw 4.73606038k 04SBN. 2.52285346E-12 THETAO. 5.23598766E-01 In 9.09999990E 04

T70.12304688 XSe 1.36717965E 04 vS. 3.28119481E-01 IS- 2.36802217k 04S8u 4.17326820E-12 THETAO0 5.23598766E-01 In 9.09999990E 04

T=0.12329102 XS. 1.19628124E 04 YS. 3.32682869E-01 IS- 2.01201740F 04SPNw 5.375S3537E-12 THETAOw 5.23598766E-01 1I 9.09999990E 04

Ta0.12353516 XS. 1.02538282k 04 YS. 3.376S5S45E-01 IS- 1.77601261E 04SbN. 7.81293780E-12 THETAO. 5.23S98766E-01 In 9.09999990E'04

T=0.12377930 XSw 8.54484403k 03 YS. 3.43219540E-01 IS- 1.48000783E 04SBNu 7.74229228E-12 THETAOs 5.23598766E-01 1- 9.09999990E 04

T0o.12402344 XSw 6.83585995E 03 VSw 3.49361733E-01 ZS. 1.18400304E 04SUNs 1.01076473E-1t THETAOu 5.23598766E-01 In 9.09999990E 04

T0o.12426758 XSs 5.12687588k 03 YS. 3.56262615k-01 ZS- 8.87998259E 03SBNm 1.16481241E-11 THETAO= 5.23598766E-01 Is 9.09999990E 04

T=0.12451172 XKS 3.41789183E 03 VSw 3.63495785E-01 ZS- 5.91993487L 03SBN. 3.13464960E-11 THETAO. 5.23598766E-01 1 9.09999990E 04

T10.12475586 XSu 1.70890781k 03 YS. 3.7129541OE-01 ZS- 2.95980712E 03SUN= 2.242?5646E-10 THETAOs 5.23598766E-01 1 9.09999990L 04

1.0.12478638 XSw 1.49528480E 03 YS& 3.72229624E-01 ZSm 2.58988112E 03SN. 3.29098102E-10 IHETAO. 5.23598766E-0 1= 9.09999990k 04

T=0.12481689 XS. 1.28166176E 03 YS- 3.73080048E-01 ISm 2.21987516k 03SUN. 5.33841622E-10 THETAOs 5.2359b766E-01 1 9.09999990E 04

T=0.12484741 XKS 1.06803S75k 03 VSm 3.73782223E-01 ISm 1.84986918k 03SBN. 9.09414876k-10 THETAO. S.23598766E-01 Is 9.09999990k 04

1=0.12487793 XSm 8.54415739E 02 YS. 3.742290021-01 15. 1.479863181 03SN- 1.78430790E-09 THkTAO= 5.23598766k-01 Is 9.09999990E 04

T.0.12490845 XS. 6.40792739E 02 YS. 3.74116006E-01 IS= 1.10985720E 03SBNs 4.23544306E-09 Tk1TAO 5.23598766E-0l 1 9.09999990E 04

1.0.12493896 XS- 4.27169734E 02 VS. 3.72633803E-01 IS 7.39851230[ 02SBN. 1.43085200E-08 THETAOu 5.23598766k-01 In 9.09999990E 04

1=0.12496948 XKS 2.13546732E 02 ySs 3.66441509E-01 ISs 3.69845262k 02SUN. 1.15127730E-07 THETAO- 5.23598766E-01 In 9.09999990E 04

1.0.12497330 XSm 1.86843859k 02 YS. 3.65049127kE-01 IS 3.23594517i 02SBN. 1.71858864E-07 THETAOu 5.23598766E-01 Is 9.09999990E 04

T10.12497711 XSs 1.60140982E 02 YS. 3.62731770k-01 IS* 2.71343768k 02SBNu 2.12918949E-07 THETA0s 5.23598766E-O In 9.0999999UE 04

1=0.12498093 XS. 1.334381071 02 VS. 3.58945140E-01 IS= 2.310930191 02SBN. 4.71843117k-07 THETAOs 5.235987661-O 1 9.09999990t 04

1.0.12498474 XS. 1.06735234E 02 YS. 3.52617535E-01 ISs 1.84842274E 02SBNn 9.22188616E-07 THEUAOa 5.23598766E-01 I- 9.09999990k 04

T00.12498856 XS. 8.0C323606E 01 VS. 3.41315258L-01 ISs 1.38591525k 02SBN. 2.18771857k-06 THETAOu 5.23598766E-01 Is 9.09999990E 04

T.0.12499237 XS. 5.33294928E 01 YS. 3.18204600E-01 IS- 9.23407781E 01SBN. 7.39739656E-06 THErAOm 5.23598766E-01 In 9.09999990k 04

1=0.12499619 XKS 2.66266599E 01 VS- 2.55109090E-01 IS* 4.609003251 01SBN. 5.95122355L-05 THkTA0C 5.23598166k-01 1 9.09999990E 04

80o.12499666 XS. 2.32888177k 0l VS. 2.42183891E-01 IS= 4.03086889E 01SBN. 8.8981508C0-05 THEFACm 5.23598766E-01 Is 9.09999994E 04

1&0.12499714 XS. 1.99510045E 01 VS 2.21120162k-01 IS* 3.45273459E 01

54

ASD-TDR-63-72

EXAMPLE 1 (Cont'd)SUN- 1.416IS552E-04 THETAOw S.23596766E-01 Is 9.0 ;99999GE 04

T=0.12499762 XSs 1.66132691E 01 YS. 1.89245924E-01 Z15 2.87460023E 01SSNa 2.45494032C-04 THETAO- 5.23596766k-01 In 9.09999990L. 04

Ta0.12499809 XS. 1.32757287E 01 YS. 1.3S916935k-Ol IS* 2.29646590E 01SbNa 4.81853497E-04 TIHETA0w 5.23598766E-01 Is 9.099'd9990C 04

7-0.12499857 XS. 9.93884802E 00 VSu 4.15555513E-02 iSv 1.718331,59E 01SON- 1.15202455k-03 THETAOs S.23596766E-01 Is 9.09999990E 04

T-0.12499905 XSw 6.60475606E 00 YS--1.514263?6k-01 ISm 1.1.4019726E 01SON= 3.95852604-03 THETAOw 5.23598766E-01 I- 9.09999990k 04

T=0.124999S? XS- 3.29055926k 00 YSe-6.8813021SE-01 LSs 5.62062967F 00SBNm 3.29504369E-02 TI4ETAO- 5.23596766E-01 In 9.09999990L. 04

T*0.12499958 ES.; 2.884365351 00 YSu-8.05117249E-01 iSu 4.59796174*: 00SONe 4.921034401-02 TI4ETAOw 5.235987661-01 In 9.09999990k 04

T=0.12499964 Es. 2.50030756E 00 YSs-9.98963726E-01 ZSw 4.115293866 00SON* 1.61023402E-02 THETAOw 5.23596766E-01 I* 9.09999990L. 04

T-0.12499970 ES. 2.17861009E 00 YS--1.31636144E 00 iSm 3.45262S99E 00SUN- 1.16113782E-01 TI4ETAOw 5.23S98766k-Ol I- 9.09999990E 04

TaO.12499976 XSv 2.04136419E 00 YS.-1.82070948E CO IS= 2.72995015k 00SON= 1.44860710E-01 THETAO- 5.23598766E-01 1s 9.09999990k 04

T-0.12499982 XSs 2.35086636k 00 VSn-2.44662902E oo IS- 2.00729030E 00SON= 1.119S7596k-Ol THETAOw 5.23598766E-01 In 9.09999990E 04

7-0.12499986 ESu 2.39211169E 00 YS--3.20519513E 00 ZS- 1.2646224ak 0058~s1-7.93218619E-02 THETAOw 5.235987661-01 In 9.09999990i 04

T-0.12499994 ESw 2.43209299E 00 YS--3.96382996E 00 IS= 5.61954659E-01SON= 5.23858684E-02 7THETA0 5.235986766-01 Is 9.09999990k 04

7-0.12499995 ES- 2.43904898E 00 VS-4.05655608E 00 ZS- 4.71621186E-01SUN- 4.96550816E-02 THETAO- 5.23598766E-01 Is 9.09999990E. 04

T-0.12499996 ES- 2.44806322t 00 YS--4.153131071 00 1S- 3.81287709t-01SUNm 4.70463049E-02 THETA0- 5.23S96766E-01 In 9.09999990E 04

T=0. 12499996 ES- 2.45920953k 00 YS--4.24750260k 00 Z5v 2.90954232E-01SON= 4.45616293E-02 THSiTAC- 5.23596766E-01 In 9.09999990E 04

T=0.12499997 Es- 2.47253785E 00 YS--4.34161667E 00 15- 2.00620756E-01SUN= 4.2201606CE-02 IIIITAO. 5.23596766E-01 to 9.0999999 41k 04

T=0.12499998 ES- 2.48807681E 00 YS--4.43S41783E 00 iS- 1.10287280E-01SUN= 3.99654624E-02 THI7AOw 5.235967661-01 I- 9.09999990E 04

T=0. 12499999 ES- 2.50563595k 00 YSO-4.52680103k 00 iS- 1.99538060E-02SUN- 3.76512147k-02 THETAOw 5.235987661-01 In 9.09999990k 04

T=0. 12499999 ES- 2.52560539E 00 VS-4.62186354 00 IS--7.037966651-02SUN- 3.58558762E-02 7111140- 5.235967661-01 In 9.09999990E 04

7-0.12500000 ES- 2.54797307k 00 VS--4.71440530E 00 IS--1.60713141E-01SUN- 3.391S6146E-02 THETAO- 5.23598766E-01 In 9.09999990E 04

T=0.12500001 ES- 2.57229695E 00 YS--4.80642992E CO iS--2.51046613E-01SUN- 3.220597271-02 THkTAO- 5.235967661-01 Is 9.09999990E 04

T-0.12500001 ESn 2.59873712t 00 YS-4.89769516E 00 LS--3.41380084E-01SUN- 3.05420542k-a? THETAC. 5.2359$6766-01 to 9.09999990E 04

T-0.12500CC2 ES. 2.62724274k 00 VSn-4.96676333k CO ZS--4.31713551k-01SUN- 2.691664376-02 7111140- 5.23598766E-01 In 9.09999990k 04

1-0.12500003 ES- 2.65775676k 00 Y$=-5.07900143E 00 ZS--5.22047019k-01

55

ASD-TDR-63-72

a, 0

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at 0Sn 0 " f " F N f" Ae " f " I

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N .940- 46 .0 - .4 .4 1% N N I% 0 N~ '40- '4%4P 0 0 'I %0 0vz -IiO I- IoN 6- 0- .1 foo90 wo0N 4 1-4 % 4-40 9. 0- b. b.1

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ASD-TDR-63-72

EXAMPLE 1 (Cont'd)SON= 3.83258954e-14 IHETAC. 1.04719754E 00 Is 1.00COUCt 03 O

T*O.12426?58 XSm 6.67997762E 03 VSA 1.32?662251-03 IS& 5.12684381t 03SUN* 7.03746041E-14 THETAOn 1.04719754E 00 Is 1.UCoo0O0oUE 03

T=0.12451172 XS- 5.91993022t 03 VSs 1.3149431SE-03 IS* 3.4L785946E 03SON= 2.52?08134E-13 ThiEIACs 1.04719754E 00 Is 1.OOOCOOCOI 03

1-0.12475586 XS. 2.95968256E 03 VS. 1.40794121E-03 IS= 1.1088?t07L 03SUN= 1.750288361-12 ThETAOs 1.04719154E 00 In 1.000C000UkE 03

1.0.12478638 XSz 2.569876S9E 0i VS. 1.410695361-03 IS= 1.49525201E 03SBNz 2.6706588CE-12 THETAC. 1.04719754Ek 00 1- 1.OCOOOOOOL 03

1-0.12481689 XSm 2.21987060E 03 VS& 1.4t132S77E-03 IS= 1.281626d9S 03~bNw 4.15660727k--12 THiETAO. 1.04719754E 00 1- 1.00000000E 03

T=0. 12484741 XS- 1.849864163t 03 VS. 1.40870796k-03 iSs 1.068005891 03SBNs 7.18311238t-12 THETAC. 1.04719754E 00 Is 1.OCOCOOOOf 03

T-0.12487793 XSm 1.47985867E 03 VSs 1.40052226L-03 IS= 8.5438282Sk 02SbNx 1.414257111-11 THETAO. 1.04719754E 00 Is 1.0000(0001,k 0)

r=0.12490845 XS. 1.10985272E 03 VS. 1.38121949E-03 IS= 6.4075917SE 02SON= 3.407216551-11 THETAC. 1.04719154E 00 Is 1.OCOOOOcOi. 0;

1-0.12493896 XSw 7.39846766E 02 VSu 1.334561661-03 IS= 4.2713672SE 02SBN. 1.15255839E-10 TIETAOs 1.04719754E 00 to 1.0OO0uOOCI 03

1-0.12496948 ES. 3.69840828t 02 VSm 1.19480796E-03 IS* 2.135136811 02SON& 9.274300101-10 THETAOs 1.047197S4E 00 Is 1.OCOOOOOOE 03

T-0.12497330 ES. 3.23590082E 02 VSw 1.16554150E-03 IS& 1.86810197E 02SBNs 1.38549213E-09 ThE1A0z 1.04719754E 00 In 1.UiOOOo0UE1 03

T=0.12497711 XSs 2.77339339E 02 VS. 1.11862916E-03 '5 1~ .6Ct079I51 0?SON. 2.20060202E-09 TI4ETAO. 1.04719754E 00 In 1.OCOOOOOOE 03

T-0.12498093 ESw 2.310665971 02 VS. 1.04369006E-03 IS* 1.33405033L 02SON. 3.80484438E-09 U-IrAQ. 1.047197541 00 Is 1.OOOOOOOuE 03

T-0.12496474 XS- 1.84637655k 02 YS. 9.20271254E-04 iS. 1.06702150t 02SON. 7.43600706E-09 THETAC. 1.04719754 00 In 1.OCOOOOOOE 03

Ta0.124968S6 ES- 1.3687114k 02 VS- 7.020902101-04 ZSw ?.9999268U- 01,SON. 1.764561591-08 THEIAOs 1.047197541 00 Is 1.0000000GE 03

Ta0.12499237 XS- 9.23363733k 01 VSa 2.58938473E-04 25. 5.329638761 01SON= 5.96659827E-08 THETAOm 1.04719754E 00 In 1.00000000t. 03

T=0.12499619 X5. 4.60856342E 01 VS.-9.450233701:-04 Z5. 2.65935069t 01SON= 4.6004725CE-07 11,1180- 1.04719754k 00 In 1.0000000CE OJ

T-0.12499666 XSm 4.03042918E 01 VSs-1.19122364E-C3 IS= 2.325564651 01SONz 7.17745411E-01 THETAO- 1.04719754E 60 Is 1.00000000t 03

1-0.12499714 XSs 3.45229495k 01 YS--1.56C54501-03 ISO 1.99177864E 01SBNs 1.142246011-06 T14ETA0m 1.047197541 00 In 1.UOOOOOOCOE 01

1.0.12499762 ES. 2.67416C711 01 VSu72.1916893SE-C3 ISs 1.65199263E 01.SON= 1.97967023E-06 THETAD- 1.04119754E 00 In 1.00000000L 01

Tu0.12499609 ESu 2.29602650k 01 YS&-3.20985746E-03 IS. 1-.342066?E 01SON. 3.88490909E-06 IhETAG. 1.04719754E 00 Is 1.00000000E 03

T=0.12499657 ES. 1.71769230t 01 VS.-4.99754572E-03 15. 9.904206261 00SON. 9.260962621-06 THETAO. 1.04719754E 00 In 1.000000001 03

T-0.12499905 ES. 1.13975615k 01 VS*-8.6395665DE -03 iSu 6.56634623E 00SBNs 3.18293935e-05 THETAO. 1.04719754E 00 In 1.OOOOOOOUt 03

1.0.12499952 XS. 5.61624432f 00 YSa-1.66532559E-02 iSu 3.22848621F 00SON* 2.68290704t-04 THETAO. 1.047197541 00 Is 1.U00000000t 03

Ta0.124999S6 XSs 4.89357859E 00 YS=-2.07466281E-02 ISm 2.81125310C 00SON. 4.0?1584?CE-04 TNETAO. 1.04719754E 00 Is 1.00000000E 03

Tm.0.12499964 XSs 4.17091656k 00 VSa-2.41265199E-02 ZSa 2.394C21161 00SgNm 6.620193001-04 THETAOs 1.04719754E 00 Is 1.00000000t- 03

T-0. 12499910 ESw 3.44626433E 00 VS*-2.959046301-02 15. 1.976786668 00S8Ns 1.16117553k-03 THETAO. 1.04719754E 00 to 1.0000000GE 03

1.0.12499916 ESm 2.72564036E OC VSA-3.819041171-C2 IS* 1.S5955619ik 00SON. 2.46196992E-03 1111180z 1.04719754k 00 In 1.00000000k 03

T=0.12499982 ESs 2.00311461E 00 VS*-5.57010446E-02 I5. 1.14232369E 00SON. 6.954104361-03 THETAOs 1.04?19?54E 00 In 1.00000000E 03

1T-0.12499966 XS. 1.261052901 00 YS.-9.2441949SE-C2 IS= 7.250911951-01SON.m 4.914223671-02 1111180. 1.04719754E 00 In 1.0000000Ek 03

57

ASD-TDR-63 -7.

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ASD-TDR-63 -72

EXAMPLE I. (Co'nt'd)SBN. 2.59469527E-14 THETAO- 1.5707963CE 00 Is I.OCOOOOOOE 03

T*0.12304688 XS. 2.13435712E 04 VS. 6.7781127YE-04 ISs 8.149021861ý-04S8Nw 1-89693928E-14 THETAOw 1.57079630E 00 Is 1.00000000E 03

To0.12329102 XSu 2.39256024E 04 VS. 7.09358388E-04 IS. 7.13038784E-04SON. 3.1895714?E-14 ThETAO. 1.57079630k 00 In 1.0C0000000k 03

T=0.123S3516 XSm 2.05076337k 04 VS. 7.4344903bE-04 IS, 6.11175382k-04SON. 1.8494651kt-15 THETAOw 1.57079630E 00 In 1.00000000E 03

1.0.123?7930 XS. l.70896649E 04 VS. 7.?SC72912E-04 ISm 5.09311974E-04SON. 4.84908283E-14 rHETAOm 1.57079630k 00 In 1.000C00000k 03

Tm0.12402344 XSz 1.36716962k 04 VSa 6.16563702e-04 L~s 4.07448566k-04,SON= 3.66296861E-14 THETAOs 1.57079630E 00 In l.CiOOOOOOGk 03

1=0. 12426758 XSm lo02537274E 04 VSs 8.54359090k-04 IS* 3.05585161E-04SON- 7.50018156k-I'. THETAO= 1.5707963CE 00 1- 1.OCOCO0O0k 03

Tz0.12451172 KS. 6.83575886E 03 YS- 8.97579086E-04 IS. 2.u312l7!)6k-04SON= 1.56972529E-13 THtETAOu 1.57079630k 00 1n 1.000000001 03

T=0.l2475586 KS. 3.41779014E 03 YSs 9.29255116k-04 ZSm 1.01858351E-04SBN. 1.4247392CE-12 THETAOm 1.5707963CE 00 1- 1.00000000E 03

T-0.12478630 KS. 2.99OS4405S. 03 VS. 9.31456757k-04 IS= 8.912542461ý-05SON= 1.97095662E-12 THETAOs 1.57079630E 00 1n 1.00000000L 03

T=0.124S1609 XSu 2.56329796E 03 V59 9.31207490E-04 ZSx 7.63924986k-05SON. 3.02007326E-12 THETAO& 1.57079630k 00 1n 1.00000000k 03

T*0.12484741 XSm 2.13605186k 03 VS. 9.2119S156E-04 IS= j.36595732L-05SON. 5.40'D19536k-12 THETAC. 1.57079630E 00 Is 1.OOOOOOOOE 03

Ta0.12487?93 XSw 1.70880578k 03 YS- 9.16456741k-04 ZSx 5.09266472k-O5SON. lo03694180E-11 THETAC. 1.57079630E 00 1- 1.00000000L 03

T.0.12490845 KS. 1.28155971k 03 VS- 8.92823911k-04 ISs 3.819372151-05SON= 2.60150012k-l1 THETAOs 1.57079630k 00 1& 1.00000000E 03

T=0.12493896 KSw 8.54313624E 02 VS. 8.36775875E-C4 iS& 2.5460195OF-05SON. 8.73S01182E-11 THETAO. 1.57079630E 00 1- 1.00000000E 03

T-0.12496948 KS. 4.27067554E 02 YS- 6.719O5482E-04 ZS. 1.272N100k-O5SON* 6o98259556E-I0 THiETAO. 1.57079630E 00 1- 1.00000000k 03

T=0.12497330 XS. 3.73661795E 02 VS- 6.37702447E-04 ISm 1.11362542E-05SON. lo04568829E-09 THETAOs 1.57079630k 00 In 1.00000000E 03

T=0.12497711 XS- 3o20Z56037t 02 VS. 5.83141285E-04 ZSz 9.544630511-06SON. 1.66191210k-09 THETAOs 1.57079630E 00 In 1.0000000Gk 03

r-0.12498093 KS. 2.66850281k 02 VS. 4o96225238E-C4 ZS. 7.95302284E-06SON. 2.87537494E-09 THETAO. 1.57079630E 00 In 1.OOOOOOO0i 03

T-0.12498474 KS. 2.13444S22k 02 VS- 3.533308866-04 IS= 6.36140710E-06SON. 5.61737198E-09 THETAO. 1.57079630E 00 In 1.00000000E 03

Tm0.12498856 X5. 1.60038765k 02 VS. 1.01079486E-04 IS= 4o769791361-06SON. 1.33345401E-08 THETAO. 1.57079630k 00 In 1.00000000E 03

T=0.12499237 KS. 1.06633009E 02 VS.-4.1074901ýk-04 ZSu 3.17817569E-06SON= 4.50838649E-08 THETAC. 1.57079630E 00 Is 1.OOOOOOCo& 03

10O.12499619 XS. 5.32272530k 01 YS2-1.80005731E-03 ZS. 1.58656C01k-06SON* 3.62636C12E-07 THETAOs 1.57079630k 00 In 1.00000000C 03

1.0.12499666 KSm 4.65515333k 01 YS=-2.0839038SE-03 IS* 1.38760600E-06SON. S.42190742E-07 THETAO. 1.57079630E 00 In 1.00000000E 03

T=0.12499714 KS. 3.98758137E 01 YSs-2.53242844E-C3 ZSs 1;.18865608k-06SON. 8o6285872SE-07 THETAOz 1.57079630k 00 Is 1.00000000E 03

Tm0o12499762 KS. 3.32000944k 01 YS.-3.24287710L-03 ISu 9o89704108E-07SON. 1.49568796E-06 TIIETAOs 1.57079630k 00 In lo.00000000E 03

1=0.12499809 KS. 2.65243751k 01 YSs-4.40691751k-03 ZS= 7.90IS2M4E-07SON= 2o93551192L-06 THETAOs 1.57079630k 00 Is 1.00000000k 03

T.0.12499857 KS. 1.98486562E 01 VS*-6o45964360E-03 iSs So91800143E-07SON. 7.01755869E-06 Tt4ETAOm 1.57079630E 00 In 1o.00000000E 03

1.0.12499905 KS. 1.31729379E 01 YS.-1.06287850k-02 iS. 3.92846223E-01SON= 2.41266736E-O5 THETA0- 1.57019630E 00 Is 1.00000000E 03

To0.12499952 KS. 6.49722415k 00 VSe-2.19950724E-02 ZSs 1.93896264E-07SBN. 2.06427974E-04 THETAC. 1.57079630k 00 Is 1.00000000E 03

T.0.12499958 KS. 5.66276145k 00 VS.-2.43217397E-02 ISm 1.69027272t-OTSgNm 3o15022290E-04 THETAO= 1.57079630k 00 Is 1.00000000E 03

1-0.12499964 KSs 4.82830250k 00 YS=-2.79967386E-02 £5. 1.44158310E-01

59

ASD-TDR-63-72

EXAMPLE 1 (Cont'd)SONu 5.16075644E-04. THtEWACs 1.57079630E 00 1- 1.00000000E 03

T-0.12499910 KS. 3.99385294E 00 VS--3.3796S402E-02 iS. 1.L9269342E-07SbN- 9.3410062BE-04 THETAO- L.5?079430E 00 Is 1.00000000k 035

To0.12499976 KS. 3.15942842E 00 VS.-4.31999S64E-02 ZSx 9.4420361SE-08SON. 1.96432231L-03 liHETA0m 1.51079630E 00 1- 1.0000000DE 03

T=0.12499982 KS- 2.32507950k 00 VSe-S.93126839E-02 ISw 6.955133l4E--OsSON. S.2990927?E-03 THETAOs 1.57079630E 00 In 1.00000000L 03

1-0.12499988 XS. 1.49099770k 00 YSs-B.92S63021E-02 ISs 4.46621874E-08SBNw 2.40346363t:-02 IHEIAOu 1.57079630E 00 In 1.00000000E 03

1=0.12499994 KSs 6.58000022E-OL YSs-1.49397792E-01 ZS- 1.98075067E-08SON= 0. THE7AO. I.S7019630E 00 In 1.00000000t 03

1.0. XS. 1.74999981E 06 VS. 0. ZSs S.Z154058SE-02SBN- 1.02206862L-15 THETAO. 1.57079630E 00 In 1.00000000E 04

1-0.01562500 XS. 1.53124981E 06 YS& 3.l159S663L-04 ISs 4.5634800SE-02SONs 2.95918807E-15 THETAOs 1.57079630E 00 In 1.00000000E 04

T-0.03125000 XSw 1.31249981E 06 IS- 3.81550997E-05 LS* 3.91ISS428k-02SONs 3.3161078?E-1S THETAOu I.5707963GE 00 Is 1.00000000E 04

T*0.04687500 XS- 1.09374981L 06 VS--6.9S259S71k-04 IS= 3.2S962847L-02SON- 4.46993113E-15 THETAOu 1.S7079630E 00 In 1.00000000L 04

T=0.06250000 KS. 6.74999809E 05 VS. 3.13729468k-OS ZS. 2.60770267E-02SON. 1.49906300E-L5 THETAC. 1.57079630E 00 In 1.0C000000F 04

Tw0.C7812S00 XS- 6.56249809E 05 VS. 1.15062836E-03 ISw 1.9~5576b9E-02SBN- 6.0870963S9E-15 THETAO. 1.57079630k 00 In 1.00000000E 04

1.0.09375000 KS. 4.37499815E 05 VS. 9.5047632SE-04 IS* 1.303851O8k-02SBN. 2.45301035k-IS 1IHk1A0. 1.57079630E 00 In 1.00000000L 04

1=0.10937500 KS- 2.18749818k 0S VSs l.454S4231E-03 iSs 6.51925296E-OS58Nw 1.90789104E-14 THETAOw 1.51079630E 00 I- 1.OOOOOOOOL 04

T=0.11132813 KS- 1.9140607CE 05 VS. 1.61214171k-03 IS= 5.70434570k-03SBNz 4.98389059E-15 1I4EFAO. 1.57079630k 00 In 1.0C000000F~ 04

1.0.1132812S KS- 1.64062320E 05 VS. 1.17292059E-03 IS- 4.88943845L-03SoNa 5.08771902E-15 THETAO. 1.51079630E 00 In 1.OOOOOOOCE 04

T*0.11523438 KSs 1.3671857CE 05 VS. 1.91886163E-03 ISs 4.07453120E-03SBN= 7.54412279E-14 THETAO. 1.57079630E 00 In 1.0C0000000k 04

1.0.11718750 XS- 1.09374820E 05 VS. 2.4409403SE-03 IS= 3.25962394L-03S6Nm 6.65033203k-14 THET4O. 1.S7079630k 00 In 1.0OOOOOOCE 04

1=0.11914063 KS. 8.20310712E 04 VS. 3.?9686866E-03 IS= 2.44411669E-03SON. 9.44858956k-IS THETACm 1.5707963CE 00 1s 1.000U00(00E 04

1.0.12109375 KS. 5.46873218k 04 VS. 4.16392517k-03 15. 1.62980944L-03SONx 2.59469515k-13 THiETAO. 1.57079630E 00 In 1.OO000ooOE 04

To0.12304688 KS. 2.13435133E 04 VS. 6.35523909E-03 iSs 8.14902166t-04SON. 1.8969403SE-13 TWETAO. 1.57079630E 00 Is 1.00000000t 04

1.0.12329102 XSx 2.392S6045k 04 VS. 6.6442605SE-03 IS= 7.1303B784k-04SON* 6.32930660E--13 1THETAO. 1.57079630E 00 In 1*0OOOOO0uE 04

1=0.12353516 KS. 2.05076358k 04 VS. 6.98379534E-03 IS= 6.111753ts2E-04SON. 3.9246518CE-13 THETAC- 1.57079630E 00 Is I.OCOOOOOOL 04

1.0.12377930 KSu 1.10896675k 04 VS. 7.35460740E-03 ISO 5.093119141-.-04SONm 4.60490274E-13 THETAO. 1.57079630E 00 Is 1.00000000E 04

1.0.12402344 Ks- 1.36716989E 04 Vs. 7.7621413SE-03 ZSs 4.07440566f~-04SONw 3.40133703E-13 THETAC. 1.S70?963CE 00 Is 1.00OCOOOOL 04

1.0.12426758 KS. 1.02537304E 04 V5n b.15924358E-03 IS. 3.0!)SB5l61E-04SON= 7.03503561E-13 TI'ETAO. 1.57079630E 00 Is 1.OOOOC0OUE 04

1.0.12451112 KS. 6.83576202E 03 VS. 8.6022460SE-03 ZS- 2.03r21t76F-04SON= 1.S8717568L-12 THETAC. 1.5707963CE 00 Is 1.0CC00000k 04

1-0.12475586 KS- 3.41779357E 03 VS. 6.94789135t-03 ZS- 1.01858351E-04SON- 1.2l721484E-11 L HETAOm 1.57079630E 00 In 1.&00C000006 04

1=0.12478638 KS. 2.99054751k 03 YS. 8.976234S6E-03 ZS- 8.91254246E-O5SBN. 1.97496831E-11 THkTAC. 1.5101963CE 00 Is 1.OCOGOOO0k 04

1.0.12481689 KS. 2.56330144L 03 VS. 8.98011839E-03 IS= 7.639249b61-iUSSONs 3.00379226E-11 TI9ETAOs 1.57079630E 00 Is 1.000o000toE 04

T10.12484141 XSs 2.13605538k 03 VS. 8.946S7433E-03 ZS. 6.36595732E-05SON= 5.4119773SE-11 THETAO. 1.57019630k 00 Is 1.OCOOOOOO( 04

1-0.12487793 KS- 1.70880933k 03 VS. 8.04566S45E-03 15= 5.09266472L-05

60

ASD-TDR-63- 72IiAMWLIZ (Cont'I8)

SBNu 1.076432SE-10 TI4ETAO- 1.5?0?9630E 00 1n 1.00000006t1 0'.Ta0.12'.9084S ES. 1.201.56328E 03 vS. 8.6t038160E-03 IS* 3.61937215k-OS

SON= 2.553tS402E-1O THETAO. 1.57079630k 00 10 1.00000000k 04T=0.12493896 XS. 8.54317224k 02 VS. 6.0569698SE-03 ZS- 2.S46079S#E-05

SIN. S.73393500k-10 ITiETAO& I.57079630E 00 In 1.0000000CE 04Ta0.12496948 XSu *.2707119CE 02 VS. 6.41546693E-03 iSw 1.2727870SE-05

SIN. 6.9901260?E-09 TI4ETAOm 1.57079630E 00 In 1.00000000L. 04T=0.12497330 ESu 3.73665431E 02 VS. 6.0741923SE-03 ZS. 1.1136254l6-05

SBN. 1.04493083E-08 TI4ETAOu 1.57079630E 00 1- 1.0000000GE 041=0.12497711 XSm 3.20259675k 02 VS. S.S2948195F-C3 IS= 9.54463899t-06

SBN. 1.66175392E-08 THETAOm 1.57079630E 00 Is 1.00000000t 0'.T&0.12498093 XSn 2.6685392A1 02 vs. 4.66125363E-03 iS* 7.95302331E-06

SIN. 2.874902316-06 THiETAOu 1.57079630E 00 Is 1.00000000E 04T-0.12498474 XSw 2.13448170k 02 YS. 3.?33334?1E-C3 IS= 6.36140764E-06

SIN. S.61862397L-08 THETAO= 1.57079630E. 00 I= 1.00000000L. 04T=0.12498856 ES. 1.60042416E 02 VS. 7.11600554E-04 iSs 4.76979196L-06

SBNu 1.33329423E.-07 THETAO. 1.57079630E 00 12 1.0000000CE 01T=0.1249923? XS. 1.06636663k 02 YSs-4.40559286E-03 iSu 3.17817631k-06

SIN. 4.507426386-07 THETAO. 1.57079630E 00 In 1.00000000t 04T-0.12499619 XSm 5.323091156 01 YSa-1.82957143E-02 Z5. L.B6S65664E-06

SIN. 3.62552974E-06 THETAOm 1.51079630E 00 to 1.00000000E. 041.0.12499666 XS. 4.65551931E 01 VS.-2.11335579-02 IS= 1.38760866E-06

SIN. 5.420S1176E-06 TI4ETAO. 1.57079630E 00 Is 1.OOOOOOOUE 04T=0.12*99714 XS. 3.987947*9k 01 YS.-2.56177592E-02 iSs I.1886610k-C6

SBNu 8.6261429$E-06 THETAO. 1.57079630E 00 Is 1.OOOCOOOOE 04T&0.12*99162 XS. 3.32037583k 01 VS.-3.27204600E-02 iSs 9.69704740E-01

SIN. 1.49519105k-OS TIIETAOs 1.57079630E 00 Is 1.00000000k 041-0.12*99609 XSu 2.65280470L 01 VS--4.43575722E-02 IS= 7.90752780-07

SBN= 2.93426803k-O5 THETAO. 1.57079630k 00 Is 1.00000000E 0'.T=0.12499857 XSm 1.96523512t 01 VSw-6.48777?71L-C2 IS= S.918C0839E-07

SON= 7.01351798E-O5 TIIETAO= 1.S7079630E 00 Is 1.00000000L. 041.0.1249990S ESu 1.31767204E 01 YS.-1.06549945t1-01 ZSm 3.92849091E-01

SIN. 2.41034585L-04 THiETAO. 1.570796306 00 Is 1.00000000k 04T-.12*3499952 XSm 6.5015367SE 00 VSo-2.20124274E-Cl ISs 1.93897199E-01

SIN- 2.056502916-03 THETAO& 1.57079630E 00 Is 1.00000000L. 04Ta.0.12499958 KS. 5.66729*566 00 VSs-2.43346789E-01 L5m 1.690283181-07

SBN- 3.133633351-03 THETA~a 1.S7079630E 00 Is 1.00000000E 04T=0.12499964 XSs 4.83342379E 00 VSu-2.79962856E-01 ZS= 1.441SMU23-01

SIN. S.1173240SE-03 THETAO. 1.51079630E 00 li- 1.00000000E 04T-0.12*99970 XSw 4.000*787*6 00 YSs-3.37689447E-01 ZSm 1.19289559E-07

SIN. 9.19026136E-03 THETAC. 1.S70796306 00 1& 1.00000000E 04T=0.12499976 XSs 3.16999075E 00 YS.-4.30866103E-01 IS- 9.44185030E-00

SIN- 1.88796706E-02 THETAOm 1.57079630E 00 Is 1.00000000.. 04T-0.12499982 XSs 2.34676042E 00 VS.-5.88720452E-01 IS= 6.954289VIE-08

SIN- 4.65634876E-02 ITHETAC. 1.57079630E 00 In 1.OOOOOOOCE 04T-0.12499988 XS., 1.5*1557626 00 VS.-6.71187183E-01 IS= 4.4634SS381.-OM

SIN. 1.26268327E-01 THETAOu 1.57079630E 00 12 1.00000001.6 04T-0.12499994 ESw I.270101E-01 VS.-1.37901781E 00 IS* 1.93167554k-OS

SIN. 1.8065747CE-01 THETAC. 1.57079630E 00 Is 1.0000000UE 04T-0.12499995 XSm 7.403198766-Ol YS.-1.44608973E CO I~s 1.614S1655k-06

SON= 1.7*057561-0l THETAG. 1.57079630k 00 In 1.00000000L 04Ta0.12499996 X5. 6.55635226E-01 VS.-1.51666414E 00 IS* 1.2949787$E-08

SIN. 1.63562746E-01 THETAO& 1.57019630E 00 In 1.0000000CIE 04To0.12499996 ES. 5.7372S1766-01 VS.-1.59060696E 00 15- 9.110734376-09

SIN. 1.50*351906-01 ThETAOm 1.51079630E 00 Is 1.00000000E 04T=0.12499997 XS. 4.9461935$E-01 VS.-1.66763699E 00 IS% 6.43166322E-09

SIN. 1.35967317?-01 THETAC. 1.57079630E 00 to 1.00000000E 04T=0.12499998 ES. 4.16306756E-01 VSm-1.7*1535S1C 00 IS= 3.138040166-09

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SINO 1.111603316-01 THETAOw 1.57079630E 00 In 1.00000000k 0*T=0.12499999 XS. 2.73784667E-01 VS.-1.91*90576E 00 ZS=-3.S22647711.-09

61

ASD-TDR-63- 72

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63

ASD-TDR-63-72

PARTICLE POSITION In X Y- PLANE

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64

ASD-TDR-63-72

APPENDIX III

DATA FROM EXAMPLE 2 PROBLEM

65

ASD-TDR-63-72

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Figure 1lU-1. Deflection Current for Sbc Different Energy Particles Versus Incident Angle

68

ASD-TDR-63-72

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ASD-TDR-63-72

APPENDIX IV

DATA FROM EXAMPLES 3 AND 4 PROBLEMS

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ASD-TDR-63-72

EXAMPLE 4 (Cont"d)0. U. 2.0320E-O0 3.8643E-01 1.0000E 04 0. 3.8643E-01O. -0. -0. 3.8801E-01 1.0000f 04 0. 3.86011-010.2618 1.0518E 00 3.9255E 00 1.8090E-02 1.0000E 04 7.4682E-03 1.6403t-020.2618 9.9925E-01 3.7293E 00 2.1366E-02 1.0000E 04 8.8695E-03 1.9340E-020.2618 9.46668-01 3.5330E 00 2.5494E-02 .O0000E 04 1.0648E-02 2L3•LCE-020.2618 8.94078-01 3.3367E 00 3.0773E-02 1.0000E 04 1.2938E-02 2.7732E-020.2618 8.4147L-01 3.1404E 00 3.7635E-02 1.0000E 04 1.5940E-02 3.3818E-020.2618 7.8888E-01 2.944LE 00 4.6730E-02 1.0000E 04 1.9952E-02 4.18358-020.2618 7.3629E-01 2.7479E 00 5.9052E-02 1.0000E 04 2.5441E-02 5.2604E-020.2618 6.83701-01 2.5516E 00 7.6192E-02 1.0000E 04 3.3160E-02 6.?374E-020.2618 6.311LE-01 2.3553E 00 1.0082E-01 1.0UOOE 04 4.44058-02 8.8054E-020.2618 5.1851E-01 2.1590E 00 1.3775E-01 1.0000E 04 6.1548E-02 L.1745E-010.2618 5.2592E-01 t.9628E 00 1.9736E-01 1.0000L 04 8.9062E-02 1.5905E-010.2618 4.7333E-01 1.76658 00 3.2012E-01 1.0000E 04 1.3430E-01 2.1497E-010.2618 4.2074E-01 1.5702E 00 3.8563E-01 1.0000E 04-2.1213E-02 3.3802E-010.2618 3.6814E-01 1.3739E 00 3.5288E-01 1.0000E 04-3.7733E-03 3.3663E-010.2618 3.1555E-01 1.1777E 00 3.5053E-01 1.0000E 04 4.42408-03 3.4294E-010.2618 2.6296E-01 9.8138E-01 3.5724E-01 1.0000E 04 6.5954E-03 3.5331E-010.2618 2.1037E-01 7.8SILE-01 3.6660E-01 1.0000E 04 5.6445E-03 3.6450E-010.2618 1.5718E-01 5.8883E-01 3.7551E-01 1.0000E 04 3.6221E-03 3.1444E-010.2618 L.05188-01 3.9255E-01 3.8245E-01 1.0000E 04 1.6983E-03 3.8200E-01u.26L8 5.2592E-02 1.96288-01 3.8672E-01 1.0000E Q4 4.2L87E-04 3.8660E-010.2618-0. -0. 3.8801E-01 1.0000E 04 O. 3.6801E-010,5236 2.0320E 00 3.5195E 00 1.6190E-02 1.0000E 04 1.2150E-02 L.0314E-020.5236 1.9304E 00 3.3436E 00 1.9081E-02 1.0000E 04 1.4362E-02 1.2050E-020.5236 1.8288E 00 3.1676E 00 2.2717E-02 1.0000E 04 L.7153E-02 1.4203E-020.5236 1.7272E 00 2.9916E 00 2.7361E-02 1.0000E 04 2.0727E-02 1.69078-020.5236 1.6256E 00 2.0156E 00 3.3399E-02 .O0000E 04 2.5380E-02 2.0357E-020.5236 1.5240E 00 2.6397E 00 4.1412E-02 1.0000E 04 3.1552E-02 2.4837E-020.5236 1.42248 00 2.4637E 00 5.2312E-02 1.0000E 04 3.9914E-02 3.0766E-020.5236 1.3208E 00 2.2877E 00 6.7592E-02 1.O000E 04 5.1504E-02 3.8914E-020.5236 L12192E 00 2.1117E 00 8.9846E-02 1.0000E 04 6.?9468-02 5.0451E-020.5236 1.1176E 00 1.9357E 00 1.2393E-01 1.0000E 04 9.1687E-02 6.77258-020.5236 1.0160E 00 1.7598E 00 L.8012E-01 1.0000E 04 L.2571E-01 9.5400E-020.5236 9.1440E-01 1.5838E 00 2.86B9E-01 1.0000E 04 L1.031E-O 1.4138E-010.5236 8.1280E-01 1.4078E 00 3.98038-01 1.00008 04 1.01368-02 2.9061E-010.5236 7.1120E-01 1.2318E 00 3.654LE-01 1.0000E 04 2.0665E-02 3.2001E-010.5236 6.090"C-01 1.05598 00 3.6724E-01 1.O000E 04 2.0470E-02 3.4276E-010.5236 5.08b.--0l 8.?988E-01 3.726&E-01 1.0000E 04 1.6311E-02 3.58788-010.5236 *.0640E-01 ?70391E-01 3,?797E-01 1.0000E 04 .L1250E-02 3.7016E-010.5236 3.0480E-01 5.27V3E-01 3.8235E-01 1.0000E 04 6.5941E-03 3.7830E-010.5236 2.0320E-01 3.5195E-01 3.8558E-01 .O0008E 04 2.9172E-03 3.83866-010.5236 L.0160E-01 1.7598E-O 3.8749E-01 1.O000E 04 7.2701E-04 3.8707E-010.5236-0. -0. 3.8801E-01 .O0008E 04 0. 3,8801E-010.7854 2.8737E 00 2.8737E 00 1.3606E-02 1.0000E 04 1.2697E-02 3.05758-030.7854 2.7300E 00 2,7300E 00 1.5980E-02 1.0000E 04 1.4871E-02 3.4382E-030.785.4 2.5863E 00 2.5863E 00 1.8954E-02 1.0000k 04 L.75768-02 3.8665E-030.7854 2.4426E 00 2.4426E 00 2.2739E-02 1.0000E 04 2.0989E-02 4.3395E-030.7854 2.2990E 00 2.2990E 00 2.7643E-02 1OOOOa. 04 2.5362E-02 4.8429E-030.7854 2.1553k 00 2.1553E 00 3.4143E-02 1.0000E 04 3.1070E-02 5.33858-030.7854 2.0l16E 00 2.01168 00 4.3000E-02 1.0000E 04 3.8687E-02 5.73478-030.7854 1.8679E 00 1.8679E 00 5.55198-02 1.0000b 04 4.91408-02 5.81828-030.7854 1.72428 00 1.7242E 00 7.4156E-02 l.UO000 04 6,4035E-02 5.0687E-030.7854 1.5805E 00 L.5805E 00 1.0424E-01 1.0000E 04 8.6488E-02 2.0554E-030.1854 1.4368E 00 1.4368E 00 1.6079E-01 1.0000E 04 1.23871-01-8.4323E-030.7854 1.2932E 00 1,2932E 00 3.2976E-01 1.00008 04 1.9505E-01-6.97,28-u20.7854 1.1495E 00 1,I495E 00 5.30718-01 1,00008 04 1.0307E-01 3.3802E-010.7854 1.0058E 00 1.00588 00 4.4324E-01 1.0000E 04 5.7802E-02 3.5475E-010.7854 8.62118-01 8.62LIE-01 4.16698-01 1.0000k 04 3.6563E-02 3.66808-010.7854 7.1842E-01 ?.1842E-01 4,0393E-01 1.00008 04 2.3474E-02 3.7493E-010.7854 5.7474E-01 5.7474E-01 3.9678E-01 1.0000E 04 1.4431E-02 3.8045E-01

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ASD-TDR-63-72

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