NASA CR-54738
A COMPUTER PROGRAM FOR ELECTRON OR ION GUN ANALYSIS:
OPERATIONS MANUAL
by
V. Hamza
M. L. Report NOo 1369
September 1965
Microwave LaboratoryW. W. HANSEN LABORATORIES OF PHYSICS
STANFORD UNIVERSITY. STANFORD, CALIFORNIA
Interim Report
Prepared for
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
Contract NAS 3-4100
NOTICE
This report was prepared as an account of Governmentsponsored
work. Neither the United States, nor the National Aeronautics
and SpaceAdministration (NASA), nor any person acting onbehalf of NASA:
A.) Makesany warranty or representation, expressed or
implied, with respect to the accuracy, completeness,or usefulness of the information contained in this
report, or that the use of any information, apparatus,
method, or process disclosed in this report maynot
infringe privately ownedrights; or
B.) Assumesany liabilities with respect to the use of,
or for damagesresulting from the use of any infor-
mation, apparatus, method or process disclosed in
this report.
As used above, _'personacting on behalf of NASA'_ includes
any employeeor contractor of NASA,or employee of such con-
tractor, to the extent that such employee or contractor of NASA,
or employeeof such contractor prepares, disseminates_ or
provides access to, any information pursuant to his employment
or contract with NASA,or his employmentwith such contractor.
Requests for copies of this report should be referred toNational Aeronautics and SpaceAdministrationOffice of Scientific and Technical InformationAttention: AFSS-AWashington, D. C. 20546
NASA CR-54738
A COMPUTER PROGRAM FOR ELECTRON OR I0N GUN ANALYSIS:
OPERATIONS MANUAL
by
V. Hamza
M. L. Report No. 1369
September 1965
Interim Report
Prepared for
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
Contract NAS 3-4100
MIcrowave Laboratory
W. W. Hansen Laboratories of Physics
Stanford University
Stanford, California
TABLEOFCONTENTS
Pag___e
I. Introduction ............... • ......... 1
II. Computerprogram for beamanalysis ............. 3
A. Data input ....................... 5
B. Fortran coding form .................. 13t
C. Data output ....................... 13
III. Computer program for spectral radius calculation - XR -
calculation ......................... 46
A. Data input ...................... 46
B. Data output ....................... 47
Appendices
Ao Flow chart and Fortran II. Statements for beam
analysis ........................ 52
B. Flow chart and Fortran II. Statements for XR-ealcula-
tion .......................... 80
C. Detailed flow charts .................. 89
References ........................... 102
- iii -
F
I. INTRODUCTION
This report describes a computer program, shown at the end of the
report 3 which is used to analyze the space-charge flow in an electron
or ion gun. It determines the nature of the beam profiles for practi-
cally any specified two-dimensional or axially symmetric gun electrode
system. The basic process that is followed is to initially assume that
the space-charge density is zero, solve LaPlace's equation by finite-
difference methods_ and find the potential variation in the region of
interest shown in Fig. i.o With a knowledge of this potential variation_
the motion of charged particles from the emitter source is determined_
and the current density emitted is found by the Child-Langmuir law in
the neighborhood of the emitter. The whole process is then repeated
through several iterative cycles (solving Poisson's equation instead
of LaPlace's equation), until the final solution converges to a self-
consistent solution. The use of the program will be illustrated by
an example of an ion propulsion gun design.
It is beyond the scope of this report to explain the mathematical
method used; the reader is referred to the references for this_
The computer program has been written in the IBM 7090 Fortran II
programming language_ which requires at least a 32_000 word core for
execution.
Subroutines of the computer program will be now listed with a
brief expl_nation of their function.
-i -
o>z
_000oo0ooo00oooo0 _
4o-
QO-
it •
°0
z
,qQ----,qp_ _ • • • • •
d
wz z
_ ooi
z K
00
o
o
(3NI-I _( ) _AN
o _ - -__5 6 6
(S3HONI) 3 J._NIG_O03 -J(
- 2 -
a_
_,'_
0
_._
4-
0
q_0
4-'
0
I
,-4
I--I
II. COMPUTER PROGRAM FOR BEAM ANALYSIS
It is to be emphasized that all Fortran statements referring to
plotting may haCe to be changed in accordance with the particular in-
stallations where the program is being used. The statements herein
refer specifically to the plotting routines at the Stanford Computation
Center, and may not be accurate elsewhere.
Subroutines Required:
io MAIN _NE*
Starts the program, brings in all the data input, calculates the
matrix coefficients_ plots the electrode boundary points and calls UCAL
for LaPlace's solution and then _hNTRI.
2, ARC
Calculates the emitter length, determines the width of the current
tubes (ARCL) and establishes the beginning trajectory coordinates (ETX,
ETY)o ARC is called by _KNTRI.
3,_ CALR
Calculates the right hand side (RHS) of the matrix equation (space-
charge density). CALR is callea by NLNTRI.
Checks on trajectories intercepted by the electrode system.
C_RRC_ is called by TRCU.
5o
_,alculate_ the equipotential line coordinates throughout the region
of interest, starting with the potential VAT, and continues by increment
of SIZE until the potential of VBT is reached for each cycle if KCY(J) _ 0
(where J represents cycle number), otherwise, no calculation (if SIZE = 0
no equipotential line coordinates calculation). EOLINE is called by UCALo
*_ Represents OU to distinguish from 0 as zero.
- 3 -
6. MATRIX
Solves the matrix equation for each !ine_ e.g._ matrix equation
Aw = k
w = A-ik
MATRIX is called by UCAL.
7. MNTRI
Governs the whole solution once the initial (LaPlace's) potential
distribution is known. MNTRI is called by MAIN.
8. PEQ
Calculates the equipotential line coordinates through a given point
NP_T (NP_TX_ NP_TY) for current density calculation. PEQ is called by
MNTRI.
9. TRAJ
Calculates the trajectory coordinates through the region of interest
once the trajectories were initialized. TRAJ is called by TRCU.
i0. TRCU
Initializes trajectories and calculates current density distribution
along the emitter. TRCU is called by MNTRI.
!i.
Prints out the RHS distribution through the region of interest for
each cycle if IX¢ _ 0 and KCY(J) _ 0 Otherwise_ no print-out.
TROUT is called by MNTRI.
-4-
P
12° TW_UT
Prints out the potential distribution through the region of interest
for each cycle_ if KCY(J) > 0 .if The final solution is printed auto-
matically. TW_UT is called by UCAL.
13. UCAL
Solves for potential distribution inside the region of interest.
UCAL is called by MAIN for LaPlace's solution_ then by MNTRI for the
space-charge-flow solution.
14o 7090 PLATING R_UTINES (Fortranll) for the CalComp Plotter (Stanford
University Computation Center Library Program No. 157).
A. DATA INPUT
It is recommendedl that a scaled graph of the configuration to
be analyzed be drawn as shown in Fig. i. Attention is given to two
different sets of coordinates, e.g.; x-y line coordinate and x;y
coordinate in inches (dimension in inches is not essential).
t
The f_rst data card is the number of heading cards (NH) which will
follow (e,g._ identification of run by serial number 3 date 3 description,
etc.)_ It is particularly useful to differentiate _repeated machine deck
executions of the program.
The second data card is as follows:
NXF
NYF
NEM
total number of X-lines
total number of y-lines
number of x_y coordinates specifying emitter surface
(a minimum of two are, required, n_mely_th9 end points).
- 5 -
NTJ
NDIM
NRL
NUL
NURL
Nc m
IDEC
NFUL
KRHX
KRHY
_BPAN
number of trajectories
two-dimensional geometry < 2, axially symmetric geometry > 2
number of cycles (e.g., NRL = 2; LaPlace's solution is con-
sidered as zeroth cycle, then 2 cycles plus last cycle;
altogether 4 cycles); must be greater than 0
number of iterations for LaPlace's solution
number of iterations for Poisson's solution (after last
cycle NURL used as a switch to terminate the problem)
positive, emitter coordinates are beginning trajectory coor-
dinates; negative or zero, beginning trajectory coordinates
are calculated
negative, emitter is concave (for flat emitter use IDEC < 0
with )[EMIT _ _); zero and positive, emitter is convex
0 for the case of axial symmetry or for the case of two-
dimensional geometry when symmetry about the axis is used to
91imina_e the lower half plane from the computation; i for the
case of two-dimensional geometry when the full problem is
considered in the calculation.
number of lines in x-direction for which noncalculated points
(outside the region of interest, e.g., electrode) will be set
to a potential of the emitter (VA); in most cases this can be
taken to be the number of x-mesh lines up to the face of the
first electrode beyond _he emitter
x-line coordinate of the test point for RHS
y-line coordinate of the test point for RHS
The third data card is as follows:
positive s RHS prints out-condition to KCY > O; negative or
zero, RHS will not print out
number of x-lines to traverse to obtain equipotential line for
current density calculation; this is used for conserving time
- 6 -
NP_TX
NP_TY
YAXS
KR_N
KRTX
KRTY
VAT
VBT
S IZE
VA
VB
VC
HGH
in the scan for the equipotential used in the calculation
used in the calculation of emitter current density
fx- and y-line coordinate of a point whose potential will be
used for determining the coordinates of the equipotential lineor current density calculation.
y-coordinate of the axis of symmetry
The fourth data card shows:
number of test points (test _point determines whether its
potential is lower than the emitter potential; if so, the
calculation procedes; if not, EXIT is called
x- and y-line coordinate of a test point.
The fifth data card gives this information:
upper potential in equipotential calculation (see definition
of subroutine EQLINE)
lower potential in equipotential calculation
step size in equipotential calculation
emitter potential
highest negative potential, otherwise zero
y-distance in inches for y-positioning of the output plot
[VC = i0.0 (maximum width of the graph paper is i0") moves the
pen to point (0.0, i0.O) and makes that the reference point]
The sixth data card is:
the largest y-coordinate (in inches) of the second elec-
trode chosen for checking on trajectories for possible
interception
-7-
HSL
XLSL
the largest y-coordinate (in inches) of the first
electrode chosen for checking on trajectories for
possible interception (e.g._ in example given_ only
the second accelerator electrode was chosen to check
on trajectories)
not used
slope of a line to which normal derivative should be
zero, (see sketch below)
___\ _jinl of symmetry
/_ Axis of symmetry
VD
AXX
BXX
Note_ the first calculated point of each line should be
taken directly above or on the line of symmetry and must
be identified by ND(3) _ 0 in addition to NS = i
scaling factor for plotting purposes_ H times VD gives actual
inches on plot.
The seventh data card gives_
the x-coordinate in inches where subroutine C_RRCT
starts to check on XL_W for possible trajectory inter-
ception
the x-coordinate in inches where subroutine C_RRCT
stops to check on XL_W and starts to check on HGH for
possible trajectory interception
-8-
CXX
DXX
XR
the x-coordinate in inches where subroutine C_RRCT stops
to check on HGH for possible trajectory interception
a constant -- not used
the spectral radius of the matrix (the largest eigenvalue)
obtained by a separate program using essentially the same
data input (see Spectral Radius Calculation).
The eighth data card consists of:
the distance in inches from the axis (for axially geometry
only) when the axis is not part of the region of interest.
See sketch below
Focusing Electrode --i Electrode_----T--,
# / t" ,
i .L'_.I-U.[I U.L -L£1bt_l'_ b " ., // ./
__]i[">_-":""" - • ,'.', ".,,'.'.'._.'", ..... Z .'v..'.Emitter
, ,/ //,
Focusing Electrode J
I
/Axis
Accelerator
-9-
EPS
XEMIT
H
YEP
x_
ATOM
VTH
VTHX
VTHY
ATX
ATY
KCY
convergence test for matrix equation. (Data output
prints EPS IL_N)
x-coordinate in inches of the emitter radius (XEMIT is equal
to the emitter radius only if the emitter x-coordinate passes
through :_ero) and must be a very large number for a flat emitter.
mesh size in inches. (Data output prints MESH SIZE-H)
The ninth data card shows:
permittivity of free space (Data output prints EPSN_T)
specific charge-to-mass ratio for proton (or electron)
atomic weight number of ion flow (for electron flow,
ATOM = l.O)
transverse thermal velocity of emission
not used.
The tenth data card is as follows:
x- and y-corrdinates (in inches) of the emitter shape
(three (x,y) coordinates per card). Total number of x,y
coordinates must equal NEM, and they must follow in order
of increasing y-coordinate.
The eleventh data card gives:
positive, all print-outs occur (condition to IX_ > 0 and
SIZE > O) ; negative or zero, no print-outs.
Note: Last cycle (final solution) is automatically
printed out.
- i0 -
The twelfth data card consists of electrode voltage register (7
voltages per card, 4 cards needed). Twenty-eight voltages available,
labeled from NV_LT(or NV_LTI) = I to NV_LT(or NV_LTI) = 28.
The thirteenth data card consists of the boundary points of an electrode
system. The calculation is broken up into a series of lines consisting of
simply connected interim points. There maybe more than one of these lines
for each x-line. The boundary points are specified by proceeding from the
top to the bottom and left to right, one boundary point per card.
NS = i the first and uppermost calculated point inside the region of
interest for each set of simply connected interim points
= 2 the last and lowermost calculated point inside the region of
interest for each simply connected set of interior points° In
case the axis of symmetry constitutes the boundary of the electrode
system as shownin Fig. i, the whole card specifying the last
calculated point for that x-line is not necessary for any point
= 0 inside the region of interest containing any information about
the boundary of the electrode system (excluding the two cases
above for which NS= i and 2).
ND(1)_ specify the zero normal derivative of the potential of thatI
ND(2)J point according to the direction as shown:
ND=2
ND=3 --_
ND = 4
ND=I
- Ii -
> o
There is a possibility that 1_To normal derivatives may be
zero at one point but not more° It is also possible to set
one derivative equal to zero and specify a potential on
the same boundary card.
indicates that the boundary point faces two different
potentials_ as shown below:
I
INVpLT1
NV_LT _ HNS
NXC
NYC
HEW
HNS
NV_LT
or that the normal derivative is zero to some prescribed
line given by the slope of XLSL _ 0 _ otherwise zero
x-line coordinate of the boundary point
y-line coordinate of the boundary point
represents the distance left or right from the boundary
point to the solid boundary (electrode) in percent of
mesh size (maximum = 1.0 - one whole mesh). The distance
to the right (Eas_) is positi'_e, whereas the distance to
the left (West) is negative)
same as HEW for up and down boundary. The distance up
(North) is positive, whereas the distance down (South)
i_ _egat i _,e
is the index number of the oltage register specifying
the voltage of the boundary point to the left or right
- 12 -
NV_LTI
NCHECK= i
sameas NV_LTfor the boundary point up or downwith
ND(3) _ 0 Note: In the case (NV_LT= NV_LTI) or
when the boundary point (up or down) is the only boundary
potential, it is not necessary to specify NV_LTIwith
ND(3) _ O In this case, it is sufficient to specify
NV_LTonly.
for the last boundary point. (This is important because
check is madeon the last data card if NCHECK= i in case
of no, the EXIT is called). For this card one must put
NXC= NXFand NYC= NYFeven if this requires a dummycard.
B. FORTRANCODINGFORM
The format of the Data Input Deck is shownon the next three pages.
C. DATAOUTPUT
The output consists of a plot shownin Fig. 2. The trajectories and
electrode boundaries are given to scale.
The Data Output print-out starts on page 23. The first three pages
consist of Data Input for the record. Every "read in" data card is
automatically printed-out with identification. Page 26 shows the in-
formation on zeroth cycle -- No space-charge-LaPlace solution. Iteration
No. = 45, indicating that 45 iterations were completed for calculating
the potential distribution, with point 731 (or x-line = 43, y-line = 17)
- 13 -
/f
- 17 -
o
r-_0
o
o
l
o,1
r_
displaying the largest error of _ = 25.78 [Note:
c a
2(A m x)
i
-I-
where
= (um+lAU max -max
l<i<N
and m + i is the last iteration number (N _ total No. of points). It
is not, therefore; the difference in the potential of the last two
iterations.] EPSIL_N = 0.01 is the given error in the Data Input to
compare with c The total length of the emitter circular arc in
inches is ARC : 0.13524 DELTA ARC LENGTH = 0.01424 is the arc in-
crement of each current tube (or the spacing between two adjacent
trajectories). The X,Y-EMITTER prints-out coordinates of the emitter
given in the Data Input_ and X,Y-BEGIN TRAJ. gives the calculated be-
ginning trajectory coordinates. (Note: No. i is always the first pair
of coordinates given in Data Input (X,Y-EMITTER discussed above), like-
wise the last one located along the axis.
The expression X,Y-EQUIP_TENTIAL represents the (x_y) coordinates
in inches of the equipotential line through the given point NP_T(NP_TX,
NP_TY) specified by the Data Input, for the current density calculation.
- 18 -
The intercepts of two normals to the emitter on the equipotential line
for the current density calculation of the seventh current tube (number
shown in the last column) are XI, YI and X2, Y2. The normals are drawn
from the points of the seventh and the eighth beginning trajectory
coordinates. The arithmetic mean distance between the emitter surface
and the equipotential line used in the Child-Langmuir formula for calcu-
lating the current density of the seventh current tube is represented by DX.
The current density in amp/in 2 (or amp%unit area in the case of dif-
ferent dimensions used for unit length) is CD. The last-but-one column
displaying -- i indicates that the first x-line closest to the emitter
for the seventh or for both the seventh and the eighth trajectories is
less than one half of the mesh width away_ thus the trajectories have
not yet been initialized. (Here 0 indicates that the trajectories
have been initialized and from that point on the coordinates of the
trajectories are calculated from the potential distribution. This point
will be more apparent when the last cycle is discussed where the x-coordi-
nates are also shown°) The order of current tubes printed_ given by the
last column_ is given in order of machine calculation.
EMITTER CURRENT IN TUBES shows the total current in amps., (in two-
dimensional cases amp/in of emitter length out of paper) for each tube.
T_TKL EMrTTER CURRENT _ 0.0023 amps (for two-dimensional cases amp/in
of emitter length out of paper).
Page 27 gives similar information on CYCLE No. i. The only difference
from the previous page is RHTEST = 0.01825 and UTEST = 2034.5567. Here
RHTEST is the value of the RHS (right hand side of the matrix equation_
containing information on space-charge density) at the point KRH(KRHX, KRHY)
- 19 -
specified in the Data Input_ and UTESTis the value of the potential at
the point KRH. The information on the emitter coordinates and the be_
ginning trajectory coordinates shownfor the previous cycle are not given
because they are identical. The rest of the page contains information
discussed in the previous cycle. Page28shows similar information for
CYCLENo. 2. Page29 starts the information for the final solution.
The print-out of the previous cycles is given primarily for checking
purposes. Namely, RTESTmust increase from cycle to cycle and must
approach an asymptotic value if the number of cycles has been allowed
to increase indefinitely (in other words, the difference between two
following cycles must be decreasing). Likewise, the indicated ERROR
must be decreasing from cycle to cycle.
Next, the information on pages 29-31 is the U-FIELD of LAST
CYCLE_ (discrete potential value for each point through the region of
interest given in Fig. i). The first column indicates the x-line number_
the next 8 columns represent the y-line number, thus defining every point
in the region of interest. Columnsi0 to 17 correspond to the respective
potential values for each point given by x-line, y-line (e.g._ the
potential of the point given by x-line = 8 and y-line = 6 is 1759.447 volts.)
The X,Y C_DINATES _F EQUIP_ENTIALLINES shownon pages 31-32 are
the (x,y) coordinates in inches for a given equipotential, starting with
the potential specified by the Data Input VAT = 2000.0 and continued by
an increment given by SIZE = 500.0 until final potential given by VBT
= 500.0 is reached. The order of print-out of the coordinates is in
order of machine calculation.
- 20 -
The next information given on page 32 is the coordinates of the
equipotential line for the current density (X,Y-EQUIP_TENTIAL)calcula-
tion. Then the current density for the current tubes (7, 8, 9, and i0)
are printed; this could be calculated at the station shownby X = 0.01
(for the rest of the beginning trajectory, x-coordinates sre greater
than X = 0.01 and thus they could not yet be initialized). Then for
each x-line (e.g., X = 0.01) the y-coordinate of the initilized trajec-
tories No. 9 and No. i0 are given. (Notice 0 above the statement
X = 0.01 in the last-but- one column for the current density calculation
for the current tube 9 and i0 and -i for the tube 7 and 8%indicating
that trajectories 7 and 8 will be initialized again on the next x-line
because the distance from the emitter to the x-line was less than one
half of a meshsize.)
The columns VX and VY correspond to the x- and y-velocities of the
ions. Pages 33 to 42 show the rest of the (x,y) coordinates of the
trajectories and their respective x- and y-velocities. The right hand
side (RHS) of the matrix equation is shownon pages _2 to 45 for each
point. This print-out occurs because of the IX_ > 0 specification given
in _ata Input. From this RHSdistribution, the current density profile
in the beamcan be obtained for any desired x-line location. For axially
symmetric geometries we have
Pms = rh2VX
- 21 -
Thus_ knowing RHS_r_ h_ and VX it is easy to calculate J
for two-dimensional geometries we have
Similarly,
RHS = h2 _JVX
The last information on page 45 contains the total current distribution
in each current tube at the emitter and finally the total emitter
current.
- 22 -
DATA OUTPUT PRINT-OUT BY THE COMPUTER
DEFLECTING PLATES FOR ION ENGINE NF).I
NASA-LEWIS FOR F. KAVANA(,H/S. JF}NES
NXF NYF NEM NTJ NDI M NRL NUL NURLNCODR IDEC NI?_ _CD
55 17 8 10 _ 2 45 45 0 -I 0 14
IXONSPANNPOTXNPOTY Y_S
1 13 5 17 0.0
K_TN KRTX KRTY KRTX
1 2 17
VAT VBT
ZCCO.OCO0 50C.eOOO
HGH XLOW
-0. 0.0800
AXX BXX
0.2800 C._203
RO
O.
EPSNOT
KRTY KRTX KRTY
.88540E-II.95790E
SIZE VA VB VC
500._090 210C.000_ -0. 8.0300
4SL XLSL VD
-0. -C. 25.3003 _
CXX DXX XR
0.5400 0.5400 0.980_
_PSILON XEMIT MESH SIZE - H
C.010_5000 0.13999Q99 0.91300300
XQM ATOM VTH VTHX
08.13299E C3. . .
CATHODE ConRnINATES
0.0600 0.0449 0.9500 L.C520 0.94C3 9._520,
0.0250 0._809 O.Ol¢O C.120O V.236_ ].123C
0.0020 0.1400 -_. C.l_O_
-0PRINT-OUT OF CYCLE NO.
-0 -O -0 -0 -0 -C' -3 -0 -_
VOLT-1
2100.0000
1400.0C00lO0.OCO0
-0-
-2 -3 -4 -5 -6
C. 9. 50C.3303 2_30.99C, 3 I_3].D)OZ
1200.0003 1000.0000 80C.OOGO 690.3003 40].0300
50.0003 -?. -L. -3. -].-0. -O. -_. -j. -3.
I000
CO00
£000
CO00
0000
2000
tOO0
COCO
lbO0
leO0
ICO0
1230
C300
Z30G
2300i000
1200
1200
1200
1200
1200
1200
BDUNDARY POINTS OF
2 12-0.I00 0.200
2 13-(]. 400-0.
2 14-0. 650-_].
2 15-C. 800-?.
2 16-0. 950-C.
2 I?-I.OOC-Q.
3 IO-C.15L, 0.300
3 II-C.700 -r_.
4 9-6.500 0.700
5 8-C. 75C t.80 n
6 7-0.90C _. F_O0
7 I-S. -9.
7 2-0. -0.
7 3-0. -C.7 4-C. -I.50S
7 6-C. 70!7 0.5'3.,')8 I-C. -e.
9 I-0. -C.
10 I-C. -'i.
11 l-O. -C.
12 I-(Z,. -9.
13 l-C. -S.
ELECTRODE SHAPE
I -3 -0
i -_ -C
I -L -C
t -0 -0
I -C -6
I -_ -0
I -u -0
i -v -O
I -_ -O
I -0 -C
I -C -C
I -C -C
1 -_ -C
I .... C
1 -J -0I -0 -0
I -C -0
I -C -C
7 -& -C
9 -0 -0
ii -_ -C
13 -_ -0
08/02/85
KRHX KRHY
2 17
VTHY
-7
I007.33002CC. 00]
--b.
23 -
1200
1200
1200
COO0
CO00
CO00
ODOU
CtOO
CO00
0000
CO00
CO00
I000
I000
lO00
lOOO
I000
I000
lOOO
1200
CO00
OCO0
CO00COO0
O000
0_00
CO00
CCOO
COOO
1200
12001200
1200
OCO0
0000
CO00
CO00
CO00
0000
0000
CO00
ICO0
15.30t:OG
leO0
ICO0
1200
6900
C'O00
CC,OO
CC,OC
COO0
0000
C(;O0CO00
1200
i200
1200
1200
14 I-3. -3.
15 i-0. -0.
16 i I.OO0-C.
16 2 1. 000-0.
16 3 l. O0]-O.
16 4 i. 000-0.
16 5 1.O00-D.
16 6 1.00]-3.
16 7 1.003-3.
16 8 1.000-3.
16 9 1.000-3.
16 I0 I.O00-C,
17 ii-0, 1,309
18 II-0, 1.000
19 ii-0. 1,000
20 II-C. 1.000
21 ii-6, 1,009
22 Ii-0, 1,000
23 II-C. 1.000
24 i-i.000-$.
24 2- I. 00:3-3,
24 3- i, OC!O-C,
24 4-I.000-0.24 5-I.003-9.
24 6- I. 00'7-S.24 7-I.000-C.
24 8-i, 00£_-0,
24 9-1,000-9,
24 IC-l, 000-0,
25 I-0, -0,
26 l-d. -9.27 I-[. -C'.
28 I 1,000-0,
28 2 I,OOC-O,
28 3 I. 000-9.
28 4 I. OOC-O.
28 5 I. 000-0.
28 6 I. 000-0.28 7 I.OOC-O.
28 8 I.OOC-?.
28 9 I. 006-0.
29 IO-C. l. OOO
33 lO-C. l. OOC
31 IO-C, 1,009
32 IO-G. I.C99
53 lO-C, I, C_03
B4 l-l. O00-O.
34 2-I,000-0,
34 3-I,000-0,
34 4-I, OOC-O,
34 5-I. O00-C.
34. 6-I. OOO-3.
34 7-1,000-0,
34 8-I.000-0.
34 9-I,000-0,
35 l-C. -_.
36 I-0. -n.
37 I-0. -9.
38 I-0, -C,
2 --L --_
2 -0 -0
2 -3 -C
2 -C -C
2 -C' -0
2 -0 -0
2 -£, -O
2 -_ -O
2 -L -C
2 -{; -0
2 -0 -0
2 -U -0
2 -5 -0
2 -C -0
2 -0 -0
2 -<, -0
2 -_ -G2 -r -0
2 -_. -0
2 -u -C
2 -0 -0
2 -C -C
2 -_ -0
2 -C -O
2 -C -0
2 -b "-0
2 -_ -,9
2 -L -C
2 -0 -0
2 -'L -C
2 -t -C3 -. -0
5 -C: -0
3 -L -0
3 -C -0
3 -O -0
3 -[ -0
3 -C -0
3 -,.', -G
3 -C -0
3 -C -0
3 -C -0
3 -C -C
3 -_.' -0
3 -0 -0
3 -C -03 -C -_
3 -C -0
3 -0 -C
3 -0 -0
3 -0 -03 -" -03 -O -O
3 -V -C'
3 -U -03 -C, -0
3 -C -0
3 -0 -0
3 -0 -C
- 24 -
1200 39 I-0. -0.1200 40 I-0. -¢.1200 41 I-C. -0.
1200 42 1-6. -0.1200 43 I-0. -0.LZO0 44 i-0. -n.
L200 45 I-0. -3.
1230 46 i-0. -C.
1200 47 I-0. -0,
1200 48 I-0. -0.
1200 49 I-G° -0,
1200 50 I-0. -2.
1200 51 i-0. -O.
1200 52 I-0. -0.
1200 53 1-O. -3.
1200 54 I-C. -9.
1200 55 I l. 000-0.
C'003 55 2 1.009-0.
CCO0 55 3 I.OGO-C.
bOO0 55 4 1.00<-9.
GO00 55 5 I. 000-0.
CO00 55 6 i. O00-C.
CO00 55 7 1.000-0.
CO00 55 8 l. OOv-?.
COO0 55 9 1 • 00( -.".CGO0 55 i0 1.00C-9.
CC'O0 55 II I.OOG-_.
¢C00 55 12 I.O00-C.
0000 55 13 I. CCO-_.
6000 55 14 i. OO_-C.
IGO0 55 15 I.CO0-C.
GO00 55 I6 I.O00-O.
2600 55 I7 I.ODG-[.
TW
3 -0 -0
3 -U -0
3 -c -0
3 -O -0
3 -0 -0
3 -0 -0
3 -C -0
5 -G -0
3 -G -0
3 -6 -C3 -C -0
3 -6 -_
3 -0 -0
3 --3 -O
3 -_ -03 -C -C4 -0 -0
4 -b -0
4 -C -C
4 -C -C
4 -C, -04 -C -C
4 -C -0
4 -0 -C4 -0 -0
4 -t -0
4 -_" -_
4 -C -0
4 -C -0
4 -C -O
4 -_ -C
4 -C -0
4 -_ I
IS ENDS OAT_ CARDS
- 25 -
'_3
00
r)
J
N
Z
I-- Z
.d ,.J _t"
W ILl ,--I
Z __ Z
_' _ .J
_ Q tu
7 w _ _
1,- r,_ j,m _ X
,4-,,,-i
A
r;
<)¢M,.-4
r_
,+'3
g
i'M
f)
N,0
O
4"
('%1
gom
g
_gO,,._
OO
O',OO
OO
O,
c_
w
C,
b
w_
,-=l
AJ
•,o ¢_
I I I I
- 26 -
h-
,:1"
I
h
I
cO
,,,4
O"
II
N_
J_N
Zll
_00_
,.//
4
0'q)
0
g
Inaot_
(%1
_Ln _n
0
_. _'Ju') _0
uJ _.I...- LU
n,"n."ILl
z_"
Z
II 2"
I-- (3
uJ I--
ku
i-q
'_e_° ___ c')
c-) 1_
1-.- d-
7_g
_g
c_ t-)
gg
_g
O0• •
O0
Ln
h- a30 _¢_ _'_ P.- _0 L_ n'_ -_1- (',.J _'t_ t_i --.I
I I I I
I I I I I I I I I
r,_C =) _ p,. L_ C_ OD _ l...- -4k O_
C_CIO • • • • • • • • •
_ II II II II II II I| II
,0
g_g ,;'
N2g_• • • fe_
if.3 ¢-..i 0 ,-0
0o0 I
• • eft4
I I
,_ ,_ •
I I
I I ! I I
,0 _t 0,1 4- _
O000C_II II II II
I I !
-××--
! ! !
_NNN_
,, . ,,
I I I
g gg..,_0
I
...J 4"
_ ¢%1 _- ,-I !
OOC.,O0000000r_C_
I I I I I I_j uj m,I LIJ LL _ LU _ LL_ U._ U.l _A._UJ
Ite IIe I/ l; ,r
C) O0000000000C_I I I ! !
_ _ L/'_ _#- I._ UJ _U ,ll UJ LU U.a U_ UJ _J U.& UJ U_ _J
<_ . . e_'_...wO0¢."_'_.-41'--.,41".-,00_#'CO¢_"_u.; 0 0 0 4" ,,t ,,t _" ,,t ,,t" .,t .,t" _ _n _n _n _n ,0
II II II tl II II II II II II II
X _-mX _X X XXXXXXXXX_
('i
h,
CI
o
-0
r_C)
g
_'_ _0
ILUW
_J
f_o I
t_
c'_ o _'_
ua ua _'_
r..- 0', ,-,
I,.- 0, o
u'_ e,j1%1,-..4
LU • •"_00
I" 0 0 L._
_ e¢'_ cr, I.-
_Ollg
- 27 -
w
I,-
,r30
Z0
1.1,,I
L] I,/1
I"
LP, _J._% ,-4
w
4) o ¸,
I I
ILL;4-
4"r
!
2.,ou_fxl
,.n
4-
I
,.t"
I
LUi_-
0 _
(10ur_
g
'4"
,,t ,ID
I IuJ LIJ_n r_
oO ..-_,41"0',
gg
,-_J
U.I I._ ,-I
I,-- Z
Z _
m ,,1" _
:7 I I
:::,4",,'1"1'--
c,c_ _ {'_ L_er" t_l_- ¢" ,.o .'_ t-- t'-- I-.- ,4"/o ,or-- eqo, eoco _-- c,4 ¢xJ u'_ c,_u_
• • ! • • o o o o • • • • • • • • • • • o , • • • • , • • • • o • • • • • • • • • • • • • • • • • •
,-:o° ........... ............ _ .......... • ,_ ..... .I: "_ "• • • • • • • * , * * • • • • • • • • • * • • • • * • • • • • • • • • • • • • * • • • • • • • • • •
• • • • , • • • • • • • • • • • • • • • _ • • • • • • • • • • • • • • • • • • , . • • • • • • • • •
4"
- 29 -
• • • , . • • • • • • , • * • o • • • • • • • • ° • • • • * • • • • • • • • • • * * • • * • • • • * • • * • • • • • •
• • • • • • • • • • • • • • • • • • • • • • • • • • • • * • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
30 -
et_ _ ,..,_ u,_ _ _£_ c,, e,l (3_ coo, c'._ c,_ ,...4,..4 _.. _j,, coo ¢_ 4-4- re, _ ._ t_./r ct ._ '._
• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
e_
g0
_2
Z
C')
:
0
.0
A
g
Ixl
o
eo
- 31 -
,_ee,o,-4
gg,...i N
e.-4"
Ln :'4
orb
r,* 4"
c_ ¢-.
r)( _, h- _0 _ o
,0,,I"
or) I I
N e4 _ ¢M
c, ooo
I I ! I
_-- A WLU UJ 'JJ
OO r'- _D ,_ ,t
'O * * * *
. . - ,O1000_l" _ II II II
OO L) _.J L) U
n4NN",DO0
I I ILU UJ _S
I_ m- "0
O r'J O _ O O O
II II II
I
4" 4" 4" 4" _ •
OOOOO_
LU LU _U
,'-, C"s ,-$ _C% C_ 0 .'%
• , / I I I !_'*Og ..... , i , I ,lu I UJ / lUj/ /LU LU LU LU . _: LU UJ LIJ lU _"_ "_ C_ _ III Iu _ _ _ IU _ _ O
_ m _r uj Lu w uj x o o o o _ o a, m N N LU..U '-u X O () O O '-)-'_ _ N m _ _ X O O O _
000 C) 0
000 l" I ' , I , I , //
....... _,_ o _., ._........ =_-• * otM_n,t
.... )- )- )- C-_; ; g g dd g g c ",)- )" ..... oooo g O O O O C_...... ggl_d
I I
4r _ _lr _f
OOr}OO<._OOC_OL)_J _)C. OO(JOO -- O_ In , II II O
°°°°°°3°°ooo_oo°_°°°oo •••OC) OOO
_u u_ uJ
_DD"D'_DDD'-)DD'9-_DDDDDD _ II II .
.. ,,o),( )< _ 0
,,_ ,,.,+ ,,-+ (_
I.L_ J.I uJ
_; ,,
_0
.%
u_
m)
,X
II
X
- _2 -
5 0.908814E-01
6 0.I05282E-00
7 0.I18741E-00
8 9.131176E-00
9 O. L42816E-O010 0.154537E-00
XI=.559E-OI X2=.520E-0I YI=.79BE-01
Xl=.520E-01 X2=.48bE-01 YI=.913E-01
X= 0.04000 NO. Y
1 _.2 O.
3 0.641055E-01
4 0,819782E-01
5 0,967159E-01
6 0.I09439E-03
7 0.121900E-03
8 0.133435E-03
g O.14_IIIE-O0
IO 0.155106E-03
XI=.597E-OI X2:.559E-OI YL=.656E-ul
Xl=.559E-OI X2=.52OE-OI YI=.793E-OI
X= 0.05000 NO. Y
I 0.
2 0.541993E-013 0.736950E-01
4 0.889451E-01
5 0. I019IbE-00
6 0.I13256E-03
7 0.12_808E-0_
8 0, I35519E-00
9 0.145325E-00
I0 0.L55642E-00
XI:.597E-OI
X= 0.06000
Xl=.633E-OI
X= 0.07000
X= 0.08000
X2=.559F-01 YI=.656E-EI
NO. Y
I 0.
2 0.659549E-61
3 0.816731E-Ol
4 0.948744E-CI
5 0. I06558E-_0
6 0. I16755E-00
7 O,127486E-GO
8 0.137442E-00
9 0. I_6458E-00
I0 3.156144E-00
X2=.Sg7E-OI YI=,488E-OI
NO. Y
I 0.585000E-012 O.751146E-GI
3 0.879915E-CI4 O.IO0019E-OD
5 0.II0714E-00
6 0.I19953E-00
7 0.129946E-00
8 0.139213E-00
9 0.147511E-00
i0 3.I56b09E-_3
N0. Y
I 0.697770E-01
2 0.817708E-0I
0.631387E 34 0.396732E 040.870459E 04 0.380850E 04
0.102586E 35 0.3_0038E 04
_.I13439E 35 0.258181E 04
0.123555E 35 3.151778E 04
0,124044E 05 0.724668E 03
Y2=.913E-31DX=.255E-O1CD=O.1151E-O1 -I
Y2=.lO3E-_O DX=.297E-OI CD=O,SI32E-02 0
VX VY
I.OO000DE-04 O.
1.000003E-34 9.
0.263289E 34 0.2_9603E 04
3.72_4_5E 34 0.55522bE 04
0.103477E 05 0.57537bE 04
3.123633E 35 0.494791E 04
0.136814E 05 0.4t6iB3E 04
3.1_5942E 35 0.317650E 04
D.I51921E 05 0.191169E 04
0.154858E 05 0.850775E 03
Y2=.793E-D1 DX=.199E-51 CD=0.2048E-01 -1
Y2=.913E-D1DX=.255E-Ol CD=O.1151E-O1 0
VX VY
1.000003E-34 O.
0.322731E 34 0.379355E 04
3.838487E 34 0.834363E 04
0.120775E 05 O.7BO924E 04
0.143159E 35 0.737212E 04
0.159155E 35 0.594438E 04
3.17309_E 35 0.476416E 04
0.177713E 05 0.356873E 04
O.IQ2733E 35 0.214941E C4
0.185225E 35 0.954749E 03
Y2:.Tg3E-_I DX=.I99E-DI CD:0.2048E-01
VX VY
1.000033E-34 0.
0.10142_E 35 O.II92BOE 05
3.143271E 35 0.130793E 05
D.165125E 35 0.914295E 04
D.181445E 35 J.TgQ633E 04
0.193960E 05 0.651262E 04
3.202_02_ 35 0.522155E 04
0.209070_ 35 0.396914E 04
0.213243E 35 J.233556E 04
0.215331E 35 3.134274E 04
Y2=.656E-DI DX=.II2E-0I C0=0.7223E-01
VX VY
0.122137E 35 3.177099E 05
0.171115E 35 0.I)3_38E 05
0.191970E 05 0.III025E 05
0.205232E 35 0.996212E 04
0.218189E 35 3.Sb1267t 04
3.227927E 35 3.b_7977E 04
0.234954E 35 0.554874E 040.243029E 05 D.438662E 04
0.243463E 35 0.247399E 04
3.245193E J5 _.i39987E 04
VX VY
0.187982_ 35 0.172622E 050.225195E 35 0,133383E 05
3
4
2
3
- 33 -
X _
X=
X=
X=
X=
O. 090OC
O. IOOGC
O. i I OCO
O. 12001
O. 130GC
3
4
5
6
?
8
0
I0
NO.
I2
3&
5
6
?
8
9
I0
I
2
5
6
?
8
9
I0
N0,
i
23
6
?
9
I0N0.
I
2
c
5
67
8
9
ICNO.
I
2
3
R
6
_.933111E-010.I0_543E-00
O.l14447E-gO0.122809E-000.132201E-C0O.140842E-500.I#8487£-00
9.157040E-50
Y
0.77_085E-CI
0.871033E-CI
0.979078E-_I
_.108554E-00
_.117807E-009.125525E-30_.134205E-009.I4233TE-00_.149389E-000.157438_-]0
Y
0.830877E-01
0.g15359E-01
9.I01934E-00
0. I12133E-60
O.12083BE-CD
0.1279416-09
_.13b1496-00
0.143707E-00
0.150221E-00
0.157808E-03Y
0.8751286-01
0.952948E-0I
0. I05486E-0]
0.I15334E-G0
_.1235746-C0
0.130136E-60_.13786BE-C0
0.14_9606-C0
9.1509886-G0
0.15B151E-00Y
0.913367E-019.985101E-LIO.IO_625E-GO9.I182016-C]
_.126043E-G_3.132125E-c)0.139433E-00
0.146104E-00
9,151&946-00
9.1584706-C0
Y
9.94&3976-61
C.I01258E-00
0.1113925-09
_.1207o3E-09
0.12B2655-05
0.13392_E-C3
3_
0.2354176 05
3.2445976 95
0.2534495 35
0.26096#E 05
0,2654405 35
0.279459E 95
0.27_257f 35
G.274677E 05
VX
9.249515E _50.2715B26 95
9.275197E 05
0.2809395 35
0.2871876 05
_.2929476 35
0.2970926 35
0.3002I_E _5
9.30243IE 35
3.3935946 05
VX
0.2987616 35
0.3123856 35
0.31208?6 35
3.3151336 05
0.3193815 35
_.323595£ 35
0.3256916 35
9.329029E 35
O.3597&OE 359.33169BE 35
VX3.34389_E 35
0.3504146 05
0.34579&E 35
0.34741_E 35
3.3#992_,E 35
0.352982£ _5
9.35499BE J5
9.35665B6 95
D.3579226 35
0,5986916 95
V×
0.3795516 95
3,385556£ 35
3.379017E 355.3776256 05
0.3785326 35
0.3805B16 05
0.381799E _5
0.3B278_E U5%,.3836576 J5
0.384262E 35Vx
3.415164E 353.#181746 35
0.409291_ _5
_._956776 35
C.4952_36 05
D.436213_ 35
9.I15329E 05
0.13_335t 05
D.898992E C4
0.72771_E 04
0.575972E 04
_.422853E 04
0.2568765 04
0.I1398Bt 04
VY
0.151254E 05
0.1315266 05
0.I18_81E C5
0.I3o529E 05
_.9176896 G4
3.7%3302E 04
0.5_6823E C40._B0259E 04
0.2524436 040.116577t 04
VY
0.150126E 05
9.I2732_ _5
O.IISJ69E 05
0.1367636 05
0.920860E 04
j.7%6512E C40.598797E 043.4316145 04C.25456BE 04
0.I180&95 04
VY
0.I_9324£ 05
0.12181_E C5
0.I15903E 05
0.135359E 05
3.9155875 040.738593E C4
0.5B29516 040.4275_3E 04
0,253_435 04
0.118636[ 04
VY
3.12_955E Q5
O.Li4_20E 05O.III94?E 05
J.1324935 C5
0.8B8357_ 04
0.720732t 043.55990_5 04U.4185976 64
0.250324E D#
0.11_54_E 04
0.I17642E 05
].I)63295 35
0.IDo174_ 05
0.�BI618E C4
9._53808E 049.0)3575E 04
X=
X=
X=
X=
0.14000
0.15000
0.1600O
0o17000
0.18000
789
10NO.
123
56
789
1CNO.
123g
5S78
910
NO.123456789
10NO.
123656789
10NO.
I
2
3
4
5
6
7
8
9
0.160856E-03
_.I_7147E-00
O. 152344E-00
3. 158768E-03
Y
0.973126E-0I
9. I03584E-00O. I13807E-03
O. 123038E-00
_.130257E-00
O.135560E-GO
D.162160E-O0
0.148097E-00O.152961E-GO
O. 1 59049E-03
Y
D. 99096TE-01
O. I D5514E-O0
0.I15876E-00
O.125039E-O0
O.IB203OE-O0
O. 1 36985E-00
O° 143297E-00
O° I4896IE-00
0.153491E-00
0. I59315E-C0
Y
0. I00681E-00
0. I07049E-00
0. II7603E-00
0.I26778E-03
0. I33600E-03
0. I38270E-00
O. I44337E-GO
9. I_9748E-GO
0.153998E-00
0. I59569E-00
Y
0.I01781E-_0
O. I08205E-00
O. 1190i IE-03
_. I28269E-00
_.I3_983E-33
0.I39407E-00
0.165271E-C3
O.15D665E-CO
0.15_468E-$0
O. I59813E-GO
Y
0.1C2693E-00
3.I09043E-OD
O.12014IE-O0
0.I29534E-00
0.136202E-00
9.I43412E-03
O.146IlIE-OO
0.151125E-03
0.I54909E-00
3.159948E-00
0.606472E
D.607331E
0.637596E
D.698327E
VX
0.668398E
0.669075E3.637374E0.631156E
0.629267E3.629613E3.628872E0.628955E0.629279E
0.629563E
VX
0.679869E0.677426E0.662165E0.653394E0.450122E3.449610E
0.648427E
0.468129E
0.668272E0.648436E
VX0.507042E0.503669E0.482192E3.471647E0.467302E0.665292E
0.466707E
3.66qlq_E
0._66205E
0.664292EVX
D.518139E0.513353E
0.49639_3.485085E3.68332&E
0.679188E2.677515_
D.67687OE3.675911E
0.676976EVX
0.523983E3.523987E0.505977E3.695175E0.693266E
O.688965E
0.687216E
3.686522E
0.685552E0.686624E
35 3.550021E 0605 0.435520E 0405 0.254009E 0635 0.117976E 06
VYD5 0.136526E 05
05 0.957238E 0405 0.982768E 0405 0.922168E 06
_5 0.838069E 0605 0,657505E 0695 0.523731E 04
D5 0.388766E 0605 0.265953E 0405 0.117124E 06
V¥
35 0.889575E 0635 0.831038E 0635 0.877794E 06D5 0.867716E 0605 3.751757E 0405 0.613282E 0435 0.692131E 0605 0.359155E 06D5 0.236614E 0635 0.116207E 06
VY95 0.676019E 04
35 0.659739E 0435 0.752850E 0435 3.75_780E 0635 0.o87850E 0605 0.553110_ 06
95 0.457266E 0635 0.3_80_1E 0695 0.220254E O#35 J.II5433E 04
VY
35 0.453477c 0435 0.533387E 0435 3.625250E 04
35 0.656310E 04
35 0.623377E 0635 0.511676£ 06D5 0.422252E 04
35 0.327265E 06
35 0.216546E 04
35 0°II4964E 06
VY
35 0.288636E 0635 0.353_63E 0635 0.537802E 0405 J.57387#E 0605 0.550223E 0635 0.451474E 0405 0.388884E 0495 0.337969E 0435 3.2)8319E 0605 -0.114861E 04
35
X _
X=
X=
X=
X=
X=
O. 19060
0.20000
O. 2 IOGZ
O. 2200C
0.230u0
0.24000
NO.
I
2
3
5
5
7
9
NO.
I
2
3
4
5
6
7
9
IC
NO.
I
2
4
5
6
7
9
tC
N3.
I
2
4
6
7
R
9
Ir
NO.
I
?
3
6
7
8
9
NO.
1
2
Y
0. I02916E-00
0.139626E-C0
0.12103oE-00
O.130598E-]J
n. IBT272E-GD
9.141298E-03
O.146872E-O0
0.151735E-00
O.155326E-GD
9.15971_E-79
Y
0.I03107E-03
9.11OOOIE-C9
0.121730E-03
0.131480E-00
0.138200L-C0
0.[42075E-00
0.I_75o2E-C3
9.152396E-6D
n.155725E-C_
9.159481E-[3
Y
O.IJ30996-GO
C.I13203E-03
_.I22252E-OJ
9.132190h-V9
m,158984_-OD
_.lJ5111E-¢f
Y
0.102916E-03
n.l13247E-<S
3.122625E-_ S0,13273_E-_3
n.1396256-C0
0.1:3294E-C0
_.14_740E-G)
O.153349E-L]
_.1564_7E-03
5.159315E-6_
Y
9.192576E-C3
0.II0163E-09
_.1228bBb-3J
O.1331_E-CD
9.1_JIITE-_ D
0.I_3790E-00
0.I_92)3E-00
_.153828E-_
3.156858E-:3
O.158782E-GD
Y
0.I02112E-09
n. IJg975E-{ 3
9.123001E-03
36
VX
3.527391_
_.525816E
0.512550E
0.502626E
_.497_53_
3._95_2_
0._940_4E
?.493351E
_._93435_
D.4934S5E
V×
2.529386E
$.52S886E
3.517123E
_.5C8105E
9.5_1972£
3.503141E
].4_B_ggE
0.40773D_
3.697S1_E
D._9793_E
VX
D.530311E
j.53_619E
O.51999TE
0.5_5617E
3.53_555e
3.SDI25_E
5.50035_z
7.5C9445_
t.5J]555E
V_<
0.539981E
_.571_73E
".5216_E
3.51423]E
0.508737_
3.5959_9E
_.552193E
3.573_93_
0.59[19cE
,,.591_13!_
V×
D.5277E5E
0.533321E
C.522795E
_.515927_D.511392E
0.5077I_E
O.5D2997E
0.5D16_=
D.5_i_536
D.5022_IEVX
0.525A96_
D.529462i
0.522751_
VY
35 3.156341E 04
35 _.2571_9E O_
35 0._33189E 04
05 O.4B7841E 04
35 U.496747E O_
35 J._IIT52E 04
05 0.3572525 04
35 3.290425k 04
05 D.23DTB2E O_
35 -0.I15134h O#
VY
35 3._9992E 03
35 D.311339E O_
05 0._3658t O_
35 0.429871E O_
D5 O.35IR26E C4
35 0.327884E 06
D5 D.275119_ 6#
35 _.19488b_ 04
D5 -0.I15_22E G4
VY
95 -0.527079E 03
35 J.624550L _3
95 0.23C243E C_
35 0.320271E 04
35 0.356629_ 04
35 3.3394_9_ 04
35 3.297259t 04
35 0.25C73oh C4
55 ).1_99065 C#
35 -3.116399t £4
VY
95 -0.1%2300t 04
35 -J.IBI681E 33
35 3.15_187£ 0435 0.2%2575E 04
05 0.2Bglg_E 04
35 j.245746f f4
35 J.257427C 04
35 D.2%5323_ 04
35 9.186552c 64
35 -J. I171_,2_ C4
V?
35 -).216599E 04
35 -_.75_301_ 03
35 j.95932_£ 63
35 3.173730E 04
35 S.21_231E 04
35 _.155935E 04
35 3.237918E O_35 _.2_3865E G4
25 0.185720E 04
35 -3.I17371h 04
VY
D5 -3.27283_ 04
_5 -0.123872E Ok
D5 3._315926 03
X _
X=
X=
X=
X=
56
8
9
IO0,250C0 NO.
]
?
.r
4
5
E
7
8
9
0.260C0 NO,
I
2
6
7
8
9
O. 270C0 NO.
]
2
3
5
6
7
9
O. 2 ROOi] NO.
I
2
4
5
5
7
q
IO
0.290GD NO.I
2
3
4
5
6
7
O. 133421E-0_9. 1434oJE-09O. 1439_3E-0C)O. 149506E-030.[54283E-C.3_. 15722_E-_
O. I58548E-00
Y
3. I_I546E-C0
?. 13970e.E-_
9. [23040E-G3
m. I 33590E-C0
_. 140666E-C0
3. I4qO33E-CUO. 1 49831 E-COC".15471 'DE-C 3
"_j. 157585E-C=0
3. tS_3lOE-t3Y
3.130886E-: 3O.109359E-L):]_.122998E-C_O. 133065E-0,9
m. 149762£-:" 3O.l_40G3_-_J3.150C IOE-_ ]
0.155087E-C3
3.157923 E-_9.15BO58E-63
YO. 190131E-J]
?. l Z_945E-L i_C. i22879E-'_S'. 133559E-CO3. 140772t-03_. 143884E-b_9.15_ICBE-* ?
r.155395E-(3O. 15B2_2E-L3_. 157779E-v ;'
Yq. 992695[-V1
n. IS8455E--,3_. 122682E->_
q. 15_573_-', DO. t40698E-COn. 1436_0E-03
O. I50128E-33n. I55637E-C ]
O. 158515E-C3
_. 157468E-09
Y9. _82884E-I i
n. IOTBTOE-C 3
9. 122431_-_3_. 133397E-_0
].143520E-c]
0.143365E-00
O. 153067E-n3
D.51713' ,E3.512_53ED.5Ogb4IE3.53519cE3.5D_787=3.573955E
vX
].52490RE
3.52B946E
3.523027E
2.5]821_E
0.514693E
3.512257E
0.509109E3.505955E
3.5D5586_
3.595639EVX
0.52482eES.5PSS£DE3. 5232"_&=D.51994_EL_.SI6153Ej. SI4327E
._.512459E
D. 559447_
.,.5"_561E
_. 53_50_,E
V X
C.525433EZ,.5291 lg_-
D. 5272_#_3.51_z,E
C. 51 _3_
].512544E3.539:23_-
3.53R577_VX
0.525365'7
5.52_3v52D.52276Z_
3.517922_3.51_552E
0.5123_oE2.5:' 9_.59E:
3.5372225
2o 50,67EI_i
J.5C558_VX
7. 526603_]
0.52918eE
D.52175_Z9.516237_
3.51222B_0.5094_gE3.52522CE
35 ].llB2C2L C,_-
35 ).1379_J_ :'435 O.BI5035L 0335 3.157542_ 04
_5 _.22370_ 04
35 J.I_651E 0405 -0. I17921L 04
VY
35 -D.321973E 04
35 -3. 153750E 04,
35 -0.238384E 02
35 O._llTZ_lt ,33 ,35 9.735698_ 03
35 3.998833E _;235 0.111990E C4
35 0.237357E 6435 0.178_37E 0435 -3.122t63E 04
VY35 -0.37C433E C4
35 -D.23C254E 04
35 -3.425127E 0335 O.171932E 03
35 0.251782E C3
35 -_.439118E 03
35 0.733760_ 63
35 _.ITbISIE (_4
35 ).154699E C4
05 -].133567E 04VY
35 -D.422774E 04
D5 -J.2379_4E 04D5 -0.SIBI5IE 0335 -0.231533_ 0335 -_.15C814E 0335 -C.SD9903E 03
35 ].333123E 0335 0.137922F 04
35 1.1_9251E 04
35 -3.150398E 04VY
35 -0.4_3189_ 04
D5 -_.2_L525_ C,435 -,]. t237_ 8£ 0435 -].65181_E b3
35 -O.OIISI4E 03
D5 -3. 128672E 0435 -0.131208E C3
35 J.I)8238E 04D5 0.13_324k 0435 -:'.155831E 04
vY
35 -9.5(,9979E 0435 -D.329739E 04
35 -O.17D626E 04
35 -J.l1584_E 04
35 -0.I2_850E 0435 -0.193420E 04
35 -G.517127E 03
- 37 -
X=
X=
X=
X=
X=
O. 30000
0.31000
0.3200'3
O. 33060
0.34000
O. 350C'_
8Q
i0
NO.
I
2
34
67
e9
tONO.
I
23
4
5
7
8
g
ICNO.
I
2
3
5
6
7
89
I
2
34
5
&?
R
9
IC
NO.
t2
4
F
6
?R
9
I?
NO.
_.I55837E-OD
0.158784E-09
0.157131E-03
Y
0.971780E-CI
0.I07203E-00
0.122023E-0_0.133118E-00
O.1402L7E-C3
0.1429IOE-00
0.I49923E-00
0.156021E-00
0.I59049E-000.156781E-00
Y
Q.gSQ300E-GI
O.IO6414E-G3
O.121540E-GO
0. I32722E-0SQ.139777_-C_
_.I_2309E-L_
O.t49697E-O0
O.156201E-J_
0.159314E-00
O.15542TE-uDY
_.945290E-01
O.I05593E-OD
9.120945E-G2
9.I32203E-0C
0.139206E-C9
C.141575E-00
0.1494C2E-C9
n,155379E-S3
0.I59579E-00
0.155070E-03
Y0.929637E-CI
O.IO_468E-J9
3.I23235E-00
0.1315506-00
0.138518E-C0
_.140729E- 3
O.I_9050E-LOO.t5555oE-O0O.159B45E-C90.155798E-09
Y0.912496E-01Q.IO3317E-303.119413_-S_
9.133799E-3]
_.137729E-00
0.139792E-C0
t.l#_658E-C_9.155731E-C!3
O,159888E-t9
0.155341E-00
Y
3.504315E 350.504083E 35
0.503064E 35VX
D.52511BE 350.528215E D5
0.520057E 353.513975E 353.53955#E 350.506563E 350.502312E 35
0.501439E 353.531683E 350.501145E 35
VX0.526455E 353.525153E 35D.517538E 350.511387E 350.5_6379E 353.533841E 35
0.509552E 050.499719E 35
_.499958_ 35
3.4994256 35
VX
D.521O&3E 353.5226D_E 35
3.514555E 353.507613E 35
3.5_292&E 350.5_973_E 353.499_52E 350.498075E 95
_.W98399£ 353._97779£ 05
VX
0.515419_ 35D.517[&2E D5
9.539633E 35
3.503483E 35
3.499305_ 35j.407397E 353.495952E 35
0.496259i 35
3.4954576 35
0.4_5963E 35VX
0.535293E 352.519817E 353.5D4472_ 35
3.49_99bE 350._g55745 05
_.493912E 359.49431_ 35
3.49375gE 350.493985E 95
0.493451E 35VX
0.961539E 03
O.IB3653E 04
-0.174355& 04
VY-9.619057E 04
-3.385300E 04
-0.222622E 04
-O.I?21IIE 04
-3.1B9588E 04-0.258340E 04
-0.916187E 030.9_5853E 033.1_2_56E 04
-0.176856E 04
VY-3.692083E 04
-9.4_6D56E 04
-0.278443E 04-0.233095E 04-0.257574£ 04
-0.33938B_ 04
-0.I_2191E 04
0.896017E C3
0.132446E 04-9.177739E 04
VY
-0.772702E 04-3.539124E 04-0,3356396 04
-0.295692E 04-J.318546E 04-0.39845SE 04
-0.153558_ 04
0.SB5903E 03
J.[323_16 04
-3.178744E 04VY
-9.6_6457E 04
-5.557437E 04-5.391134E 04
-0.355079E 04
-0.370946E 04-3.4%5903E 04
-3.lBb539E 04
0.871504E 03
0.1521951 04
-O.19U447E G4
VY
-0._997166 04
-D.615612E 04
-3.4_2378E C4
-9.437158£ 04
-0._13792h 04
-9.4B_223E 04
-9.23253DE 04
0.85_489E 03
-0.152177E 04
-O.IB2433E C_
VY
X--
X=
X=
X=
X=
I2
3456
89
IO0.360C0 Nn.
I
2
3
4
5
6
7
8
9
IO
0.37000 NO.
I
2
3
4
5
6
7
8
9
0.38000 NO.I
2
4
5
6
7
8
9
I?
0.390C0 NO.
I
2
3
4
5
7
8
9
IC
0. 40000 _!0.
I
2
3
O.ag_172E-OI
O.tG2066E-O0
9.118486E-_3
3.129935E-03
0.136857E-00
0.158780E-03
0.148235E-00
9.I56904E-Ob
0.159620E-00
0.I54969E-00
Y
D.87490IE-CI
0.I00728E-C,0
0.117462E-00
0.128983E-C0
D.IB5917E-CO
0.137707E-00
0.147788E-00
9.157076E-00
O.1593DOE-C3
0. I54591E-00
Y
0.854857E-GI
_.993138E-010.I16352E-00O. 127959E-O!?
O. I3_925E-03
_.I35585E-OD
O. I47322E-00
9. I57249E-00
9.159077E-03
9.I5_209E-_3
Y
3._3_155E-GI
0.97_324E-CI
_.I15162c-__.126875E-__.I33892E-JOO.135426E-D_
0.145840E-_9
0.157422E-6_
0.158803E-C9
9.153822E-0]
Y
_.812855E-CI
0.962903E-_i
_.II3905E-u3
0.125745E-00
n.132829E-O]
?. I ?4236E-_ $
9. 145346E-[ 3
9. 1575966-00
O. t58527E-t_0.153432E-50
Y
_.791011E-01
0.945928E-i)i
9.112591E-609.1245_DE-_D
0.497598E
0.59454tE
3.49931_E
3._9_145E
0.491638E
0.490211E
0.491215E
3._93833E0.491053E
0._90491_
VX
3.&99277E0.497995E
0.%93425E
_.489534E
3._8772S_0.48649#E
0.487959£
3.687643E
3._87997E0.487318E
VX0.4£3527E3.491982E0.4_80596
0._85056E
3.493824E
3.4_2711E0.48_41E3.484427E9.484731E
3._R4DBgE
VX
0.4775_46
0.4_5421E
3.4£3113_
3.48091_3.493391Z2.&79053E_.4RI38SE
0.4812TIE
0.491551E
O.4qO921E
VX
0._722_IE
0.4_1365E
J.4?8575_0.47715bE
_.47957_
_.475675_
3.47B29_E
3.4782_5&0.4785a2_
j._778g_EVX
3.4_7315_0.47679_E3.4v#527ED.47378_
05 -0,937983E O#35 -3.654588E 0405 -9.457985E 0435 -0.450_5IE 0405 -0.4#76096 0635 -0.512719E 0435 -u.214165E C4
35 C.8%6385E _3
05 -0. 132245F 04
35 -O.IB3966E 04Vy
35 -0.955753E 0405 -O.686614E 0635 -0.527789_ 04
35 -3.435758E 0435 -}.4129_9£ 0435 -0.555281E 04
35 -3.2231596 04.35 0.8%0557E 0335 -3.IB2337E 0435 -0.185153E 04
VY35 -0.996186E 0495 -0.713304E 0495 -0.552534E 04
35 -3.5129456 04
35 -0.4910_9E 0435 -3.551766E 0435 -9.2302196 04.
05 0.837523E 03
35 -0. 132415E 0435 -3.1B0187= 04
VY
95 -0.13C342E 05D5 -?.736122E O#
35 -0.592492 / 04
35 -/,.533619E 04.05 -3.53b970E 04
35 -,,.553517£ 04.
35 -0.2353825 04.
35 J._36429_ 03
35 -{.132454E 06
35 -0.136985E 04.VY
35 -3.1319476 0535 -_,. 756336E 04
35 -3.et_75IE 0435 -0.5_887b_ 04.35 -J.51360_E 04
35 -'i. 572,_89e 0435 -J.23933IE 04.35 3.836_51r 03
35 -J.t32z_25[: 0 _,35 -3. IB74.9_£ 04
VY
35 -0.133292£ C505 -0.774337E 04.
35 -9.bB5435h C4
3_ -0.559445E 04
39
X _
X=
X=
X=
X=
0.41000
0.42000
0.43000
0.44000
0.450C0
5
67
8
9
tO
NO.
t
2
3
4
5
6
7
8
9
I0
N q.
I
2
3
5
6
7
8
9
I0
NO.
I
2
4
5
6
7
B
9
i?
NO.I
2
3
5
6
7
8()
l0
NF).I
2
4
5
6
7
8
9,131740E-00
O, 135023E-00
O, 145842E-S0
9, I57772E-03I%_.,I58253E-00
O, I53038E-00
Y
O,768691E-GI
O. 9BO447E-OI
0,II12326-C_
9. 123388E-00
q. 133633E-00O. 1 31791E-00
O. 145330E-609. 1579_9E-00
O. 157971E-C0
n, 152642E-00
Y
_. 745963E-C_I
0,913507E-01
O. i09837E-0 _
O. 122177E-03
D,129511E-O0
n. 130544E-00
O. I_4812E-0_
n, 158128E-OJ
_, I57692E-CD
O, I52244E-00
Y
9. 722876E-01
9. 895157E-0I
O. I0841bE-O0
O. 120952E-0S
0.12B379E-CD
O. 129287E-DO
O. 144290E-00
7.158307E-093,157412E-00
S.151845E-33
Y
C. 699476E-01
')._78457E-01
9, I06977E-CD
9. I19719E-09
9.127241 E-Z!O
9. 128023E-00
?. 143765E-03
O, 158488E-0C
"),157132E-C 0O. 151445E-CD
Y
O. 675823E-0I
0.860465E-C I
O, I05526E-00
0,11848IE-C0O. 12bOQgE-OJ
O, 126755E-C 0
O, I43238E-C9
O, 158670E-GO
40 -
3,#73602E 35
2,472622E 35
D,475466E D5
0,475488E D5
0,475776E 35
3,475II2E 35
VX
0,46292&E 05
3,_72795E 35
J,47IOgTE J5
3,473863E 35
0,470902E 35
0._69937E 35
0,472968E _5
j,473C_#DE 35
_.473330E 35
0._72655E 35
VX
D,459295E 35
0._69175E 05
0,46_212E 05
_,46_418E 35
3.468623E D5
3.467665E 059.473845_ 953.#79955E 05
D,_7124bE 35
0.470562E D5
VX
J.4560_7E 35
3.465181E 35
0.465858E 35
0.465455E 35
0.466779E 053.465_25E 350.65913_E 35
O.469274E 35D.#69565E 35
3.468875E 35VX
3.4533_4E 353.4630R4E 35
J.45407_E 350.46495_E D5
0.4653626 350.464424E 35
0,467859E 35
0,468015E 35
0.468BORE J50.46751&E 35
VX0.4512796 350,461837E 353.462815E 359.4&39&5h 350.464415E 35
J.46348?E 35
3.46731BE 35
0.467189E 35
-O.520656= 04
-0.578#88E 04
-0.2%1694E C40.838472E 03
-O.I_23G8E 04
-j.187734E 04VY
-0.134343E 05-0.7905245 04
-O.b_9728E 64-0.55648#£ 04
-0,525509i 04
-0.583036E 04
-3.243596c C4
O.8%JT55E 63
-0.132104E 04-J.IS775IE 04
VY-3.135238E 05
-0.835089E 04
-0._$0166E 04
-0.5711096 0#-_.528593E 04-0.58599oE 04
-Q.244907E 04
0.8%3364E C3
-0.[31813E 04
-0.187592E 04
VY
-0.13o3655 C5
-0.817686E 04
-0.b571546 04
-0.573805_ 04
-3.530251E 04
-).5_7628_ 04-9.245782E C4C.8_6078E 03
-O.lBI438E G4
-0.187504E 04
VY
-0.136735_ 05
-0.SZS172E 04-9.b71513E 04
-3.574893_ 04
-_.530746E 04
-_.5_S129E 04
-3.2%6303E G4
9.8%8695E u3
-2.1309926 C4
-).IB6935E 04VY
-9.137236h 05
-0.687132E 64
-0.073732E 04
-0.574671E 04
-0.530_04_ 04
-0.5B77041 04
-0.2%6524E 04
0.8510905 03
X Z
X=
X=
X=
X=
X=
0.46000
0.47000
0.48000
0.49000
0.50000
0.510CJ
9
NO.
I
2
34
5
6
7
B
9
I0ND.
I
2
3
¢
5
6
7
8
9
I0
NO.
1
2
3
4
5
6
7
8
9
IO
ND.
I
2
3
&
5
6"7
80
I?
NO.
1
2
A
5
5
7
R
c)
19
NO.
I
9.155853E-C0
O. 1510_bE-O0
Y
0.651975E-01
O. 842239E-01
9.1040695-00
9.1 17243E-03
O. 124958E-00
O. 125488E-009.1¢2710E-OD
0.I 58852E-00
9.155574E-GO
O. 153646E-00Y
O. &27979E-Of
O.82385¢E-OI
0.I02611E-6]
0.I160C8E-03
• 123819E-00
O. 124223E-OD0.142182E-C0
9.159035E-C0
O. 156297E-00O. 150248E-03
Y
q.603890E- 1
9. 805589E-01
O. I01158E-00
n.[l%779£_U3
_. 122685E-_ 2
O. 122962E-00O. l¢Ib55E-C3
O. i59219E-6 39. I55G2IE-O]
n. 14985 1E-COY
m. 579761_-C 1
3. 785912E-CI
O. 997121E-01
9. I13557E-C]9.121556E-53
9.121707E-L_9
O. 14113OE-t,O
?. 159432E-.9_.155747E-C3
O. i49455E-d5
Y
O. 555036E-? I?. 758483E-CI
Q. 9827&7E-L 1
n. I125_+5E-2C
_. 1234BbE-_]
n.123461E-C3¢. 1436L, 75-C3
O. 159585E-CO
2. I_5474E--_I_
t'.I_9061E-0[
Y
?.531559E-01
O.¢674elE
G.465785E
VX
0.44981¢E
0.¢635956
D.¢b208_E
3.¢63419E
0.463931E
3.¢b2999E
O.466608E3._66793E
9.¢G7083E
0.4_385E
V×
3.4¢8861E
0.459908E
0.461893E
3.4633¢qE
0.46390_E0.462977E
0.466631E
0.46682_E0.¢67113E
0._65415_
VX
3.¢_859_E
0.¢59_32£
D.#62197E
3._537_5ED.464392E
0.463403E
0.467077E
D._67260_
3.4675516
0.¢66865E
V×
3.¢GDBB4E0._629996
3.¢645o6E
3.¢651OLE
3.¢5425_2
9.46795563.468121E
5.¢5_415ED.¢6772_E
VX
3.4&962BE
5.461¢79E
D.¢6#265£3.465B71E
_.465457_
0.¢655_2E9.469182E
0.46935£E3.4596_IE
VX
0.451059g
J5 -3.13C485E C4
D5 -O.196522E C4
VY
35 -0.137657E 05
05 -J.8#41D36 04
35 -0.673908E 04
35 -O.573388E 04
]5 -0.5291816 C4
35 -0.SB6598E O_
05 -J.2¢O470E 04
35 0.853210_ 03
35 -0.129923h _4
35 -0.I_6078_ 04
V_
05 -0.137982E 05
35 -0.848220E G4
95 -9.6726¢2£ 0435 -0.511299E 0435 -9.527552E 04
35 -0.5_4991E 04
35 -0.2¢61896 04
35 3.855D21E 03
05 -0.129512E 04
35 -0.185613E 04
VY
35 -O.13BI87E 05
D5 -0.850056£ 04
35 -O.b_OS¢OE 04
35 -0.558620E 04
35 -0.525529£ 0435 -0.5929925 0435 -0.2&5747_ 04
35 0.856¢99£ 03
35 -J.12865_E 04
05 -0.185153E 04
VY
D5 -0.138324E 05
_5 -_.851290£ 04
95 -0.657285_ 04
35 -0.555581_ C4
35 -3.523232E C4
35 -i3.5_3712E C435 -J.245218E C435 0.857527E 0335 -G.127993E 04
35 -0.194731E 04
VY
35 -D.ID8411E 65
35 -2.8%8854£ 04
35 -0.653734E 04
35 -3.552438E 04
35 -6.52080_i 04
35 -3.578287E 04
D5 -0.2¢_678E 0435 5.858414E 8335 -_.127317E G4
95 -0.I_582E 04VY
05 -O.13U4_gE 05
- 41 -
++.+...._,.°+..°°..+.+++
• . • • • • , • • , • • • • • • • • • • • • • •
• • • • • • • . • • • • • • • • ° ° • • • • • •
• • • • . • • • • . • • • • • • . • • • • • • •
co ,_ c_ co co co c_
• • • • • • • • . • . • • • • • . • • . • • • •
0_0000 _00 00_0 00000 0000
m_
...........................I I I ! I ! I I I I I I I I I I ! I I I ! I ! I I
.. lle • • .i Ii+i .+ .._ggo_og_ og .... 3g ......... g_og ....
00000
I I I I i | I I I I I | I I I I ! I I I I | ! I I
0
_0 ,Q aD
ggdgggg_g g_,g_g,_g,_dg gdgJ, gdgg_'d
Iii+++i.+.++i..-i+....+.
O_O00,_O000_O0_O0_OcJ_)_O
g,
Im m o m m o m m o _r_ m (-_ m m c_ m m c-_ m m r_ u_ m o
g0 0
u_
< _ N 0 _J N 0 0 N 0 0 _I c) _ i_ o 0 N _} 0 N 0 u N (-_ 0
O4 ('%a N ,...4- o4 ,JO r_J• • e • • • • • • • • • • • • • • • • • • • • • • • • , • • • • ° o • , •
• • • • • • • • • • • • • • • • • • • • • • * lee • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • , • • •
_ ........................................... ; ..............0000000000000000000000000000000000000000000 00_00000000000
eeee,,,, • 00000000_0000000000_3Z_3_o_oooooo_g_g_Z_Z_Z_Z_Z_ZoZ ..................
g_..._ ............................
============================================================
. _-_ -
O_ ,-4_ .t_0 co_ cO r_
• • • • • • • * • • • • • • • • • • • • •
0 C) C, _ 0 ('_ .-_ 0 ',.._ _ e3 0 0 o ¢) 0 C, c_ ,:) c) -:)
o o o 0 0 0 ¢. o 0 0 _ ca 0 _ 0 0 c_ 0 0
OQO OOOo0_ 00000o00 _,_00
o_oO_oc)_oc*t)o_oooou%f_o0
I_u
o
I
o,/
0
¢--,
d"
,.-I
b-
I I
uJtu
r, N
r'_4-
O0
ooo4
Noo,-_oo_oo_oo,_,Jo_oo_oo._,..., ,.., .-, .-, .-, u.,ww_" _:LU
_Eo_ P,,, ','-_ ua
III. COMPUTERPROGRAMFOR SPECTRALRADIUSCALCULATION
(_-CATCUmT_O_)
The subroutines used for these calculations are:
i. MAIN_
Same as before, but it calls MATIN only.
2. MATIN
Calculates the largest eigenvalue.
3. MATRIX
Same as before.
4. 7090 PLATING R_UTINES (Fortran II) for the CalComp Plotter (Stanford
University Computation Center Library Program No. 157).
A. DATA INPUT
The Data Input for this calculation is the same as for the beam
analysis program with an additional card at the end shown on page 50 of
Data Output by arrow. This card indicates how many iterations (MIT = i00)
to perform and whether the print-out for each interation is required
(_,'R > 0).
- 46 -
h
B. DATA OUTPUT
The print-out of Data Output consists of the Data Input (pages 48 to 50)
and then the L_ and HIGH eigenvalues for the first two iterations. The
last two columns show the point numbers where the lowest and the highest
eigenvalue_ respectively, were found. At the end the square root mean
value of XR is given (page 51) o
- 47 -
DATA OUTPUT PRINT-OUT BY THE COMPUTER
DEFLECTING PLATES FOR ION ENGINE NO,I
NASA-LEWIS FOR F,KAVANAGHIS.JONES
NXF NYF NEM NIJ NDIM55 17 8 tO 3
08102165
NRL NUL NURLNCOOR IOEC N'FUL NCO KRHX KRHY
2 45 45 0 -1 0 14 2 17
1XONSPANNPOTXNPOTY _TAXS1 13 5 17
0o0
KRTN KRTX KRTY KRIX KRTY KRTX KRTY
VTHY
17VBT SIZE VA VB VC
50C.O000 500.0000 2100,0000 -0. 8,0000
XLOW HSL XLSL VD
C.O8CO -0. -C. 20.0000BXX CXX CXX XRC.3200 0.5400 6.5400 0.9804
EPSILON XEMIT MESH SIZE - H0.0100_000 0.13999999 0.01000000
EPSNOT XQM ATOM VTH VTHX
.88540E-II.g5790E 08.13290E 03. • •
I 2
VAT2C00.0000
HGH
--C=
AXX
C.28C0
RO
O.
CATHODE COORDINATES
G.C600 0.0440 0.0500 0.0520 0.0400 0.06200.0250 0.C800 0.0140 0.I000 0.0060 0.1200
0.0020 C.1400 -0, 0.1600
PRINT-OUT OF CYCLE NO.
-0 -0 -6 -0 -0 -0 -C -0 -0 -0
VOLT-I -2 -3
2100.0C00 C. O.
1400,0000 1200.0000 I000.0000
I00.0C00 5_.0000 -0.-0. -C. -0.
-4 -5 -6 -7
500.0000 2000.0000 1800.0000 1600.000080_.0000 600.0000 400.0000 200.0000-0, -0. -0. -0,
-0. -0. -0, -0.
BOUNDARY POINTS OF ELECTRODE SHAPE
1000
CO00
COO0
C000
CO00
2000ICO0
OCO0
10001000
I000
1230
0300
030023001000
12001200
1200
1200
12001200
1200
2 12-0.I00 0.200 I -0 -0
2 13-C.400-0. I -0 -0
2 14-C.650-0. 1 -0 -0
2 15-0. 800-0. 1 -0 -O2 16-G.950-0. I -0 -02 17-1.000-0o 1 -0 -0
3 IC-C. 150 0.300 I -0 -0
3 11-0.700-0. I -0 -04 9-(_.50C 0.700 I -0 -05 8-C.75e 0.800 1 -0 -06 7-0.900 0.800 1 -0 -0
7 l-C. -0. I -O -0
7 2-C. -0. I -0 -0
7 3-C. -0. I -0 -0
7 4-0, -I.000 1 -0 -0
7 6-(.,. 700 0.500 1 -0 -08 l-G. -0. I -0 -09 l-C. -0. I -0 -0
I0 l-G. -0. 7 -0 -O
I I I-G. -0. 9 -0 -012 1-O. -0. II -C -0
13 I-0. -0. 13 -0 -O14 l-G. -0. 2 -0 -0
48
12001200CCO0co00CO"JOeGO0C(.}O0GO000000OCO00000
I000I000I(_00I0001000I0001_001200CO00GO00CGO00000
GO00GO00CO00cO0000001200120012001200
CO00CO00CCO0
CO00CO00(.bOO(_CO0eGO0I000IOCOI000I000I0001200CO00CO00CO00(.,OOOGOOCGO00CO00COO0120012001200
L2001200
1200
15 I-0. -0.16 I l.COC-O.
16 2 I.COC-O.16 3, I.O00-O.16 4 I.OOC-O,16 5 I.OOC-O.16 6 I.OOO-C,16 7 I.000-0.
16 8 I.000-0.16 9 I.000-0.16 lO I.000-0.17 11-0. 1.0001B ll-C. l. O0019 ll-C. 1.00020 ll-C. 1.000
21 ll-G. 1.O0022 II-_. 1.00023 11-0. 1.00024 l-l.OCO-O.24 2-I. 000-0.24 3-I.00C-0.24 4-I,000-0.24 5-1.GOC-O.24 6-1.O00-C.24 7-I. OOC-O.24 8-I. 000-0.24 g-I.OOC-O.24 IO-l. OOC-O,25 I-0. -0.
26 I-0. -0.27 l-O. -C.28 I I.OOC-O.28 2 1. 000-0.28 3 I. 00C-0.28 4 I.COC-O.28 5 I. OOG-O.28 6 I. 000-0.28 7 I. OOC-O.28 8 1. 000-0.28 g I. 000-0.29 IC-C. 1.00030 IC-C. 1.000
31 IO-C. 1.00032 I0-0. 1.00033 lO-O. 1.0003t, I-I.OOG-O.34 2-1.OOC-O.34 3-I.000-0,34 4-I.000-0.34 5-I.00_-0.34 6-1.C00-0.34 7-I. OOO-O.34 8-I. OOC-O.34 9-1.O00-O.
35 l-C. -0.36 I-0. -0.37 l-C. -0.38 I-G. -0.39 I-0. -0.40 l-C. -G.
2 -C -0
2 -o -02 -0 -02 -o -02 -0 -0
2 -O -02 -o -02 -o -02 -0 -02 -0 -02 -0 -02 -G -02 -0 -02 -C -0
2 -0 -02 -C -02 -0 -02 -_ -02 -0 -02 -0 -02 -0 -02 -0 -02 -0 -0
2 -0 -02 -O -02 -0 -02 -0 -02 -0 -02 -0 -02 -o -03 -0 -03 -0 -C3 -0 -03 -o -03 -0 -03 -o -0
3 -O -03 -G -03 -0 -03 -0 -03 -o -03 -_ -03 -0 -03 -o -03 -0 -03 -C -03 -0 -03 -i_ -0
3 -0 -03 -_ -03 -0 -03 -6 -O3 -0 -C3 -c -O3 -0 -03 -0 -03 -0 -03 -c -0
3 -C -03 -0 -0
- 49 -
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
1200
0000
C000
CO00
0000
00000000
('000
0000CO00
COOO
CO00
0000
0000
0000
0_00
2000
I00
41
42
43444546
47484950515253545555555555555555555555555555555555
1LOWLOWLOWLOW
LOWLOWLOWLOWLOWLOWLOWLOWLOWLOWLOWLOWtOWLOWLOWLOWLOWLOWLOWLOWLOWLOWLOWLOW
I-_. -0.
1-C. -0.
I-G. -0.
I-G. -0.
I-C. -0.
I-G. -0.
l-O. -0.
l-G. -O.
I-0. -C.
l-C. -O.I-0. -0.
I-0. -0.
I-0. -_.l-C. -0.
I l._OC-C.
2 i. OOC-C.
3 I. 000-_.4 1.000-0.
5 I. 000-0.6 I. 000-0.
7 I. 000-0.
8 1.000-0.
9 I. 000-0.
I0 I. 000-0.
II 1.000-6.
12 i. C00-0.
13 i. 000-0,
14 I. 000-0,
15 I. OOG-O.16 1.C00-0.
17 1. 006-0.
HIGH
HIGH
HIGH
HIGH
HIGH
HIGH
HIGH
HIGH
HIGH
H IGH
H IGH
HIGH
HIGH
HIGH
HIGH
HIGH
HIGH
HIGH
HIGH
HIGH
HIGH
HIGH
HIGH
HIGH
HIGH
HIGH
HIGH
HIGH
3 -C -0
3 -0 -0
3 -0 -0
3 -0 -0
3 -0 -0
3 -0 -0
3 -0 -0
3 -u -0
3 -0 -0
3 -0 -03 -0 -0
3 -0 -0
3 -0 -03 -0 -0
4 -0 -0
4 -0 -04 -0 -0
4 -0 -0
4 -0 -0
4 -0 -0
4 -0 -04 -C -0
4 -0 -0
4 -0 -04 -C -04 -0 -0
4 -O -0
4 -C -0
4 -6 -04 -C -0
4 -0 I
2 0.00241877 0.99999999
4 0.5302_603 0.99999996
6 0.73457834 0.99999996
8 0,75031348 0,99999996
I0 0.75074767 0.9999999612 0.75144236 0.9997'3973
14 0.75244007 0.99916768
16 0.75377956 0.99830127
18 0.75550042 0.9971953520 0.75764639 0.99595493
22 0.76026683 0.99466971
24 0.70341622 0.9934040826 0.76715223 0.9921991028 0.77153189 0.99107761
30 0.77660624 0.99006657
32 0,78241381 0,98917856
34 0.78897274 0,9883780036 0.79627310 0.98765965
5_ 0,80426996 0°98701709
40 0.81287961 0.98'64%357
42 0.82197957 0.98593245
44 0.83141293 0.98547738
46 0.84106071 0.98507245
48 0.85055589 0,98471230
50 0.85989034 0.98439204
52 0.86884899 0.98410731
54 0.87730087 0.9838542056 0.88515513 0.98362923
29
2929
392392392392392
392392392
392392392392392392392
392392
392392
392
392
392392
392
392
154
188
664
7(?I
7_4
731
7_I
73k
731
731
731
731
731
731
748
748
748
748
748
748
748
748
748
748
748
7%8
748
748
20 -
=.
LOW HIGH
LOW HIGH
LOW HIGH
LOW HIGH
LOW HIGH
LOW HIGH
LOW HIGH
LOW HIGH
LOW HIGH
LOW HIGH
LOW HIGH
LOW HIGH
LOW HIGH
LOW HIGH
LOW HIGH
LOW HIGH
LOW HIGH
LOW HIGH
LOW HIGH
LOW HIGH
LOW HIGH
LOW HIGH
XR =0 • 98144202END OF
58
6062646668
7072
74767880828486
889092949698
100
PROBLEM
0.892359880,898898810,904784950,910053220,91475304
0,918941640,922678980,926023890,929031450,931751580,934228380,93649992
0,938598530,940551280,942380530,942967800,943261380,943532330,94372708
0,94388814
0,944017050,94414704
0,983429290.983282370,9831fi969
0,983048680.982948140.982857120.982774670°982699980,982632330°982571050,98252056
0,982488800,98245867
0.982430120,982403140,982377710,982361380,982348680,982335700,982323820,98231713
0.98230983
392392
392392392392392392392392
392392392392392323323
306306289289289
748782782782782782782782
782782816816816816816816
850850850884884918
l
0 0
--T--
|
o ,,t N
n
I
_ 0
_T
! 0
i | 0
_M
0
.,-I
_3
i1)
%0
4._
,rl
.- 52 -
MAIN ONE -DATA INPUT MAINI
CSPACE-CHARGE SOLUTIUN.VLAD HAMZA MICROWAVE LAaORATORY.
COMMON URH_U_JT,RHtU_XT,KT_LINCtXRtNTOPtNUL_NLINtARCL_EQXt_QYt
l NPIT,XEP_NXEP,CU_LI_CI_AXtAY,VXtVY,DXtDELYtYEP,XQM_htKISwtETX_
2 ETY,PTY,PTX,NAJ,NTJ,VAtVB,VCt_C[IORtKCH,HSL,XLSL,EPS,NPUI,
3 IDEC,JUTtNSPA_,RXtNRLvKRL_KRHtVATtVBT,SIZEtKRTtRHUP,RHDUwNt
4 XCU,_qUT,MOtKCYtNSWP,ATXtATYtLINC2tNXFtNYF,NURL_NJOT,XEMITt
5 IXU,H_H,XLUW_XMPRtNEM_A_X_JDYtAXX,BXX_CXX,DXX_NOIM,VDtVIHp
6 VTHX,VTHYt YAXS_ NFUL'
DIMENSION KRT(Z),JT(4OOO),RH(400O),
l U(4OOO),XT(4OOO),KT(5),LINC(I50)_L[NC/(L50)tLINCZIISO),
2 _(180)tX(60),CU(40),VX(40)tVY(40),KCHI40)_AX(40)_AY(40),
3 ATXI_O),ATY(_O),ETX(_O),ETY(_OI,XCU(_O),KCY(IO),PTX(60)_
PTY(60)
DIMENSIUN ND(3)iKRTX(IO),KRTY(IO),WOLT(28)
200 MO=[
READ INPUT raPE 5_IO0_NH
DO I] J=I_NH
READ INPUT TAPE 5tlO?
13 WRITE UUTPUT TAPE b,IOl
READ INPUT TAPE 5,100,NXF,NYF_NEM,NTJ_NCIM,NRL_NUL,NURL_
INCOOR, IDEC, NFUL, NCO, KRHX, KRHY
JOY = _YF
WRITE OUTPUT TAPc b,108
I08 FORMAT(SHO NXF,SH NYF,SH NEM,SH NTJ,SH NDIM,SH NRL,5H NUL,
15H NI;RL,SHNCOOR,5H 10EC,SH i_FUL,SH NCU,SH KRHX_SH KRHY)
WRITb OUTPUT TAPE 6,_IO,NXF,NYF,NEM,NTJ,NDIM,NRL,NUI.,NURL,
I NCOOR_IDEC,NFUL_ NCG, KRHX_ KRHY
READ INPUT [APE 5,3GO,IXU,NSPAN,NPOTX,NPUIY_ YAXS
WRITE OUTPUT TAPE o,I09
log FURMAT(SHO IXO,SHNSPAN_SHNPOTX_SHNPOTY, 8H YAXS)
WRITE Ot_TPUT TAPE 6,311_IXU_NSPAN,NPUTX,NPOTY, YAX$
READ INPUT rAPE 5,_CO,NRTN,(KRTX(K)_KRTY(K),K=I,NRTI_)
wRITE OUTPUT TAPE b,IIO
IIO FORMAT(SHOKRTN_SH KRTX,SH KRTY,SH KRTX,SH KRTY_SH KRTX,SH KRTY)
WRITE OUTPUT [_PE b,310_NRTN,(KRIX(K),KRTY(K)_K=I,NRTN)
READ INPUT TAPE 5_I02,VAI,VBT_SIZE,VA_VB_VC
WRITE OUTPUT TAPE 6,111
Ill FURMAT(_X_HVAT,TX3HVBT,bX#HSIZE_IX2HVA_SX2HVBeSX2HVC)
WRITE UUTPUT TAPE 6,30Z,VAT,VBT_SIZE_VA,VR,VC
READ INPUT TAPt 5_I02,HGH_XLOW,HSL,XLSL_VD
_RIIE OUTPUT TAPE b_II2
IL2 FORMAT(4X_HHGH,6X_HXLOW,bX3HHSL_TX_HXLSL,TX2HVD)
WRITE OUTPUT TAPE 6,302,HGH_XLOW,HSL,XLSL,VD
READ INPUT IAPE 5_IOZ,AXX_BXX_CXX_DXX_XR
_RITE OUTPUT TAPE 6,113
II_ EURMAT(4X3NAXX,TX3HBXX_?X3HCXX,TX3HDXX_TX2HXR)
WRITE OUTPUT TAPE b_O2,AXX_BXX_CXX_UXXtXR
READ INPUT TaPE 5_Q,RO,EPS.XEMIT_H
_RITE OUTPUT TAPE 6_114
I14 FURMAT(IX2HRO,IOXIHEPSILON_gXSHXEMIT,6XI3HMESH SIZE - H)
WRITE OUTPUT TAPE 6, 308, RO, EPS_ XEMII,H
READ INPUT TAPE 5,105_YEP,XQM,ATDM,VTH,VTHX_VTHY
WRITE OUTPUT TAPE 6,115
I15 FORMAT(I2XhHFPSNUT,6X3HXQM,bX_HATOM,bX3HVTH_TX4HVTHX_6X4HVTHY)
WRITE UUTPUT TAPE b, EO5,YEP_XQM,ATOM,VTH_VTHX_VTHY
- 53 -
NAIN ONE -OATA INPUT
IOOZ
GO
ZOO5 DO
READ INPUT TAPE 511021(ATX{J)tATY(J)vJ=ltN EN)
WR[TE OUTPUT TAPE 6,119
II9 FORHAT(_[HO CATHODE COORDINATES}
wRITE OUTPUT TAPE 6_302t(ATXIJ)tATY{J)tJ=It NEH)
READ INPUT TAPE 5tlO0_(KCY(J)tJ=ltlO)WRITE OUTPUT TAPE 6t120
120 FOKMAI|33HO PRINT-OUT OF CYCLE NO.)
WRITE UUTPUT TAPE 6tlOO,(KCY(JltJ=lBlO|READ INPUT TAPE 5tIO4t{WOLT(NN)wNN=[,28)
WRITE OUTPUT TAPE 6tll61[6 FORNAT(SHO VnLT-If7X2H-2t8X2H-3t8X2H-4tSX2H-St8XZH-6tSXZH-1)
WRITE OUTPUT TAPE 6t304t{WOLT(NN)wNN=It28)
HH=H*-2HT=.fieH
H2=2.*HXMPR=.St(FLOATFINXFeNYF))e*2/FLOATF(NXF**2÷NYF**2)
XQN=XQM/ATOMRX = H/YEP
J=l
IF (NDIN-2) 10011[001t2005
lOOI DO [002 I=I_NYFIF (l-l) lO06wlOO6wlOO7
100b XT(J+3| = 0.0XTIJ+5) = -0.5
GO TO 1008lOO/ IF (I-NYF) lO03tlOOSt1003
[005 XT(J+3) = -0.5
xT(J+5) = O.OGO TO 1008
1003 XTIJ+3) = -0.25XTIJ_5) = -0.25
1008 XT(J} = 0.25XTlJ+l) = 0.25
XT(J+2) = 0.25
XT(J+6) = l.OJ = J+6
TO 20[l
20|0 [=[_NYFRP= FLOATF(NYF-I|*H+RU
IF (i-I) IO09,lO09tIOIO
IOO9 XTIJ+3) = 0.0XTIJ+5} = -2.OeRP
GU TO [0[I
I010 IF (RP) 2009wZOO8t2009
2009 XTIJ+5) = -(RP-HT}XT|J+3| = -(RP+HT)
lOt[ XT[J) = l.O
XT(J*[| = RP
Xr(J+2) = RPXTiJ+4) = _.O*RP
GO TO 2010
2008 XTiJ) = .125XT(J+l|=.[25* H
XTIJ+2|=.I25*H
XT(J+3)=-.50 * HXTIJ*6)=.75 tH
MAIN1
E25
- 54 -
MAIN ONE -DATA INPUT MAINI
XT(J+5)=O.
2010 J = J + 6
2011NDD = I
NSS=2
NTRIP=O
NPONT=NYF
KRF=(KRHX-I)*NPUNT÷KRHY
NTOP=NPONT*NXF
KRT(I)=NRTN
I=2
DO 2 K=LpNRTN
KRI(1)=(KRIX(K)-I)mNPONI+KRTY(K)
2 l=l÷l
KTtlI=-NPONT
KTI2)=NPONI
KT(3)=-I
KT(4)=0
KT(S}=÷I
WRITE OUTPUT TAPE 6,117II7 FORMAT(4IHO BOUNDARY POINTS OF ELECTRODE SHAPE )
CALL PLOT (O.0pVC,-3)
00 2020 NX=I,NXF
DO 2020 NY=I,NYF
IF (NTRIP) 2030,204012030
2040 READ INPUT TAPE 5tZ035,NSttNDII),I=It3),NXC_NYC,HEWtHNS,NVOLI,
1 NVOLTI_NCHECK2035 FORMAT (IH 4II,21412F6.3,215114)
WRIIE OUTPUt TAPE 6,2035,NS,(ND(I)tI=I,3),NXCtNYC_HEWtHNStNVOLT_
[ NVOLTI,NCHECK
IF (HNS) 203It 2032t 203I
2031 XXX=FLOATF(NXC-L)*HeVD
yyy=-IFLOATF(NYC-I)-HNS)eHeVD
CALL SYMBOL (XXXtYYY,O.O7t I2tO.0,I)
2032 IF (HEW) 2033, 2034w 2033
2033 XXX=(FLOATFINXC-1)÷HEW)eHeVD
YYY=-FLOATF(NYC-I)*H*VD
CALL SYMBOL (XXX_YYYtO.Olt 12_0.0,1)
GO TO 20362034 IF (HNS) 2036, 2037t 2036
2037 XXX=FLOATF{NXC-I)*H*VO
YYY=-FL_ATF(NYC-[)*H*VD
CALL SYMBOL (XXXtYYY,O.OZ_ [2_0.0v1|
2036 NTRIP = [
KC = NPONTe(NXC-I)+NYC
2030 K= NPONT*(NX-L|+NY
IF (K-KC) 2060_2050,2060
2060 IF (NSS-1) 2070_2010_2080
2070 IF (NY-NYF) 2071,207212071
207_ NSS = 2
JIIK) = I + 6*(NY-I)
VOLT[= FLOATF((NXF-NX)/NXFI*VA
GO TO 2310
2071 JT(K) = I + 6*(NY-I)
GO TO 2020
2080 JT(K) = 9999
IF (NX-NCO) 2081,2020_2020
llA
577
578
579
$80S8I
MAIN ONE -U_TA INPUT
Z08[ [F (U(KI) 2020t2084,2020
2084 U(K) = VAGO TU 2020
2_50 NTRIP = 0
NSS=NS
VOLT = WULTINVOLT)
VOLT[ = WOLT(NVULI[)HEW = HEWeH
HNS=HNS*H
IF (ND(3)) 2052,2052.205_2052 VOLT[ =VOLT
2053 HN = H
HS = H
HE = H
HW = H
KE = K÷NPONT
KW = K-NPONT
KN=K-[
KS=K+[
JT(KI=J
[F (HEN) 2090_2200_2IOU
2090 H_ = -tlEW
U(KW) = VOLT
GO TU 22002[00 HE = HEW
U(KE) = VOLT
2200 [F (HNS) 22[0t2230t22202210 HS = - HNS
UIKS) = VOLTI
GU TU 22_0
Z220 HN = HNS
U(KN) = VOLT[
2230 IF (NU[M-2) [00_[004_2239
[00_ XTIJI = ((HN+HS)*(HE+HW))/([6.tHH)
XT(J÷ll = (HN÷HS)/(_oehW)
Xf(J÷2) = (HN÷HS)/(8.eHE)
XT(J÷3) = -(HE+HW)/(8°JHN)
XT(J÷5) = - (HE÷HW|/(8.eHS)
XT(J+4) = XT(J+[)+XT(J+2)-XTIJ÷3)-XTIJ+5)
GO TO 2233
223q RP= (FLOATF(NPONT-NY))-H÷RO
[F(RPI223II2232t22J[
223[ XT(J)= (HE+HW)*(HN+HS)/(4o*HH)
XTIJ÷II=((HN+HS)/(Z**HW)|*(KPe((HN-HS)/_.))XT(J+2)=HW*XT(J+[)/HE
XT(J÷3)=-((HW÷HE)/(2.eHN))=(RP+(HN/2.)|
XT(J+5)=-((HW+HE)/(2.*HS))e(RP-(HS/2.))
XT(J+_I=XT(J+[)÷XT(J÷2I-XT(J÷3I-XT(J+5)
GO T[) 2233
223/ XT(J|= (HE+HWI_(HN/|[6.eHH) )
XT(J+[}=(HN/(8°aHW) )*_
XT(J÷2) = H* HN/(8°*HE|
XT(J÷_| = - H*(HE+HH)/(4°*HN)
XT(J÷4)=(HN/8.* ((HW+HE)/(HWeHE))÷(HE÷HW)/(_.iHN) )eHXT(J+5)=-O.
2233 UU 2300 1=1_2
MAINt
L34
135A
I_IA
141
- 56
MAIN ONE -UATA INPUT
2240
2250
2260
2270
2300
23LI
2310
2330
2340
2350
2320
2020
40004DOt
502
II8
24
6
II
12
IO
14
15
NDA= NDII)+[
GO TO {2300,2240,2250,2260t2270),NDA
XT(J+I) = XT(J+I)+ XT(J+2)XT(J+2) = O.O
GO TO 2300
XTIJ+5) = XT(J+5) +XT(J+3)
XTIJ+3) = 0.0GO TO 2300
XTIJ+2) =XTIJ+2) +XTIJ+I)
XTIJ+I) =0.0
GO TU 2300
XTIJ+3) =XT(J+3) +xrtJ+S)XTIJ+SI =0.0
CONTINUE
IF (ND(3)) 2310_2310,231L
XT(J) = O.2bXT(J+I) = O.
XT(J+2) = XLSL
XTIJ+3) = O.
XT(J+4) = I.
XT(J+5) = XLSL - 1.
IF (NSS-I) 2320p2330,2340LINCt(NDD)=K
VUP = VOLTI
XTIJ+3I =-XTIJ+3)
GO TO 2320
LINC2INDD)=K
LINC (NDD)= 2*XMODF(NX,2) -I
VOOWN = VOLT[
KB=LINCIINDD)
DO 2350 KK=KBtKUIKK)= VUP +(VDOWN-VUP)oFLOATFIKK-KB)IFLOATFIK-KB)
XTIJ+5)= -XTIJ+5)
NDD=NDD+I
J=J+6
CONTINUE
NLIN=NDD-I
IF {NCHECK - I) 4000,502,4000
WRITE OUTPUT TAPE 6,400!
FORMAT (24HOERROR IN BOUNDARY POINT)
CALL EXIT
WRITE OUTPUT TAPE 6,118
FORMATI2OX2OHTHIS ENDS DATA CARDS)
DO 6 J=I,NTOP
RHIJ)=O.
NPOT=(NPOTX-I}*NPONT+NPOTY
IFINCOOR) IO, lO,ll
DO 12 J=I,NEM
ETX(J)=ATX(J)
ETYIJI=ATY(J)
GO TO 15
DO 14 J=l,40
ETXIJ)=O.
ETY(J)=O.
CONTINUE
KRL=NRL
MAINI
- 57 -
MAIN ONE -I)ATA INPUT
C UCAL SGLVES IHF MATRIX EQUATION
25 CALL UCAL
C MN[RI CALCULATES THE RHS AND TRAJECTORIES
26 CALL MNTR[
G(_ Ttl 200
FORMAT (4F[_.8}
100 FURM_T(E4[5)
[01 FORMAT(6[5)
102 F[JRMATIOFIO._)[03 FURMAT([3[5|
I04 FORMATITFIO.4)
]05 FORMAT(IOXbE[0.5)
tO0 FURMAT(3FLO. S)
[07 PDRMATI72H
L
300 FORMATI4[5, F|0.6)
302 FORMAT(|H oF|0.4)
304 FURMATI[H rFlO.4l
30_ F(}RMAT(LH 4FLS.B}
$LO FURMAT(LH L_[S)
3LL FURMAT(LH 415t PLO.6)
END(l_OtOlOvOtO_t_O_OtU_OtO_OtOtOI
- 58 -
ARC CALCULATES THE BEGINNING TRAJECTORY COORDINATES
SUBROUTINE ARC
CSPACE-CHARGE
I
15
20
3O
I0
3
2
8
100
102
103
SOLUTION.VLAD HAMZA MICROWAVE LABORATORY.
COMMON URH,UB,JT_RHtUtXT,KT,LINC,XRtNTOP,NUL,NLIN,ARCLeEQXtEQYt
NPITtXEP,NXEPtCUtLINCItAXtAY,VXtVYwDXiDELYtYEP,XQMtHtKISW,ETXt
ETY,PTY,PTXtNAJ,NTJ,VAtVB,VCtNCOORtKCH,HSLtXLSLtEPStNPOTt
IDECtJOTtNSPAN,RXtNRLtKRL,KRH_VAT,VBT,SIZEtKRTFRHUP,RHDOWN,
XCUiNOT,MOtKCY,NSWP,ATXtATYtLINCZtNXFtNYFt_URLtNJOT,XEMITt
IXO,HGHeXLOWtXMPR,NEMtA,X,JDYwAXXtBXXtCXXtDXX,NDIMtVDtVTHt
VTHX,VTHY, YAXSt NFUL
DIMENSION KRT[2),JT(4OOO|,RH(400O),
U(4OOOItXT(4OOO),KT(S;tLINC(15OItLINCI(150),LINC2(15OI,
A(IBO}_X(60)tCU{40)_VX(40)_VY(40)_KCH[40)tAX(40),AY[6O)_
ATX(40),ATY(40),ETX(4OI,ETY(_O)tXCU(60)tKCY(IO)tPTX|60),
PTY|6O)
SUM=O.
DO I J=2,NEM
SUM=SUM+SQRTF[(ATX[J)-ATX[J-I))**2÷[ATY[J)-ATY|J-I))**2)
IF [NFUL) 15,15,20
ARCL = FLOATF|NTJ) - 0.5
GO TO 30
ARCL = FLOATF(NTJ] - I.O
ARCL=SUM/ARCL
ETX[I)=ATX(1)
ETY(I)=ATY(1)
HYP=ARCL
K=I
J=l
IF(K-NIJ)3,6,6
K=K+I
XDIF=ATX(J)-ATX(J+I)
YDIF=ATY{J÷I)-ATY(J)
SA=SQRTF|XDIFJ*2÷YDIF**2)
IF(HYP-SA) 4,4,5
CSA=YDIF/SA
SNA=XDIF/SA
ETX(K)=ATX(J)-HYP*SNA
ETY|K)=ATY(J)+HYP*CSA
HYP=ARCL÷HYP
GO TO I0
HYP: HYP-SA
J=J+l
GO TO 2
K=K÷I
NN=NTJ + I
ETX|K)=ATX(NEM)
ETY(K)=ATY[NEM)
WRITE OUTPUT TAPE 6,103,SUM,ARCL
WRITE OUTPUT TAPE 6,100,(J,ATXiJ),ATY(J)_J=I,NEM)
WRITE OUTPUT TAPE 6,102,(J,ETX(J),ETY[J),J=I,NN|
CONTINUE
FORMAT (I2HOXtY-EMITTER /(7(IH ,12,2H [FS.3, IH,FS.),2H) )))
FORMAT (16HOX,Y-BEGIN TRAJ. I(?[IH ,12,2H (FS.3,1HtFS.3t2H) l))
FORMAT(22HOARC,DELTA ARC LENGTH 2FI0.5I
RETURN
END|I,O,O_O,O,O,I,O,O,O,O,O,OtO,O)
- _9 -
CALR CALCULArEs RH$
SUBROUTINE CALR(KE,KED)
CSPACE-CHARGE SnLUTION. VLAD iIAMZA MICROWAVE LABORAT3RY.
COMMON URH_UR,JT,RHtUyXTtKTtLINC,XR,NTOPtNULtNLIN_ARCLtEQXtEQY_
I NPITtXEPtNXEP,CU,LINCI,AXtAYtVXtVYtDX,DELY,YEP_XQMtHtKISWtETX,
2 ETY,PTY,PTX,NAJ,NTJ,VAtVB,VC,NCOOR,KCHtHSL,XLSL,EPS,NPOT,
3 IDEC,JDTtNSPAN,RXfNRL_KRLfKRHrVAT_VBT_SIZEfKRT_RHUPtRHDOWN_
4 XCU,NnT,MO,KCY,NSWP,ATX,ATY,LINC2,NXF_NYF,NURLtNJOT_XEMITw
5 IXO,HGH,XLOWtXMPR,NEM_A_X_JDY,AXXtBXXtCXXtDXXtNDIMtVD_VTHt
6 VTHX,VTHY, YAXS_ NFUL
DIMENSION KRT(2),JT(4OOO),RII(4000),
I U(4000),XT(_OOO),KT(5)_LINC(ISOIvLINCI(L50)_LINC2(150)t
2 A(L_O)vX(_O)_CU(40)_VX(40),VY{4OItKCH(40)tAX{_O)_AY(40}t
3 ATX(_O)_ATY(40)tETX(40)_ETY(40),XCU(40)tKCY(IO)pPTX(60)_
4 PTY(60)
JEX=KE
JD=KEDIF (NFUL) 500, 500, 60
500 XEP = FLOATF(NYF-I) • HGO T_ TO
60 XEP = YA_S
70 DO 33 JJ=L,NAJ
J=JJ
CIF CU(J)=O.,NO CnNTR|BUTION
IF(CU(J)) 33,33,1
1 IF(AY(J)+I.) 2,2,5
2 IF(AX(1)-BXX) 3_#,_
3 AY(J)=XLDW
GO I_ 5
AY(J)=HGH
CIF CU(NAJ),LAST TUBE
5 IF(J-NAJIq,6,_
IF(AY(JJ)) 7,8,8
7 AY(JJ) = - AY(JJ)
8 HT=(XEP-AY(JJ) )
RTI=HT
XH=AY(JJ)
RT2=O.
YL=XH÷HT
JX=AY(JJ}/DELY
NA=JX÷JEX
NB=JD
TB1 = VY(JJ)/VX(JJ)
DE = ATANF (TBL)
DE = CUSF(DE)
WA = VX(JJ)
WB=WA
GO TO 2_
9 HT=AY(J÷I)-AY(J)
IF(HT}I2,12_I3
12 HT=-HT
XH=AY(J*I)
RTI=XEP-XH
CJX NORMALIZES Y-DISTANCES IN THE CELL
JX=XH/DELY
NB=AY(J)IDELY +I.
- GO -
CALR CALCULATES RHS
HA = VXIJ÷l)
W8 = VX(J)
TBI=VYIJ+I)/VXIJ+I)
TB2=VY(J)/VX(J)
TBA = .5*(TBI+TB2)
DE = ATANFITBA)
DE = CQSF(DE)
GO TO 14
13 XH=AYIJ)
RTI=XEP-XH
CJX NORMALIZES Y-DISTANCES
JX=XH/DELY
WA = VXIJ)
WB= VX(J+I)
TBI=VY(J+I)IVX(J+I)
TBZ=VY(J)/VX(J)
TBA = .5_(TBI+TB2)
DE = ATANFITBA)
DE = COSF(DE)
NB=AY(J+I)/DELY +1,
14 NA=JX_JEX
NB=NB+JEX
YL=XH+HT
RT2=XEP-YL
23 DO 32 K=NA,NB
XA=K-JEX
25 XUD=(XA-.5)*DELY
26 XX=XUD+DELY
YU=MAXIF(XUO,XH)
YD=MINIF(XX,YL)
IF(YD-YU)32,32,27
27 XA=.5*(YD+YU)
W=WA+(XA-XH)*{W"-WA)/HT
CCALCULAIION OF RHS
IF(NOIM-2) 31,31,50
50 RH(K)=RH(K)+(YD-YU)*2.*(XEP-XA)*CU(JJ)/((HTeWeDE)e(RTI+RT2))
60 Tn 32
]I RH(K)=RH(K)+iYD-YU)*CU(JJ)/(HT*W *DE)
_2 CONTINUE
33 CONTINUE
_8 RETURN
END(I,I,O,O,O,0,1,O,O,0,0,O,O,O,0)
- 61 -
CORRCT CONDITIONALLY ENDS TRAJECTORIES
SUBROUTINE CORRCT
CSPACE-CHARGE SOLUTION. VLADCOMMON
I2
3
4
5
6
HAMZA MICROWAVE LABORATORY.
URH,UB,JT,RHtU,XT,KT,LINC,XR,NTOPtNULtNLIN,ARCL,EQXtEQY,
NPIT,XEP,NXEP,CUtLINCI,AXeAY,VX,VY,DX,DELY,YEP,XQMtH,KISW, ETX,
ETY,PTY,PTX,NAJ,NTJ,VA,VB,VC,NCOOR,KCH,HSL,XLSL,EPSeNPOT,
IDEC,JOT,NSPAN,RX,NRLwKRL,KRH_VAT,VBT,SIZE,KRT,RHUP,RHDOWN,
XCU,NOT,MO,KCY,NSWP,ATX,ATY,LINC2,NXF,NYF,NURL,NJOT,XEMIT,
IXO,HGH,XLOW,XMPR,NEM,AtX,JDY,AXXtBXXtCXX,DXX,NOIM,VD, VTHt
VTHX,VTHY
DIMENSION KRT(2),JT(4OOO],RH(6000),
U(4COO),XT(4000),KT(5),LINC(150),LINCI[ISO),LINC2|150|,
A(180),X(60),CU(40),VX(40),VY(40),KCH(40),AX{60|,AY(60),
ATX(40),ATY(40),ETX(40),ETY(40),XCU(40),KCY(IO),PTX(60),
1
2
3
4 PTY(60)XLOWI = XLOW
XLOW2 = HGH
IF (AX(1) - AXX} II,12,1
I IF (AX(I! - BXX) 12,2,2
2 IF (AX[I) - CXX) 13,13,1113 XLOWI = XLOW2
12 DO IC J=ItNTJ
IF (AY(J) +I.) 10,10,5
5 IF [AY{J) - XLOWI) 6,10,I0C CHECK ON THE NEXT TRAJECTORY
6 IF (AY(J÷I) +1.) 9,9,44 IF (AY(J_I) - XLOWI) 9,9,33 AYD = AY(J+I) - AY(J)
AYDS = AY(J+I) - XLOWI
AYDL = AYD - AYDS
CU(J) = CU(J) • AYDS/AYD
VX(J) = (VX(J)*AYDL ÷ VX(J÷I)*AYDS)IAYD
VY(J) = (VY(J)•AYDL ÷ VY(J÷II*AYDS)IAYD
C CHECK ON PREVIOUS TRAJECTORY (CASE 4)
IF (J-l) 14,14,7
7 IF [AY[J-I) - XLOWI) 14,8,88 AYDS : AY(J-I) - XLOWI
AYD = XABSF (AY(J-I) - AY(J))
AYDL = AYD - AYDS
CU(J-I) = CU{J-I)•AYDS/AYD
14 AY(J) = XLOWI
GO TO I0
9 CUfJ) = O.AY{J) = -1.
I0 CONTINUE
11 RETURN
END(I,I,O,O,O,O,I,O,O,O,O,O,O,O,O)
- 62 -
EQLINE SOLVES FOR THE EQU[POTENTIALS
SUBROUTINE EQLINECSPACE-CHARGE
89
28IO
II12
L3
14
15
16
L7
18
lg
COMMON
I
2
3
5
6
SOLUTION. VLAD HAMZA MICROWAVE LABORATORY.
URH,UB,JT,RH,U,XT,KT,LINC,XR,NTOP,NUL,NL IN,ARCL,EQX, EQY,
NPI T, XE P,NXEP,CU, LI NCI, AX, AY,VXtVY, DX, DELYt YEP tXQM, H,K I SW,ETX,
E TY,PTY,PTX, NAJ, NTJ,VA, VB,VC, NCOOR,KCH, HSLtXLSL, EPStNPOT,
IDEC, JOT,NSPAN, RX tNRL,KRL,KRH,VAT, VBT, S IZE,KRT tRHUP,RHDOWN,
XCUtNOT,MO, KCY, NSWP,ATX, ATY, LINC2, NXF, NYF, NURL, N JOT, XEM IT,I XO,HGH, XLOW, XMPR, NEM, At X_ JOY, AXXt BXX, CXX, DXX, NDIM,VD, VTH,
VTHX,VTHY
DIMENSION KRT(2)yJT(4OOO),RH(_O00),
U(4GOO),XT(4OOO),KT(5),LINC(ZSO),LINCL[ISO),LINC2[ 150),
A (180) , X(60) ,CU (40) ,VX(40) ,VY (40), KCH(4a), AX (40),AY[ 60),
ATX(40),ATY(40) ,ETX(40),ETY(40),XCU(40),KCY(IO),PTX(60),
PTY[60)
IFfSIZE) 1,27,1
POTEN=VAT
WRITE OUTPUT TAPE 6,101
JE= NYF + L
JD = NYF - I
JC= NXF-I
DX=I
DX=DX*HBX=C.
JED=JE+JDL=IAX=O.
DO 22 JJ=ltJC
KS=I
AAY:O.
DO 19 K=JE,JED
IF(KS) 8,8,7
M=IJ=K-NYFGO TO q
J=K-I
IF ( JT(K)-g999+JT[J)-gg99) 28,18,18
IF((U(KI-POTEN)*(U(J)-POTEN)) 10,10,18
DIF=ABSF (U(J)-U{K) )
IF(DIF) 13,13,11
IF(M) 12,14,12
VX(L) =ABSF (U (J)-POTEN)/DIF*DX+AXVYIL)=AAY
GO TO 15
VX[L) =AX÷DX
VY(L):AAYGO TO 15
VX(t) =AX+DX
VY(L)= ABSF(U(J)-POTEN)/DIF*DX+AAY
IF(L-b) 17,16,16
WRITE OUTPUT TAPE 6,100,POTEN,(VX(I),VY([),I=Ie6]L=O
L=L+I
AAY=AAY+DX
CONTINUE
IF(KS) 21,21,20
- 63 -
EQLINE SOLVES FOR THE EQUIPOTENTIALS
20 KS=CM=OJE=JE+IGO TCI 5
21 JE=JE+JDJED=JE+JORX=BX+DX_X=AX+OX
22 CONTI NUEIFIL-2) 25,23,23
23 DO 24 J=L,6VXlJI=O.
24. VYIJ|--G.WRITE OUTPUT TAPE DtlOOwPOTENt[VXIIItVY[[|t[=I* D|
25 POTEN=POTEN-S| ZEIF [Pr]TEN-VBT ) 27,20,26
26 AX=AX-BXGO TO 2
27 RETURN
IO0 FORMAT (8H EQUIPOTF8.1,2H 6( IH|F8.5, IHtF8.5, [H] ) |
IOI FORMAT(4IHO X,Y-COORDINATE OF EQUIPOTENTIAL LINES.
END( I, I,O,C,O,O, I,O,O,O,O,O,O,O,O )
64-
MATRIX IS USED FOR THE FORWARD AND BACK SUBSTITUTION
SUBROUTINE MATRIXiN,A,xj
CSPACE-CHARGE
IO
11
12
COMMON
£
23
5
6
SOLUTION.VLAD HAMZA MICROWAVE LABORATORY.
URH_UB,JT,RHeU_XT,KT,LINC,XR,NTOP,NUL,NLIN,ARCL,EQX,EQY,
NPIT,XEP,NXEP,CU,LINCI,AX,AYtVX,VYiDX,DELYtYEP,XQMtH,KISW,ETX,
ETY,PTY,PTX,NAJtNTJ,VA,VBiVC,NCOORtKCH,HSL,XLSLtEPS,NPOT,
IDEC,JOTtNSPAN,RXtNRL,KRL,KRH,VAT,VBT,SIZEtKRTtRHUP,RHDOWN,XLU,NOT,MO,KCY,NSWP,ATXiATY,LINC2,NXFtNYF,NURL,NJOT,XEMIT,
IXO,HGH,XLOW,XMPR,NEM,AtXtJDYtAXX,BXX,CXX,DXX,NDIM,VDtVTH,
VTHX,VTHY
DIMENSION KRT(2),JT(4OOOI,RH[4000),U(_OOOI,XT(4OOOI,KT(SI,LINC(I50),LINCI(I5OI,LINC2(£50),
A(180)tX[6OI_CU(60)_VX[_O)tVY(40)tKCH(60)tAX[_O)_AY(40)t
ATX(40),ATY(40),ETX(40),ETYK60),XCU[40),KCY(IO),PTX(60),PTY[60)
M=3*N-2
A(M+I)=O.
A(2)=A|2)/A
X:XIA
IFfN-I) I2,12,9K=2
DO IO J=4_M,3
A(J)=A(J)-A(J-I)oA(J-2)
A(J+I)=A(J÷I)/A(J)
X(K)=(X(K)-A(J-I)*X(K-1))/A(J)
K=K+IK=K-1
00 II J=I,M,3
NB=M-J-I
K=K-I
X[K)=X[K)-A(NB)_X(K+I)
RETURN
END(I,I,O,O,O,O,I,O,O,O,O,O,O,O,O)
- 6_
MNTRI CALCULATES TRAJECTORIES AND RHS (FOR SOLID BEAM)
SUBROUIIN_ MNTRI
CSPACE-CHARGE S_LUTION.VLAD HAMZA MICROWAVE LABORATORY.
COMMnN URH,UB,JTtRH,U_XTtKTtLINC_XRtNTOPtNUL,NLINtARCL,EQX_EQYt
i NPITtXEPtNXEPtCU,LINCI,AX_AY,VX,VYtDXtDELYtYEP_XQMtH,KISW,ETX_
2 ETY,PTYtPTXtNAJtNTJ,VA,VB,VC,NCOOR_KCH_HSLtXLSLtEPStNPOTt
3 IDEC,JOTtNSPAN,RX,NRL,KRL,KRH,VATtVBT,SIZEtKRT,RHUPiRHDOWNt
4 XCU,NOT,Mn,KCYtNSWP,ATXwATY,LINC2,NXF,NYF,_URL,NJOTIXEMITv
5 IXD,HGH,XLOW,XMPR,NEM,A,X,JDY,AXXtBXX,CXX,DXX_NDIMtVD, VTH,
6 VTHX,VTHY, YAXS, NFUL
DIMENSION KRT(2),JT(4OOO),RH(4000),
I U(4000),XT(4000),KT(5),LINC(150),LINCI(150)tLINC2(150)t
2 A(ISOI,X(6OI,CU(4OI,VXI40),VY(4OI,KCH(4C),AX(40)tAY(_O),
3 ATX(_O),ATY(_O),ETX(40),ETY(40),XCU(40),KCYIIOI,PTX(bO),
4 PTY(60)
DIMENSION EXX(40),E1Y(40)
DELY=H
DX=DELY
301 IWRL=NRL-KRL÷XABSF(MO)
00 I J:l,_O
Vy(J)=O.
VX(J)=.O00I
AY(J)=O.
XCUIJI=O.
CU(J)=O,CKCH=REFLECTION PARAMETER (ADDS CNE EVERYTIME TRAJECTORY REFLECTS)
I KCH(J)=-I
DQ 35 J=l,60
PTX(J)=O.
35 PTY[J)=O.
IF (KCY(IWRL)) 903,903,902
902 CALL PLOT (ATX(1)*VD,-ATY(L)tVDt3)
DO gOI J=2,NEM
gol CALL PLOT (ATX(JIwVD,-ATY(JIeVD,2)
903 NAJ:NTJ
IF(NCODR)2,2,3
CARC CALCULATES THE EMITTER COORDINATES
2 CALL ARC
3 DO 909 J=IvNTJ
EIX(J) = ETXIJ)
909 ElY(J) = ETY(J)
NCOOR = 1
CPEQ CALCULATES THE EQUIPOTENTIAL
CALL PEQ
AX(l) = O.
JCX=NXF-2
JEX=NYF÷I
IF (NFUL) 50, 50, 60
50 XEP = FLOATF(NYF-1) • 0X
GO TO ?0
60 XEP = YAXS
70 DO 22 JN=I,JCX
600 JD=JEX÷NYF-I
AX(1) = AX(1) + OX
LINE FOR CU CALCULATION
CTRCU CALCULATES THE CURRENT IN THE" TUBES AND CALLS TRAJ
CALL TRCUIJEXtJD)
66-
• t
MNTRI CALCULATES TRAJECTORIES AND RHS (FOR SOLID BEAMI
IT CONTINUE
IF (KCYIIWRL)) £gtLgtI8
18 WRITE OUTPUT TAPE 6,101,AX(II_(K,AY(KItVXIK),VY{KItK=ItNTJ)
XP = AXII)
DO 906 J=I_NTJ
IF IAY(J)) 906t9061905
905 YP = AY(J)
CALL PLOT (EIX(JI*VCt-EIY(J)*VDt3)
CALL PLOT (XP*VDt-YP*VDt2)
EIX(J)=AXll)
EIY(J) = AY(J)
906 CONTINUE
CCALR CALCULATES THE RHS
lg CALL CALR (JEXtJD)22 JEX=JEX+NYF
21
CUCAL
IF (KCYIIWRL)| 907,907t24
24 IF (IXn) 90Bt908_20
20 CALL TROUT
908 XMAX = FLOATF(NXF-I)*H*VD + 3,0
S = XMAX - 3.0
XMIN = ATXINEM)tVD
YMAX = - XEP*VO
SDX = I.O/VD
CALL PLOT (XMAX_ O.Ot -3)
DO 910 J=ltNTJ
EIX(J) = ETXIJ)910 EIYIJ) = ETY(J)
907 SUM = 0.0
DO 10 J=ItNAJ
10 SUM=SUM÷XCU(J)
305 WRITE OUTPUT TAPE 6tlO2t|J_XCU|J)tJ=ltNAJ)
WRITE OUTPUT TAPE 6wIO3tSUM
304 IFINURLI303_303,302
302 IF (NRL-KRL) 306_307_306
307 WW = SQRTF(2.*XQM*(VA-VB))
RHM = 2.*SUM/WW
306 DO 4 J=I_NTOP
RHIJ) = .SeRHIJ|
IF (RHM-RHIJ)) 5t6_4
5 RH(J) = RHM4 CONTINUE
IF (KRL) 8tTt87 MO=O
KRL=I
JJ=NRL
KCY(JJ}= 777
WRITE OUTPUT TAPE 6_100GO TO 9
8 WRITE OUTPUT TAPE 6_I04_IWRL
9 RT=RH(KRH)-RX
WRITE OUTPUT TAPE 6,IOStRTeU{KRH)
KRL=KRL-I
SOLVES THE MATRIX EQUATION
CALL UCALGO TO 301
303 RETURN
- 6T -
MNTRI CALCULATES TRAJECTORIES AND RHS (FOR SOLIC BEAM}
100 FORMAT(25H1 L A S T C Y C L E )
10[ FORMATI3X3H X=FI0.St5H NO, t7XLHYtZ6X2HVXtZ6X2HVYI(16X[Se3E15,6))
102 FORMAT(27HOEMITTER CURRENT IN TUBES /(7(IXI2tE16.6)))
103 FORMATI25H TOTAL EMITTER CURRENT E16.6)
104 FORMAT(LBHI C Y C L E NO. 12)
105 FORMAT(LIHO RHTEST= Fg.St6X7HUTEST= FLL.6)
END(1,0tO,O_OtOtltOtO_OtO_OtO_OtO)
68 -
PEQ CALCULATES THE EQUIPnTENTIAL LINE FOR THE CJR_ENT DENSITY
SUBRDUTINE PEQCSPACE-CHARGE S_LUTION.VLAD
COMMON JRMvUBtJTtRHtU
I NPIT,XEP_NXEP,CU,L
2 ETY,PTY,PTX,NAJ,NT
3 [DEC,JOT,NSPA_tR×t
4 XCU_NOTyMOtKCY,NSW
5 IXD,_$MtXLOW,XMPRt6 VTHXtVTHY
DIMENSInN KRT(2)tJ1 U(_bO_I,XT(_OOO)tK
2 A(I_D),X(_O),CU(403 ATX(40)tATY(40)_ET4 PTY(SC,)
C NPOT=POINT THRU WIIICH TH
POTEN=U (NPOT)
DX=H
L=O
24 AAX=_.
JE= NYF ÷ I
DO 28 JJ=ItNSPAN
AAY=O,
JED=JE÷NYF-L
DO 27 K=JEtJEDJ = K - NYF
HAMZA MICROWAVE LABORATORY.
tXT,KT,LINC,XR,NTOP,NUL,_LIN_ARCLtEQXtEOY,
INCI,AX,AY,VX,VY,DX,DELYtYEP_XQMtH_KISWtETX,
J,VA,VH_VC_NCOOR,KCHtHSL_XLSLtEPS_NPOT_NRL,KRLyKRH,VAT,VBT_SIZEtKRT_RHUP_RHDOWN_
PtATX,ATY,LINC2,_XFtNYFtWURL_NJOTtXEMITt
NEM,A,X,JDYtAXXtBXX,CXK,DXXtNDIM_VD_VTH_
T{_OOI,RH(40]]),
T(5),LINC(15D)tLINCI(150)tLINC2IISO)t
),VX(40),VY(_D),KCH(40)t_X(40)tAY(40)t
X(_O)IETY(40),XCU(_),KCY(ID),PTX(60)_
E EQUIPOTENTIAL LINE IS )ETERMINED
IF((U(K)-POTEN)*(U(J)-POTEN)) 21,21,27
21 DIF:ABSFIU(J)-U(K))
L=L÷I
PTY(L)=AAY
IF(DIF) 22_2b,22
22 PTXIL)=ABSF(U(J)-PQTEN)/DIF*DX+AAX
GO TO 2726 PTX(L)=AAX+DX
27 AAY=AAY÷DX
AAX=AAX÷DX28 JE = JE + NYF
D_ kl J=I,LLL=L-J*I
TT=O,
JJ=LL
DO _D I=I,LL
IF(TT-PTY(1)) 39,39,_39 TT=PTY(I)
NN=I_0 CONTINUE
PP=PTY(JJ)
PTY(JJ)=TTPTY(NN)=PPPP=PTX(JJ)
PTX(JJ)=PTXINN)PTXINN)=PP
41 CONTINUE
DO #k J=2,LIFKPTY(J)-PTYIJ-I)) _,_2,_
_2 NN=L-I
- 69 -
PEQ CALCULATES THE EQUIPOTENTIAL LINE FOR THE CJR_ENT DENSITY
DO 43 JJ=JvNN
PTX(JJ)=PTX(JJ+I)
43 PTY(JJ)=PTYIJJ+I)
44 CONTINUE
EOX=PTX(L-I}
EQY=PTY(L-I)
DO 210 KJ=I,LIF (PTYIKJ)-PTY(KJ+I)) 210t211_210
2II PM = MINIF(PTX(KJ)tPTX(KJ÷I))
PTX(KJ) = PM
PTX(KJ÷I) = PM
210 CONTINUE70 WRITE DLITPUT TAPE 6tZOO,(J,PTX(J),PTY(J)tJ=ltL}
60 RETURN100 FORMAT(IBHDX,Y-EQUIPOTENTIAL /t(7(1H tI2_2H (FS,3tZH_FS,3t2H)
END(ltltO_O_O_OtZ_OtOtO_O_OtO_OtO)
)})
- 70 -
TRAJ CALCULATES THE TRAJECTORY COORDINATES AND VELOCITIES
SUBROUTINE TRAJ(M,KE=KED)
CSPACE-CHARGE SOLUTION.VLAD HAMZA MICROWAVE LABORATORY.
COMMON URH,UBtJTtRHtU_XTtKT,LINC_XRINTOP,NULtNLINtARCLtEQXtEQY_
1 NPITtXEPtNXEPtCUtLINCllAXtAY_VX_VYtDX_DELY,YEPtXQMtH_KISW_ETXB
2 ETYtPTYtPTXtNAJ,NTJ_VAtVBtVCtNCOOR_KCHtHSLIXLSL_EPStNPOTt
3 IDECtJOT_NSPANtRXtNRLIKRLtKRH_VAT,VBTtSIZEtKRTtRHUP_RHDOWNt
4 XCU_NOT_MOtKCYtNSWP,ATX_ATY_LINC2_NXFtNYFINURLtNJOTIXEMIT,
5 IXO,HGH,XLOW,XMPR_NEM,AtX,JDYtAXX,BXX,CXXtDXX,NDIMIVD_VTHt
6 VTHXtVTHY
DIMENSION KRT(2)tJTI4OOO)eRH(4000),
1 U(40001_XT{4000)IKT(5)tL1NCI150),LINC1(150)_LINC2(150)_
2 A(180)_X(60)_CU(40)tVX(40)tVY(40)tKCH(40)tAX(40),AY(40)t
3 ATX(40)tATY(40)IETX(40)tETY(40)_XCU(40)_KCY[IO)tPTX[60)_
4 PTY(60)JE=KE
JED=KED
K=M
XEP = FLOATF(NYF-II*H
AD=AY(K)/DXJX=AD
XA=JX
XA=AD-XA
JP=JX+JEJS = 10
JQ = JP-NYF
UL=(1.-XA)*U(JQ)÷XA-U(JQ÷I)
UK={I.-XA)iU(JP)÷XA*U(JP+I)
C CALCULATION OF LEFTHAND DERIVATIVE
IF(XA-.5} Ltl,5
1 IF(JX) 2,2,3
2 YLA=2.*XA*(U(JQ÷I)-U(JQ))GO TO 4
YLA=(XA+.5)*U(JQ+II-2.*XA*U(JQ)+(XA-.5)*U(JQ-I)3
4 DY=VY(K)/VX(K)JOX=JX
GO TO 7
5 JX=JX÷l
JQ=JQ+IXA=XA-lo
IF (JX-NYF ÷I) 3_6,6
6 YLA=2.*XAe(U(JQ-1)-U(JQ))GO TO 4
C CALCULATION OF RIGHTHAND DERIVATIVE
7 XB=XA+DY
IF(DY) 9_9_108 JX=JX-1
XB=I.+XB
9 IF(XB+.5) 8,12_12
11 XB=XB-1.JX=JX÷l
10 IF(XB-.5) 12,_2_11
12 IF(JX) 14,17,16
13 JX=JX+2e(1-NYF)
14 JX=-JX
XB=-XB
300019
300020
300021
300022
300023
300024
300025
300026
300029
300030
300031
300032
300034
300035
300037
300038
300039
300040300041
300042
300044
300045
300046
300047
300048
300049
300050
300051
300052
300053
300054
300055
300057
300058
- T1 -
TRAJ CALCULATES THE TRAJECTORY COORDINATES AND VELOCITIES
15 JP=JE+JXYRA=(XB+.5)*U(JP+I)-2**XB*U(JP) + (XB-.5)*U(JP-I)
IF(XB) 19,20,20
16 IF (JX-NYF +1) 30,18,13
30 IF(K-l) 32,32,1532 IF(AX(1)-ETX(1)-2.eH) 36,34,15
34 XB=ABSF(XB)
17 JP=JE + JX
YRA=2.*XB*(U(JP+I)-UIJP))
XB:ABSF(XB)
GO TO 20
18 JP=JE+JX
YRA=2.*XB*(U(JP-1)-U(JP))
19 JP=JP-I
XB=I.-ABSF(XB)
20 JQ = JP-NYF
USN=(1.-XB)mU(JQ)+XB'U(JQ+I)
UQN=(1.-XB)*U(JP)+XB*U(JP+I)
DUX=°5*(UK-UL-USN+UQN)
DUXX = VX(K)**2-2.*XQM*DUX
IF (DUXX) 35,36,36
35 VXB=- SQRTF(-DUXX)
GO TO 37
36 VXB = SQRTF(DUXX)
37 DT = ABSF(2,*DXI|VXB+VX{K)))
JS=JS-1
C yA=y ACCELERATIONXD = .5*XQMIDX
YA=XDw(YLA+YRA)
C DY=DELTA Y INCREMENT
DY=DT*(VY(K)-.5*YA*DT)/DX
JX=JOX
IF(JS) 21,219 7
21 VX(K)=VXBIF (VX(_)) 38,38,39
3B CU(K) = O.
AY(K) = -1°
GO TO 26
39 VY(K)=VY(K)-YAIDTAY(K)=AY(K)+DY_DX
C REFLECTION OF TRAJECTORIES IF OUTSIDE BOUNDS
IF(AY(K))22,23_23
22 AY(K)=-AY(K)GO TO 25
23 IF(AY(K)-XEP) 26,26,24
26 AY(K)=XEP+XEP-AY(K)
IF(VY(K))27,27t25
25 VY(K)=-VY(K)
27 KCH(K)=KCH(K)+I
26 CONTINUERETURN
END[1,0,0,C,O,O,I,O,O,O,O,0,O,O,O)
300059
300061
300064
300065
300066300067
300068
300069300070
300072
300073
300074
300077300078
300079
300080
300081
300082
300083
300064
300085
300086
300067
300088
300089
300090
300091
300092
300093
300094300095
300096300097
- 72 -
TRCU INIIIALIZES TRAJ. A_D CALCULATES CUR.DENSITIES
SUBROUTINE TRCU(KE_KED)
CSPACE-CHARGE SOLUTION.VLAD HAMZA MICROWAVE LABORATORY.
COMMON URH,UB,JT,RHtUtXTtKTtLINC,XR,NTOPtNULtNLINvARCL_EQXtEQYt
1 NPIT,XEPtNXEPtCU,LINCI,AX,AY,VX,VY,DXtDELYtYEPtXQMtH_KISWtETX,
2 ETYtPTY,PTXvNAJtNTJ,VA,VB,VCtNCOOR_KCH,HSL,XLSL,EPS,NPOT_
3 IDEC,JnT,NSPAN,RXtNRL_KRLtKRH,VAT_VBTtSIZE_KRT,RHUP,RHDOWN_
4 XCU,NOT,MOtKCY,NSWP,ATX,ATY,LINC2,NXF,NYF_NURL,NJOT,XEMIT,
S IXO,HGH_XLOW,XMPRtNEMtAtX,JDY,AXX,BXX,CXXtDXX_NDIM_VD_VTH_
6 VTHX_VTHY, YAXSt NFUL
DIMENSION KRT[Z)_JT[4OOOItRH(4000),
I UI6OOO)tXT(4OOO),KT(5)tLINC(LSO),LINCI[150)tLINC2(LSO)t
2 AILBO)tX(60),CU(6OI,VX(40)tVY(6OItKCH(40)tAX(4O)tAY[4O)t
3 ATX(40),ATY(60)_ETX(40)tETY(60),XCU(40),KCY(IO),PTX(60),
4 PTYI60)
DIMENSION US(2)tUR[2)
JEX=KE
JD=KED
DO L6 K=L_NTJ
IF (NFUL) 50, 50, bO
60 XEP = YAXS
50 LL=O
KK=K
CCHECK ON TERMINATED TRAJECTORIES
IFIAY(K)+I.) 16,16,18
CCHECK ON UNINITIALIZED TRAJECTORIES
18 IF(KCHIKI)20,15,15
CCHECK IF TRAJECTORY CAN BE iNITIALIZED
20 IF (AX(1)-ETX(KK)-.Ofi*H) I6,16,2
2 KK=KK+I
IF (IDEC ) 800,80L,801
801 TB=(XEP-ETY(KK-I))/(XEMIT+ETX[KK-I))
DE = ATANF(TB)
TB = - TB
XX= ETY(KK-I)-TB*ETXIKK-1)
JJ=lGO TO 62
800 TB=(XEP-ETY(KK-LI)I(XEMIT-ETXIKK-L))
DE = ATANF(TB)
XX= ETY(KK-1)-TB*ETX(KK-I)
JDYI= ETYIKK-L)/OX +1.
DO 777 JJB=I,JDY
IF (PTY(JJB)) 774,776,775
775 JJC = PTY(JJBIIDX +1,
IF [JJC-JDYI-1) 777,777t779
779 JJ=JJB
GO TO 776
776 JJ= JJB-1776 JJB = JOY
777 CONTINUE
4 IF (PTY(JJ+I)) 62,6,42
62 PTT = PTX(JJ)-PTX(JJ+I)
PTT=ABSFIPTT)
IFIPTT-.OO01) 43,43,6663 CPX = PTX(JJ)
CPY = ETY(KK-I) + TB*CPX
- 73 -
TRCU INITIALIZES TRAJ. AND CALCULATES CUR.DENSITIES
GO TO _5
44 TA = -DX/(PTX(JJ)-PTX(JJ+I))YY=PTY(JJI-TA*PTX(JJ)
CPX=(YY-XX}/(Tfi-TA)
CPY=YY+TAeCPX
45 IFIIDECI 5,7,7
5 IF ((Cpy-pTYlJj)).(Cpy-pTy(JJ+l)l} 8,8,6
6 JJ = JJ-1
GO TO 4
7 IFIPTY(JJ+II-CPY) 3,3,8
3 JJ = JJ+[
GO TO 4
8 LL=LL÷I
IF {LL-2Ig,IO,IO
CTRAJECTORIES INITIALIZED9 AYIKK-II=ETY{KK-1I+TB*(AX(I)-ETX(KK-I))
XA=AY(KK-I)/DX
JX=XAJP=JEX÷JX
AD=JXXA=XA-AD
UP=(1.-XA|wU(JPI÷XA=U(JP+I)
PHI = 1.570795 - DE
IF (VA-UP) gOO,gOllg01
900 V = - SQRTF(2.*XC_*(UP-VA))VXIKK-1) = V*COSF(DE) + VTH*COSF(PH|)
IF (VXIKK-I)) 904,g04_903
g04 AY(KK-[) = -1.
CU(K) = Oo
KCH(K) = 0GO FO 16
901 V=SQRTF(2.*XQM'(VA-UP))
VXIKK-I) = V*COSF(DE| + VTH*COSF(PHI)
903 IF (IDEC) 850,851,851
851 VYIKK-I) = - V*SINF[DE) - VTHeS[NFIPH[)
GO Tfl q02
850 VY(KK-I}=V*SINF(DE) - VTH*SINF(PHI)
902 TB = VY{KK-I)/VXIKK-I)
AY(K) = ETY{KK-I) + TB*IAX(1)-ETX(KK-II)
10 US(LL)=CPX
UR(LL)=CPY
IF(K-NTJ)12,11,12
CSPECIAL FnR LAST CURRENT DENSITY
II LL=2
US(2)=EQX
UR(2]=X_P
PPX=.5m(ETXIKK-II+ETX(KK) )
PX=.5 .(USI1)+US[2))
ppy=.5*(ETY(KK-I)+ETY(KK))
RHO = XEP - FTY(KK-I)
PY=.5 *(URII)+UR[2))
GO TO 31
12 IF(LL-212,14,14
14 PPX = .5*(ETX(KK-2I+ETXIKK-I))
PX=.SeIUS(1)+US(2))
PPY = .5*(ETY(KK-2)+ETYIKK-I))
-,74-
TRCU INITIALIZES TRAJ, A_D CALCULATES CUR.DENSITIES
RHO=XEP-PPY
PY=.5*(UR(1)÷UR(2))
31 DEX=SQRTF((PX-PPX)eO2+(PY-PPY)ee2|
IF ([DEC) 6031606t604
603 RA = DEX/(XEMIT-ETXINTJ+II)
IF (NDIM-2I 63It63[t602
602 CR= 1.÷I,6*RA ÷ 2=06-(RA*-2)
GO TO 600
631 CR= 1. +.8*RA +.66*(RAe*2)
GO TO 600
604 RA = DEX/(XEMIT+ETX(NTJ÷Z))
IF (NDIM-2) bO5y605t606
606 CR = 1.-L.6*RA ÷ 2.6"(RA*'2l
GO TO 600
605 CR = [.-.SBRA÷.66t(RA**2)600 POTEN=U(NPOT)
DELU=VA-POTENXK=4°/g. eYEPeSQRTF(2,_XQMmDELU)*DELU
YCU=XK/(CRoDEX**2)
CCALCULATION OF CURRENT DENSITY
53 IF (NDIM-2) 54_54_55
54 IF (K-NTJ) 56_57_57
56 CU(K)= YCUeARCLXCU(K) = CU|K)
GO TO 52
57 CU|K)= ,5*ARCL*YCU
XCUIK) = CU(K}
GO TO 52
55 IF (K-NTJ) ITt19t1919 CU(K) = YCU*RHO**2
XCU(K) = CU(K)*3.1416
GO TO 52
17 CU(K) = ARCLeRHO*YCU
XCU(K| = CU(KI * 6,2832
52 IF (AX(I)-ETX(K)-,5aH} 5Iy51_58
58 KCH(K| = O
5L WRITE OUTPUT TAPE 6tlOOtUS(I)_US(2I_UR(IIIUR(2)_DEX_YCUt
I KCH(K|_K
GO TO 16
CTRAJ CALCULATES THE TRAJECTORIES AFTER THEY HAVE BEEN INITIALIZED
15 CALL TRAJ(K_JEXtJD)
16 CONTINUE
CALL CORRCT
RETURN
100 FORMAT(4H XI=E8.3v_H X2=E8.3t4H YZ=E8.3_6H Y2=E8.3t4H DX=E8.3_
IkH CD=ELO.4,2IS)
- ?_ -
TROUT PRINTS nUT THE RHS
SUBROUTINF TROUT
CSPACE-CHARGE SOLUTION. VLAD
10
13
14
7
2
6
I
8
3
IOO
I01I04
COMMON
I
2
3
4
5
6
HAMZA MICROWAVE LABORATORY.
URH TUB, JT, RH,UtXT, KT,L INC, XR,NTOP, NULt NL IN• ARCL_EQX, EOYt
NPI T, XE P, NXE P ,CU, L INCI tAX• AY,VX •VY IOX •DELY, YEP tXQM, H, K ISW, ETX,
ETY,PTY, PTX, _.AJ,NT J, VA,VB_VC tNCOORt KCH• HSLt XLSL• EPSt NPOT•
I DEC, JOT,NSPAN, RX tNRL, KRLt KRHt VAT _VBT •SIZE• KRT •RHUP,RHDOWN•
XCU,NOT,MO, KCY, NSWP tATX tATY, L INC2,NXFt NYFt NURL, NJOT,XEMITt
I XO,HGH _XLOW,XMPR,NEM_A,X, JDY_AXX, BXX_ CXX_ DXX•NDIMtVD• VTHt
VTHXt VTHY
DIMENSION KRT{2),JT[4OOO)tRH(_OO0),
U(4000) ,XT (4000) ,KT(5) ,LINC(L50) ,LINCI( LSOI,LINC2(Z50) •
A[IBO)tX(60),CU(40) tVX(40) _VY(40)tKCH(60)tAX(40)tAYI60)t
ATX(40) ,ATY(40),ETX(40)IETY(40),XCU(40),KCY(LO)tPTX{60)t
PTY(60)DIMENSION NTY(SI,NTX|ISO)
IF[MO) I0,3,10
K=IWRITE OUTPUT
NN=I
DO I N=I,NXFNTX(NN)=N
DO _ J=I,NYFNTY|K)=J
I=[N-I)*NYF+J
PTY{K)=RH(I)*RX
K=K+I
IF (J-NYF) 13,14,14
IF (K-Q) 4•2,2
DO 7 JJ=K,8PTY(JJ)=0.ONTY{JJ)=0WRITE OUTPUT TAPE
K=I
CONTINUE
NN=NN+ICONTINUE
RETURN
TAPE 6,101
6 ,IO0,NTX[NN) , (NTY(L) ,L= It8 )• (PTY|L) ,L"I• 8)
WRITE OUTPUT TAPE 6,106GO TO I0
FORMAT (IH I3,3X816,8FIO.3)FORMAT(AqHO RHS OF MATRIX EQUATION
FORMATI25HORH-FIELD OF LAST CYCLE
END[I_i,OtO_O•O,l,O,OtO,OtO,OtO_O)
- SPACE-CHARGE DENSITY)
- 76 -
TWOUT PRINTS OUT THE POTENTIAL FIELD
SUBROIITINE TWOUT
CSPACE-CHARGE SOLUTION. VLAD
IO
13
l_
7
2
6
l
8
3
100lOI104
CnNMON
i
2
3
4
5
6
HAMZA MICROWAVE LABORATORY.
URH,U_,JT,RH,UtXT,KT,LINC,XR,NTOP,NUL,NLIN,ARCL,EQXtEQYt
NPIT,XEP,NXEP,CU,LINCI,AX,AYtVX,VY,DX,DELY,YEPtXQMtHtKISW,ETX,
ETY,PTY,PTX,NAJ,NTJ,VA,VB,VC,NCOOR,KCH,HSL,XLSLtEPStNPOT,IDEC,JOT,NSPAN,RX,NRL,KRL_KRH,VAT,VBT,SIZE,KRTtRHUP,RHDOWNt
XCU,NOT,MO,KCY,NSWP,ATX,ATY,LINC2,NXF,NYFtNURL_NJOT_XEMITt
IXO_HGH,XLOWtXMPRtNEMwAtXmJDYtAXX_BXXtCXXtDXXvNDIM_VD_VTHt
VTHX,VTHY
DIMENSION KRT(2),JT{4GOO),RH(6000),
U(4OCO),XT(4OOO),KT{5),LINC(150),LINCl(150),LINC2(XSO),
A(IBO)tX{60),CU(40),VX(40),VY(40)_KCH(40)_AX{40)pAY|60),
ATX(40)t_TY(40),ETX(40)tETY(40)tXCU(40),KCY|IO)_PTX{60)t
PTY(60)
DIMENSION NTYIB),NTXII50)
IF(MO) I0,3,10
K=I
WRITE OUTPUT TAPE
NN=I
DO [ N=I,NXF
NTX(NN)=N
DO 4 J=ItNYF
NTYIK)=JI=(N-I)*NYF÷J
PTYIK)=U(1)
K=K+I
IF (J-NYF) I3,I4vI4
IF (K-g) 4t2,2
DO 7 JJ=K_BPTY(JJ)=O.O
NTY(JJ)=O
WRITE OUTPUT TAPE
K=ICONTINUE
NN=NN+I
CONTINUE
RETURN
6,101
6,100,NTX(NN),INTYILItL=I,8I,IPTYILItL=ItS)
WRITE OUTPUT TAPE 6,10%
NURL=-7777
GO TO" I0
FORMAT (IH 13,3XBI4,8FIO.3)
FORMAT(25HO U-FIELD OF THIS CYCLE.
FORMAT(25HOU-FIELD OF LAST CYCLE.
ENDII,I,OtO,O,O,I,O,O_O,O,O,O,O,OI
I
)
- TT -
UCAL SOLVES THE MATRIX EQUATION
SUBROUTINE UCAL
CSPACE-CHARGE SOLUTION,VLAD HAMZA MICROWAVE LABORATORY°
COMMON URHtUB_JT_RHIUwXT,KT,LINCtXR,NTOP,NULgNLINtARCL_EQX_EQYI
I NPITtXEP,NXEP,CUtLINCItAX,AY,VXtVYtDXtDELYtYEPtXQM,H,KISW,ETX,2 ETY,PTY,PTX,NAJ_NTJtVAtVB,VC,NCOOR_KCH,HSLtXLSLtEPS,NPOT_
3 IDEC,JOT_NSPAN,RX_NRLwKRLwKRHIVAT,VBT,SIZEtKRT_RHUPtRHDOWN_
4 XCU,NOTtMO,KCY,NSWP,ATXtATY,LINC2tNXFtNYFINURLtNJOTiXEMITt5 IXOvHGHIXLOWtXMPRtNEMtA,XtJDY,AXXtBXX,CXXtDXXtNDIM,VD, VTHt
6 VTHX,VTHYDIMENSION KRT(Z|tJT(4OOO|_RH(4000),
1 U(40001tXT(4000),KT(5)tLINC(L50),LINCIII50),LINC2(L50)p
2 A(I80),X(60)eCU(40),VX(40)_VY(40)tKCH(40),AXI40),AY(40)t
3 ATX(40),ATY(40),ETX(4C),ETY(40),XCU(40),KCY(IO),PTX(60),
4 PTY(6G)
IF (NRL-KRLI 46t6t4b
6 WRIT_ OUTPUT TAPE 6,101
46 XW:I.
DO 30 NLU=I,NUL
NEZ=NLUXEP=O.XM=.25*XR*w2
NOD=I
38 00 29 NL=I,NLIN
IF(LINC(NL))29v29,33
33 KB=LINCIINL)
KC=LINC2(NL)
JV=I
JU=IDO 28 K=KBIKCSUM=O
JZ=JTIK)27 DO 22 JY=3,5
JX=JZ+JYAIJU)=XT(JX)
22 JU=JU+I
DO 26 JY=I_5JX=JZ+JY
IF(KT(JY))3&_26,3434 IF(XT(JX)) 26,26,2525 JW=K÷KTIJY)
SUM=SUM÷XT(JX)*U(JW)26 CONTINUE
X(JV)=SUM÷XT(JZ)*RH(K)*RXJV=JV+L
28 CONTINUEN=KC-KB+L
C MATRIX IS USED F_R THE FORWARD AND BACK SUBSTITUTION
CALL MATRIX (N,A{2),X)JV=l
DO 24 K=KBtKC
23 DIF=XIJV)-U(K)JV=JV+L
C MATRIX EQUATIONUIK)=XW*DIF÷U(K)
DIF=ABSF(DIF)
- ?8 -
UCAL SOLVES THE MATRIX EQUATION
IF(DIF-XEP) 24,24,2121 XEP=DIF
NXEP=K
24 CONTINUE
29 LINC(NL)=-LINC (NL)
IF(XW-I.) 40,31,40
40 XW=l. / ( I.-XM* XW )
Gfl TO 41
31 XW=I./(I.-2.*XM)
41 IF(NOD) 37,37,3636 NOD--O
GO TO 38
37 XCON=XEP*XMPR
IF(XCON-EPS) 42,42,3030 CONTI NUE42 KNUT=KRT(I )
J=2
DO _,3 K=I,KNUT
JN=KRT (J)
IF(U(JN)-VA) 43,49,4943 J=J+l
GO TO 474g WRITE OUTPUT
WRITE OUTPUT
CALL EXIT
47 IF (NRL-KRL } 2,1,2
1 NUL=NURL2 I WRL=NRL-KRL+XABSF (MO)
TAPE 6,102
TAPE 6,100,JN,U(JN|
WRITE OUTPUT TAPE 6,104,NEZ,NXEP,XCON,EPS
IF(KCY(IWRL)) 4,4,3C TWOUT PRINTS OUT THE POTENTIAL FIELD
3 CALL TWOUT
C EQLINE CALCULATES THE EQUIPOTENTIALS
CALL FQLINE
4 RETURN
IO0 FORMAT{ISHO PO|NT NO.= IS,SXIOHVOLTAGE = F15.5)
IOl FORMAT(BQHI NO SPACE-CHARGE - LAPLACE SOLUTION )
102 FORMAT(31HOI CANNOT GET OUT OF THE LOOP )
104 FORMAT(BAHOITERATION NO.IPOINT/ERROR/EPSILDN I3, I5,2F15,6)END(I,I,O,O,O,O,I,O,O,O,O,O,O,O,O)
- 79 -
p
o H
O r--l q_ ,_
_ _oo
4._ b9 "_ (1)
_o_
_ _ .__ o0_
E.a 0 4_ _
@..o
o
f _
o
00 4._
0
0
0
or-t
o
o
!
%©
c_
d
©,--4r_
80 -
MAIN ONE -DATA INPUT MAINX
CSPAC
C
C
E-CHARGE SOLUTION.VLAD HAMZA MICROWAVE LABORATORY.
THIS SUBROUTINE IS GOOD FOR XR-CALCULATION ONLY
XR IS THE LARGEST EIGENVALUE OF THE MATRIX
COMMON URH,UB,JT,RHtU,XT,KT,LINC,XR,NTOP,NUL,NLIN,ARCL,EQX,EQY,
I NPITIXEP_NXEPtCUtLINCItAXtAYtVXIVYtDXtDELY_YEPtXQMtHtKISW_ETX_
2 ETY,PTY,PTX,NAJ,NTJ,VA,VB,VC,NCOOR,KCH,HSL,XLSL,EPS,NPOT,
3 IDEC,JOT,NSPAN,RX,NRLtKRL,KRH,VAT,VBTtSIZE,KRTtRHUP,RHDOWNt
4 XCU,NOT,MO,KCY,NSWP,ATX,ATY,LINC2,NXF,NYF,NURL,NJOT,XEMITt
5 IXO,HGH,XLOW_XMPRtNEMtAtX_JDY_AXX_BXX_CXXtDXX_NDIM_VDtVTHt
6 VTHX,VTHY, YAXS, NFUL
DIMENSION KRT(2)tJT(_OOO)_RH(4OOO)t
1 U(400O),XT(4000)tKT(5),L[NC(150)_LINCI(150),LINC2(£50),
2 A(IBO)_X(6C)tCU(40)tVXI40),VY(40)_KCH(40)tAX(40)tAY(40)t
3 ATX(4OI_ATY(40),ETXI40)pETY(40)tXCU(40)_KCY(IO)tPTX(60)t
4 PTY(6_)
DIMENSION ND(3)yKRTX(lO)_KRTY(IO)tWOLT(28)200 MO=I
READ INPUT TAPE 5,10O,NH
DO 13 J=ItNH
READ INPUT TAPE 5,I07
I3 WRITE OUTPUT TAPE 6,107
READ INPUT TAPE 5tIOOtNXFtNYF,NEM,NTJtNDIM_NRL_NULtNURL_
£NCOOR, IDEC, NFUL, NCO, KRHX, KRHY
JOY = NYF
WRITE OUTPUT TAPE 6,108
IC8 FORMAT(SHO NXF,SH NYF_SH NEM,SH NTJ,SH NDIM_SH NRLtSH NULt
15H NURL_SHNCOORtSH IDECtSH NFULtSH NCOtSH KRHX_SH KRHY)
WRITE OUTPUT TAPE 6t310,NXF_NYF_NEM,NTJ,NDIM,NRLtNULtNURL_
I NCODR,IDEC,NFUL_ NCO, KRHX, KRHY
READ INPUT TAPE 5,3GO,IXO,NSPAN,NPOTX,NPOTY, YAXS
WRITE OUTPUT TAPE 6,109
109 FORMAT(SHO IXO,5HNSPAN,5HNPOTXpSHNPOTY, 8H YAXS)
WRITE OUTPUT TAPE 6_311,1XO_NSPAN,NPOTX,NPOTY, YAXS
READ INPUT TAPE 5,100,NRTN,(KRTX(K),KRTY(K),K:ItNRTN)
WRITE" OUTPUT TAPE 6,110
II0 FORMAT(SHOKRTN,SH KRTX,SH KRTY,SH KRTX,SH KRTY,SH KRTX,SH KRTY)
WRITE OUTPUT TAPE 6,310,NRTN,{KRTX(K)_KRTY(K)tK=I_NRTN)
READ INPUT TAPE 5,102,VAT,VBT,SIZE,VA,VB,VC
WRITE OUTPUT TAPE 6t111
11I FORMAT(4X3HVAT,TX3HVBT,6X4HSIZE,TX2HVA,BX2HVB_BX2HVC)
WRITE OUTPUT TAPE 6_302_VAT,VBT_SIZE,VA,VB_VC
READ INPUT TAPE 5_I02,HGH,XLOW,HSL_XLSL,VD
WRITE OUTPUT TAPE 6,112
II2 FORMAT(_X3HHGH,6X_HXLOW,6X3HHSL,TX_HXLSL,TX2HVD)
WRITE OUTPUT TAPE 6_302,HGH_XLOW,HSL,XLSL_VD
READ INPUT TAPE 5_IG2,AXX,BXX,CXX,DXX,XR
WRITE OUTPUT TAPE 6,113
113 FORMAT(_X3HAXX,TX3HBXX,TX3HCXX,TX3HDXXtTX2HXR)
WRITE OUTPUT TAPE 6,302,AXX_BXX,CXX_DXX_XR
READ INPUT TAPE 5,8_RO,EPS,XEMIT_H
WRITE OUTPUT TAPE 6_I14
II_ FORMAT(7X2HRO,IOX?HEPSILON_gXSHXEMIT,6XI3HMESH SIZE - H)
WRITE OUTPUT TAPE 6, 308, ROy EPS_ XEMIT_H
READ INPUT TAPE 5_I05,YEP,XQM,ATOM,VTH,VTHX,VTHY
WRITE OUTPUT TAPE 6,115
- 81 -
MAIN ONE -DATA INPUT MAINI
115 FORMAT{12X6HEPSNOT_6X3HXQMw6X4HATOM,6X3HVTH,TX4HVTHXt6X4HVTHY)
WRITE OUTPUT TAPE 6_I05_YEPtXQM_ATOM,VTHtVTHXIVTHY
READ INPUT TAPE 5_I02,|ATX[J)tATY|J),J=It NEM)
WRITE OUTPUT TAPE 6,119
119 FORMAT(3IHO CATHODE COORDINATES)
WRITE OUTPUT TAPE 6,302,(ATX(J),ATY(J),J=I, NEM)
READ INPUT TAPE 5,100,(KCY[J),J=I,IO]
WRITE OUTPUT TAPE 6,120
120 FORMAT(33HC PRINT-OUT OF CYCLE NO.)
WRITE OUTPUT TAPE 6,100,(KCYIJ),J=I,IO)
READ INPUT TAPE 5,104t(WOLT(NN]tNN=I_28)
WRITE OUTPUT TAPE 61116
116 FORMAT(BHO VOLT-I,TX2H-2,BX2H-3_8X2H-4,BX2H-5tBX2H-6_BX2H-?)
WRITE OUTPUT TAPE 6,304,(WOLT{NN)_NN=l,28)
HH=H**2
HT=.SmH
H2=2.*H
XMPR=.Si[FLOATF{NXFtNYF)),*2/FLOATFINXFtt2+NYF*e2)
XQM=XQM/ATOM
RX = H/YEP
J=l
IF (NDIM-2) I001_1001,2005
I001 DO 1002 I=I,NYF
IF {I-I] I006,I006ti007
I006 XT(J+3) = 0.0
XT(J+5) = -0.5
GO TO 1008
I007 IF (I-NYF] 1003,1005,1003
1005 XT[J+3) = -0.5
Xr(J+5) = 0.0
GO TO I008
1003 XT(J÷3) = -0.25
XT{J+5) = -0.25
1008 XT(J) = 0.25J
XT(J+I) = 0.25
XT{J+2) = 0.25
XT(J+4) = I.O
J = J+6
TO 2011
2010 I=I,NYF
RP= FLOATF(NYF-I)*H+RO
IC02
GO
2005 00
1009
I010
200g
I011
2008
IF (l-I) 1009,1009,1010
XT[J+3) = 0.0
XT(J+5) = -2.0*RP
GO TO I011IF (RP) 2009_2008t2009
XT{J+5) = -(RP-HT}
XT(J+3) = -(RP+HT)
XT[J) = 1.0
XTiJ+I) = RP
XT(J+2) = RP
XT(J÷4) = 4.01RP
GO TO 2010
XT(J): .125
XT[J+I)=.I25* H
XT(J+2)=.I25*H
E25
65A
- 82 -
MAIN ONE -DATA INPUT MAINI
2010
2011
XT{ J+3)=-.50 • H
XT( J+63=.75 *H
XT{J+5)=O.
J = J + 6
NDD = I
NSS=2
NTRIP=O
NPONT=NYF
KRH={KRHX-1)*NPONT+KRHY
NTOP=NPONT•NXF
KRT ( [ }=NRTN
I=2
DO 2 K=I,NRTN
KRT ( I )= (KRTX{K)-I)•NPONT+KRTY{K)
I=I+I
KT( 1 )=-NPONT
KT( 2)=NPONT
KT(3)=-I
KT(4)=O
KT{5)=+I
WRITE OUTPUT TAPE 6,117117 FORMAT(41HO BOUNDARY POINTS OF ELECTRODE SHAPE )
CALL PLOT {O.O,VCt-3)
DO 2020 NX=I,NXF
DO 2020 NY=I,NYF
IF (NTRIP} 2030t2040,2030
2040 READ INPUT TAPE 5,2035,NSj(ND(1)_I=l,3)tNXCtNYC,HEW,HNStNVOLTt
I NVOLTI,NCHECK
2035 FORMAT (IH 611,216,2F6.3,215,14)
WRITE OUTPUT TAPE 6,2035,NS,(ND(I),I=I,3)tNXCwNYC,HEW_HNS,NVOLTm
I NVOLTI,NCHECK
IF (HNS) 2031, 2032, 2031
2031 XXX=FLOATF(NXC-I)*H•VD
YYY=-(FLOATF(NYC-I)-HNS)•HmVD
CALL SYMBOL {XXX,_YY,O.07t 12,0.0,1)
2032 IF {HEW) 2033, 2G34, 2033
2033 XXX=(FLOATFINXC-I)+HEW)•H•VD
YYY=-FLOATF(NYC-I)*H*VD
CALL SYMBOL (XXX_YYY,O.07, 12_0.0,13
GO TO 2036
2034 IF (HNS} 2036, 2037t 2036
2037 XXX=FLOATF(NXC-1)*H-VD
YYY=-FLOATF(NYC-1)•H-VDCALL SYMBOL {XXXjYYY,O.07_ 12tO.Otl)
2036 NTRIP = i
KC= NPONT*{NXC-I)÷NYC
2030 K= NPONT•(NX-I}+NY
IF (K-KC) 2060,2050,2060
2060 IF {NSS-I) 2070,2070,2080
2070 IF (NY-NYF) 2071,2072,2071
2072 NSS = 2
JT(K} = I + 6•(MY-I)
VOLTI= FLOATF({NXF-NX)INXF}•VA
GO TO 2310
2071 JT{K) = I ÷ 6•(NY-1)
GO TO 2020
71A
$77
$78
$79
S80
$81
- 83 -
MAIN ONE -DATA INPUT
2239
2231
2232
2080 JT(K) = 9999
IF (NX-NCO) 2081)2020)2020
2081 IF {UIK}) 2020)2084,2020
2084 UIK) : VA
GO TO 2020
2050 NTRIP = G
NSS=NS
VOLT = WOLT(NVOLT)
VOLTI = WOLT{NVOLII}
HEW = HEW*H
HNS:HNS*H
IF (ND(3)) 2052,2052,2053
2052 VOLTI = VOLT
2053 HN = H
HS = H
HE = H
HW = H
KE = K÷NPONT
KW = K-NPONT
KN=K-1KS=K+I
JT(K}=J
IF (HEWI 2C90,2200,2100
2090 HW = - HEW
U(KW) = VOLT
GO TO 2200
2100 HE = HEW
U(KE) = VOLT
2200 IF (HNS} 2210,2230,2220
2210 HS = - HNS
U(KS) = VOLTI
GO TO 2230
2220 HN = HNS
U(KN) : VOLT1
2230 IF INDIM-2} 1004,1004,2239
1004 XT(J} = ({HN+HS)*IHE+HWI)/(16.mHH)
XT(J+I) = (HN+HS)/(B.*HW)
XT(J+2) = (HN+HS}/(8.*HE)XT(J÷3) = -(HE+HW)/(8.eHN)
XT(J÷5) = - (HE+HW)/(B.eHS)XTIJ÷4) = XTIJ+I)+XTIJ+2)-XTIJe3)-XT|J+5)
GO TD 2233RP= (FLOATF(NPONT-NY)}*H÷RO
IFIRP)2231,2232,2231
XT(J)= (HE÷HW}*IHN÷HS)II6.*HH)
XTIJ*I)=IIHN+HS)II2.*HW)I*IRP+IIHN-HS)I6.))
XT(J÷2)=HW*XTIJ÷I)/HE
XT(J÷3)=-((HW+HE)II2.*HN))m(RP÷(HNI2.))
XT(J+SI=-((HW+HE)/(2.*HS))*(RP-(HSI2.))
XTIJ÷4}=XTIJ÷I)+XTIJ+2)-XTiJ÷3)-XT(J+5)
GO TO 2233XTIJ)= IHE+HW)*IHN/I16.*HH) )
XT{J÷I)=IHN/I8.*HW) )*HXT(J÷2) = H* HN/(8.*HE)
XT(J÷3) = - H*(HE+HW)/(6.*HN)
XT(J÷4)=(HN/8.* ((HW+HE)I(HWiHE))e(HE÷HW}/(4,eHN) )*H
MAINI
134
135A
161A
- 84 -
MAIN ONE -DATA INPUT
XT(J÷5)=-O.
2233 DO 2300 I=I_2
NDA= ND(1)+I
GO TO (2300,2240,225012260t2270)_NDA
2240 XT(J+I) = XT(J÷I}+ XTIJ÷2)XT(J÷2) = 0.0
GO TO 2300
2250 XT[J÷5) = XTIJ+5) ÷XT(Je3)
XT(J÷3) = 0.0
GO TO 2300
2260 XT{J*2) =XT(J÷2) ÷XTIJ÷I)
XT(J÷/) =0.0
GO TO 2300
2270 XT(J÷3) =XT(J÷3) ÷XTIJ÷5)
XT(J+5) =0.0
2300 CONTINUE
IF (ND(3)) 2310_2310t2311
2311 XT(J) = 0.25
XT(J÷I) = Oo
XT(J÷2) = XLSL
XTIJ÷3| = O.
XT(J+4) = 1.
XT{J+5) = XLSL - 1°
2310 IF (NSS-1) 2320t2330_2340
2330 LINCI(NDD)=K
VUP = VOLT1
XT(J÷3) =-XT(J÷3)
GO TO 2320
2340 LINC2INDD)=K
LINC {NDD)= 2*XMODFINXt2) -1
VDOWN = VOLT1
KB=LINCI(NDD)
DO 2350 KK=KBtK
2350 U{KK)= VUP ÷(VDOWN-VUP)*FLOATF(KK-KB)/FLOATFIK-KB)
XT(J÷5)= -XTIJ÷5)
NOD:NDD÷I
2320 J = J + 6
2020 CONTINUE
NLIN=NDD-IIF (NCHECK - 1) 40001502_4000
4000 WRITE OUTPUT TAPE 6t4001
4001 FORMAT (24HOERROR IN BOUNDARY POINT)
CALL EXIT
502 CALL MATIN
XMAX = FLOATF(NXF-1)oH*VD ÷ 3.0
CALL PLOT (XMAXj -VC, -3)
GO TO 200
8 FORMAT (4F15o8)
100 FORMAT(1415)
I01 FORMAT(615)
102 FORMATI6FIO.4)
103 FORMAT(1315)
104 FORMAT|TFIO.6)
105 FORMAT(IOX6EIO.5)
106 FORMAT(3FIO.5)
107 FORMAT(72H
MAINI
141
- 85 -
MAIN ONE -DATA INPUT
I
300 FORMAT(41St FIO.6)
302 FORMAT(1H 6FIO.4)
304 FORMAT(IH 7FI0.4)
308 FORMAT(IH 4F15o8)
310 FORMATIIH 14IS)
3[I FORMATIIH 4IS, F[O.A)
ENDi1_O_O_O,OwO,ItOtO_OwOtO,OlO_O)
MAIN!
MATIN CALCULATES THE EIGENVALUE
SUBRqUTINF MATIN
CSPACE-CHARGE
COMMnN
I
2
3
4
5
6
I
2
3
4
SnLUTION. VLAD HAMZA MICROWAVE LABORATORY.
URH,UB,JT,RH,U,XT,KT,LINC,XR,NTOP,NUL,NLIN,ARCL,EQX,EQY,
NPIT,XEP,NXEP,CU,LINCI,AX,AY,VX,VY,DX,DELY,YEP,XQM_H,KISW,ETX,
ETY,PTY,PTX,NAJ,NTJ,VA,VB,VC,NCOOR,KCH,HSL,XLSL,EPS,NPOT,
IDEC,JOT,NSPAN,RX,NRL,KRLtKRH,VAT,VBT,SIZE,KRTtRHUP,RHDOWN,
XCU,NOT,MO,KCY,NSWP,ATX,ATY,LINC2,NXF,NYFtNURL,NJOT,XEMIT,
IXO,HGH,XLOW,XMPR,NEM, A,X,JDY,AXX,BXX,CXX,DXXtNDIMpVD,VTH,VTHX,VTHY
DIMENSION KRT{2),JT(4GOO),RH{4OOOI,URH(4000),
U(4COC),XT(4OOOI,KT(5),LINC(15OI,LINCI(15OI,LINC2(15O),
AIIBO),X(60),CU(40),VX(40),VY|40),KCH|40),AX(4OI_AY(40),
ATX|40),ATY(40),ETX(4G),ETY(40},XCU(40),KCY(IO),PTX{60I,PTY(&'])
READ INPUT TAPE 5,102,MIT,KWR
WRITE OUTPUT TAPE 6,102,MIT,KWR
C MIT=NUMBER OF ITFRATIONS ON EIGENVALUE CALCULATION
C KWR=- OR _,NO INTERMEDIATE OUTPUT
C KWR=+,PRINT INTERMEDIATE ITERATIONS ON EIGENVALUE CALCULATIONC COLUMN VECTOR INITIALIZED
50 DO 45 J=I,NTOP
IF(JT(J)-Qgqg)44,43,4343 URH(J)=O.
U(J) = C.O
GO TO 46
44 URH{J}=I.
U(J) = 0.0
46 CONTI_IUE
JS=-I
C ITERATIVE LOOP
DO 41 M=I,MITC LOOP ON NUMBER OF LINES
DO 3I NL=I,NLIN
IFILINC(NL)) 23,31,2323 KB=LINCI(NL)
KC=LINC2INL)
JV=I
JU=I
D[I 13 K=KB,KC
SUM:C,JZ:JT(K)
14 DO L5 JY=3,5
JX=JZ+JY
A(JUI=XT(JX)
15 JU=JU+I
DO 16 JY=I,2JXmJl÷JY
JW=K÷KT(JY)
I6 SUM=SUM*XT(JX)*URH|JW)
X(Jv):SU_Jv=JV÷I
13 CONTINUE
N=KC-KB÷I
CALL MATRIX(N,A(2),X)
C MATRIX IS USFD FnR THE FORWARD AND BACK SUBSTITUTION
- 8T -
MATIN CALCULATES THE EIGENVALUE
JV=l
DO 17 J=KB,KC
RH(J) =X(JV)
17 JV=JV+[
3I CONTI NUEC SWITCH ALLOWING MATRIX TO BE APPLIED TWICE
[F(JS) 32,34t34
32 D(I 33 J=I.NTOP
U(J) = URH(J)
33 URH(JI=RH(J)Gn TO "L
C DETERMIN^T[ON (3F SMALLEST AND LARGEST RATIOS FOR EIGENVALUE
34 XL=O.
XS=I.
DO _9 JD=I_NTOP
IFIURH(JD))39,39_35
35 X = RH(JD)/UIJD)
IF(XL-X)30t37t37
36 XL=X
NNL=JD37 IF(XS-X)39t39t3838 XS=X
NS=JD
39 CONTI NUEIF{KWR) 51,5It52
52 WRITE OUTPUT TAPE 6tIOItM_XS_XL,NStNNL51 YL=RH (NNL|
DO 40 JD=I_NTOP
40 URH(JD)=RH(JD)/YLIF (XL-XS-5, OE-03 )42 t_2_6L
41 JS=-JS
42 XR=SQRTF(.5*IXL+XS) )
WRITE OUTPUT TAPE 6,I03_XR
47 RETURN
IOI FORMAT(20H LOW HIGH 15,2F13.Bt 5H 216!
102 FORMAT(IAI 5)
103 FORMAT (AHOXR= FIO.8)
END( TtL_OtO,OtO_L tOtO_OtOtO_OtOtO)
-88-
_o
H
H
o
÷
-o
[
5H_
i
i
_ _ o o
o
o
NOTE: For convenience, two forms of subscript notation are used in the
flow diagrams in this Appendix. The first is the usual algebraic
notation_ for example_ NDj _ and the second employs parenthesesfor example ND(J)
- 89 -
SUM -
ARC
i i , [ ,,, i I , ,
NEM
E [(A__j - ATXj.1)2 + (ATYj - AT_L'j_I)_ 1/2J-e
SUM_RCL ,, _,_ j._.. 0.5
m'x,Y(_)= A_X,Y(1)
•= ARCL
K=I
_[,,1
"--J is K <IITJ I-],
XDIF [ A_Xj-- ATXj+ 1][DIF ATYj ATYj+ 1
sA.._XDIF2+ YDI_'
, _ NO
CSA - YDIF/SA
SNA ,,XDIF/SA
ETX(I_) = ATX(J)-HIq_SNA
YES
J=J+l
THYP = HYP - SA
m_(K) = A_(_)+m'P.CSA IK + 1
m_ K
NN NTJ + 1
_X,Y(K) = A_X,Y(mm)
- 9o-
II
I
- 91 -
CORRCT
..
CUj -- 0
T
AYD ,, AYj+ 1 - AYj
AYDS = AYj+ 1 - X_Wl = - AYj
AYDL s AYD - AYDS
+x_wl
•- LSS
% --% •AYDS/A_D
VX0. -- [FXj • AYDL + FXj+ 1 • AYDS] / AYD
v_ --[v_j•AY_ + W_+l . A_DS!/ A_
tco_i_jt
CUj_ 1 " CUj_ 1 • AYDS/AYD
AYDL _, AYD - AYDS
A_D- IAS__ -A_I
i_A_j.I < XL_Wl
7 _YES
-| I_oisJ>l?
v
2 -,
m_D
_qL. |
1- 93 -
RETURN -i.,-"
MATRIX
I --3n-2
NO
AM+ 1= 0
I x_x/Al I
YES
K= 2
IJ_4_7_lo_.°°MI
Aj = Aj - Aj_l Aj_2
Aj+I
Aj+I - Aj
X K - (Aj_ l) (XK_ l)
XK=
Aj
K=K+l
I K=K- i
_--_x_ = x_- %-J-i "xK + i
9_ _.
it
0
A
v
v+ o
_ a
--3
%
-- _ o_°ooo #•4- _ n a n H H H
m N m
DL;_ L
- 95 -
JE = NXF + 1
I JED = JE+NYF-I = 2NYF(Initially)
PE_Q
I_-_ I
I is (uK
IDIF = IUj
L=L$1
PTY(L) = _Y
I is DIF = 0
I pTxL ;u_- PO_Nl= DIF
--_AAY = AAY + DX l--V"
AAX = AAX + DX
I
_YES
NO
- uKl l
I
DX + AAX I
PTYCLL)
Pn(_)
PTX(LL)
_X(_)
_ = MAX(PTY(1)>, I = i, (L-J + i)CONV. I
_-m'X(LL)
_-TT
.-p_C(LL)
J=2, L ]
I _ Pn(_) = PTY(J- l)
YES
I _:_-_ I
JJ=J, L-I I
I PTXjj _- I_rXjj+l IPTYjj _ PTYjj+I
NO = _ YES
- 96 -
f
--II+ i
G_
LI LI tl 110
I1 II
II
I
I i.
r
n
?
tt 11 11
,_,,,
lull _
I
&5 &l II
i:o _,
_ •II II P,4
fl II II II II II II II II
o
V
m
>
t- i_1
i ii i
t_t
m
o_+ II
T
I_: t--
I_, i
_D
V ,
, I
I
LII
r-
I
' iF
,.-t
It '11
- 9? -
%1
-.,...,
_ cJ _i
I
t
m
_E^
__i_, -D.i ^ r
÷÷
-ID _I"
_ -r_
o _r-_ • _
m
.I
- g8 -
.I
I is MO = 0 I YES
R = i "R_sOF mTRIX EQUATIONJ_SPACE CHARGE DENSITY"
I__ I
I_=_ I
_rY(:<)= j
I = (N-I)_"F+ i
P'_(K)=RI{(1)*m{
K=K+I
NO 1__<_ I_s
NO
PTYjj _ _DJ --o ,JJ= K,_i|
!
[NTYL,L = 1,8][PTYL, L = 1,8] K = 1
CONTINUE
I CONTINUE
NN=NN+ 1 I
RETURN
- 99 -
i is MO = 0 I YES
_o
R-_ LWRITE "U-FIELD C_ THIS CYCLE" V
nY(K) = J
I = (N-I)NrF+_.
P_(K)= U(1)K=K+I
NO 1 I
[ NO
___ PrY_j = _rYjj _ o , JJ = K,_ I'I |
WRITE NTXNN I
[NTYL;L- 1,8][PTYL, L = 1,8] K = 1
WRITE "FIELD OF lAST CYCLE"
TW0b'_
I CONTINUE
_o_ H_-_+_
- i00 -
_m
+
+
H N
v
l n
m
b
1
"I-I_m
ii
_. +
a
L_
liii A
l +
+
w
- lO1-
REFERENCES
l.
2
3_
V. Hamzsj "Design Analysis of Electrostatic Thrustors by a Computer
Technique," Microwave Laboratory Report No. 1327, Stanford University
(May 1965).
V. Hamza and G. So Kino, "Error Analysis of a Numerical Solution to
Space-charge-flow Problems," Microwave Laboratory Report No. 1335,
Stanford University; submitted for publication to Quarterly of
Applied Mathematics, June 1965.
V. Hamza_ "Convergence and Accuracy Criteria of Iteration Methods
for the Analysis of Axially Symmetric and Sheet Beam Electrode
Shapes with an Emitting Surface_" Microwave Laboratory Report No. 1332
Stanford University; Submitted for publication to IEEE Trans. on
Electron Devices, May 1965.
_- 102-
ERRATUM to AFCRL-TDR-65-816
In DD Form 1473, last page of above report, initial date of period covered
by the report, given as 23 Mar '63 should read 21 Mar '63.
Distribution: one copy of ERRATUM sheet to all recipients of report listed
in Distribution List in report.
MCDONNEll.