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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.
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- 41 -
++.+...._,.°+..°°..+.+++
• . • • • • , • • , • • • • • • • • • • • • • •
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• • • • . • • • • . • • • • • • . • • • • • • •
co ,_ c_ co co co c_
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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
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ggdgggg_g g_,g_g,_g,_dg gdgJ, gdgg_'d
Iii+++i.+.++i..-i+....+.
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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
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< _ N 0 _J N 0 0 N 0 0 _I c) _ i_ o 0 N _} 0 N 0 u N (-_ 0
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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
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_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
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.- 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.
