UC20
DOE/ET/51013-36
PFC/RR/82-8
USER'S MANUAL FOR LINEAR, A COMPUTER
PROGRAM THAT CALCULATES THE LINEAR
CHARACTERISTICS OF A GYROTRON
Kenneth E. KreischerPlasma Fusion Center
Massachusetts Institute of Technology
Cambridge, MA. 02139
January 1982
This work is supported by DOE Contract DE-AC0278ET-51013.
I. GENERAL DESCRIPTION
A. Purpose
Calculates the linear characteristics of a gyrotron.
This program is
capable of:
1) calculating the starting current or frequency detuning for each
gyrotron mode.
2) generating mode spectra
3) plotting these linear characteristics as a function of device
parameters (e.g., beam voltage)
4) doing the above for any axial RF field profile
B. Compatibility
ANSI Standard FORTRAN IV, 1966, with some features of FORTRAN 77.
This program was written using the MULTICS operating system on the
Honeywell 68/DPS computer.
C.
Limitations
1) The electron beam parameters are calculated assuming that adiabatic
theory is valid in the gun region [1].
2) The electron beam is assumed to be annular, azimuthally symmetric,
and to have no radial thickness.
It is also monoenergtic and has
no velocity spread.
3) The cavity is assumed to be a cylindrical open resonator.
D.
Method
The starting current of a gyrotron [2] can be written as:
-2-
S
~
I ST
2
QT
2me
(KI V )2
2me
~(K
to
~ [P
e
G(r e)
1
/-2
n
Fc -
Ir L)]
1SV,
2
2
dx
where QT is the total Q of the cavity, L.is the resonator frequency, me is the
relativistic electron mass, rL is the electron Larmor radius, S = w/K,,V,,, and
V11
and V are the electron beam's parallel and perpendicular velocity re-
spectively.
The parameter lp
represents the stored energy in the cavity
and contains the factor:
1
E
=
I
g
di
12
(2)
ZIN
where g(T)
= axial. RF field profile
Z = K1 Z
ZIN,
ZOUT
=
limits of the beam-field interaction
K11 = qK/L = axial wavenumber (K is a constant)
The variable
G(re) is the beam-field coupling term, and can be written as
follows depending on the structure of the field in the azimuthal direction:
(Standing)
G(re)
=
0.25
2
Jn
2
(KI re) + m-n
(Kire)]
(3)
21
(Rotating)
G(re)
=
0.5
J1m+n
(K r )
where n is the harmonic number and r is beam radius.
The gain function Fc is
expressed in terms of the detuning parameter x = (nw C following form:
dFC
) and has the
-
(1--
-3-
tour
Fc(X)
=
2
g(Y)e
0.5
dZ
(4)
Z IN
The frequency detuning that a gyrotron experiences can be written as:
1
2QT(-ow')
Fs
2
c2
2
W
1
Fc
where
dF5
--
2
dx
(5)
dFc
(_
2 c2
dx-
w = cavity resonant frequency with beam
wO = cavity resonant frequency without beam
Fs = detuning gain fOnction
In Eq.(5), the assumption s<< Qohmic is made.
E.
Calculational procedure
In this code, the starting current or frequency detuning is considered
the y parameter.
x and 2 .
It is calculated as a function of two other parameters
A range of x must be supplied, as well as discrete values of z
As
a typical example, for a mode spectra the starting current would be calculated
as a function of resonator magnetic field (x) for each gyrotron mode (z-).
F.
Notes
1) All parameters are in MKS units.
2) All data is inputted as real numbers unless otherwise noted.
REFERENCES
1. A.L. Gol'denberg and M.I. Petelin, Radiophysics and Quantum Electonics
16, No. 1 (1973) 106-111.
-4-
2. K.E. Kreischer and R.J. Temkin, Int. J. Infrared and Millimeter Waves
1, No. 2 (1980) 195-223.
Also, K.E. Kreischer, M.I.T. Plasma Fusion
Center Research Report PFC/RR-81-1, to be published in Infrared and
Millimeter Waves, edited by K.J. Button.
3. K.E. Kreischer and R.J. Temkin, Int.J. Infrared and Millimeter Waves 2,
No. 2 (1981) 175.
II.
INPUT AND OUTPUT
A. Variables
Eleven device parameters are required to calculate linear characteristics.
Each is referenced by a twoletter abbreviation.
The following is a table of
these parameters with their abbreviations and dimensions:
PARAMETER
ABBREVIATION
DIMENSIONS
Beam voltage
VB
volts
Anode voltage
VA
volts
Cavity magnetic field
BR
testla
Cathode magnetic field
BC
tetla
Mode
MO
none
Cavity radius
RR
meter
Cavity length
LE
meter
Cathode/anode distance
DC
meter
Ohmic Q
QO
none
Diffractive Q
QD
none
Cathode radius
RC
meter
B. File INPUT.DAT
This file, which consists of three-lines, provides information needed by the
program
1. PAR(l), PAR(2),.
,
PAR(ll)/
PAR(N) = default value of nth variable listed in A.
2. MODE(l), ZERO(l), MODE(2), ZERO(2)....,MODE(N), ZERO(N)/
MODE(N) = index of nth mode.
For TE mpq
ZERO(N) = transverse index of nth mode.
3m(x) = 0
MODE = mp.
For TEmpq
the Pth zero of
-6-
3. K, Es, QTOT, Q(l), X(l), Q(2), X(2),...,Q(QTOT),X(QTOT)/
K
=
axial wavenumber constant (see Section I.D.).
IE:= stored energy factor (see section I.D.).
QTOT
=
number of q branches calculated for each TE
Q(N)
=
value of q for nth branch.
X(N)
=
approximate value of detuning parameter X corresponding to
mode.
nth branch [3].
C. Other Information required during program execution
1. VAR, VALUE
An opportunity to change default value is given.
2. IMODE
IMODE = parameter indicating whether starting current or detuning is
desired.
3. PARX, XMIN, XMAX
PARX = two letter representation of x parameter.
XMIN = lower limit of x parameter.
XMAX = upper limit of x parameter.
4. YMIN, YMAX
YMIN = minimum value of starting current or frequency detuning.
YMAX = maximum value of starting current or frequency detuning.
5. ZPAR, ZNO, Z(1), Z(2),...,Z(ZNO),/
ZPAR = two letter representation of z parameter.
ZNO
= number of z values to be inputted.
Z(N) = value of nth z parameter.
6. ICROS
ICROS = parameter indicating cross-sectional structure of RF field.
-7-
7.
IPROF
IPROF = parameter specifying type of axial RF profile.
(see Section II.D if you are specifying profile)
8. NHAR
NHAR = harmonic number.
At this point, desired data will be calculated, followed by a prompt for
type of output.
9. IOUT
IOUT = parameter specifying type of output. IOUT = 3 terminates
program.
D. Files and information needed if profile is specified
1. LINPROF. FORTRAN
A Fortran subroutine must be included with the program that contains
the axial profile of the RF field.
It should have the following form:
SUBROUTINE LINPROF (Q,Z)
Z = G (Q,Z)
RETURN
END
In this routine, you would provide the axial profile as the function
G. Note that Q is the axial index of TE
.
2. If the profile is specified, the parameters K and Es of INPUT.DAT
are ignored.
The constant K is asked for specifically, and Es is
calculated within
the program.
-8-
E. Tabular output
1. Heading title.
2. Date and time of program execution.
3. List of variables and their values.
The x and z parameters are
set to zero.
4. Tables of detuning or starting current data for each case requested.
Each table is headed by q and z parameter values.
-9-
III.
SAMPLE RUN
A. The file INPUT.DAT
6.5e4,2.e4,5.57,.2i9,3..3.47e-3,1.5e-2,4.e--3,2.e4,1.16e3,9.18e-3,30./
11..,1.8412,21.,3.0542,i.,3.8317.31..4.2012,41.,5.3176,12.,5.3314,
51.,6.4156,22.,6.7061,2.,7.0156,61..7.5013,32..8.0152,13.,8.5363,
71.,8.5778.42..9.2824,81..9.6474,23..9.9695,3.,10.1735,52.,10.5199,
91.,10.7114,33.,11.3459,14.,11.7060,62.,11.7349,101.,11.7709,
43..12.6819,111.,12.8265,72.,12.9324,24.,13.1704,4.,13.3237,121.,
13.8788,53.,13.9872,82.,14.115,34.,14.5858,15..14.8636,131.,14.9284,
63.,15.2682,92.,15.2867,44.,15.9641,141.,15.9754,25..16.3475,102.
16.4479,5.,16.4706,73.,16.5294,151.,17.0203,54.,17.3128.112.,17.6003/
3.14159,0.5,3.,1.,-1.,2.,.4,2.,-1.4/
-TO-
B. Terminal input
vb=
bc=
le=
ad=
0.650E+05
0.219E+00
0.150E-01
0.116E+04
va=
mo=
dc=
rc=
Anv changes? .Print
br= 0.557E+01
rr= 0.347E-02
ao= 0.200E+05
0.200E+05
0.300E+01
0.400E-02
0.918E-02
'not/'
or Oparameter-tvalue'
no,/
Choose Plot tve*#(inteser)
(1)Starting current vs. two parameters
(2)Detuning vs. two parameters(sine Profile)
1
Input x ParamieteriaaaririnimunimaxIfimun
br,5.2,5.8
Input w Parameter minimumpmaximum
0.,10.
Input z parameter*aarno. of valuestvaluelvalue2p....Y/
mo 2.,3.23. /
Choose cross-sectional structurel(integer)
(1)Rotating
(2)Standing
2
Choose axial Profile'(integer)
(1)Sine
(2)Gaussian
(3)Profile wou have specified
1
Input harmonic
number(integer)
1
Select output format#(integer)
(1)Table
(2)Graphics
(3)Neither
1
Input table heading in apostrophes
Starting current for TE(031)
and
TE(231)
modes'
-11-
C. Terminal Output
Startinz current for *FE(031) and TE(231)
1131.5 est Thu
01/21/82
vb=
bc=
le=
od=
0.650E+05
0.219E+00
0.150E-01
0.116E+04
va=
010=
dc=
rc=
modes
br= 0.OOOE+00
rr= 0.S47E-02
no= 0.200E+05
0.200E+05
O.OOOE+00
0.400E-02
0.918E-02
Standing cross sectional structure.
All data is in MKS units.
mo= 0.300E+01
a = 0.100E+01
br
ISTART
0.5625E+01
0.5610E+01
0.5596E+01
0.5581E+01
0.5567E+01
0.5552E+01
0.5538E+01
0.5523E+01
0.5509E+01
0.5494E+01
0.5480E+01
0.5465E+01
0.5451E+01
0.5436E+01
0.5422E+01
0.5408E+01
0.5393E+01
0.5379E+01
0.5364E+01
0.5350E+01
0. 1290E+02
0.2891E+01
0. 1739E+01
0.1320E+01
0.1123E+01
0.1028E+01
0.9934E+00
0. 1003E+01
0.1051E+01
0.1140E+01
0.1279E+01
0.1481E+01
0.1776E+01
0, 2206E+01
0.2854E+01
0.3869E+01
0.5562E+01
0.8651E+01
0. 1520E+02
0.3395E+02
mo= 0.300E+01
a = 0.200E+01
br
0.5800E+01
0.3795E+01
0.5790E+01
0.5785E+01
0.780E+01
0.5774E+01
0.5769E+01
0.5764E+01
0.5759E+01
0.5754E+01
0.5749E+01
0.5744E+01
0.5739E+01
0.5733E+01
0.5728E+01
0.5723E+01
0.5718E+01
0.5713E+01
0.5708E+01
0.5703E+01
mo= 0.300E+01
a = 0.200E+01
ISTART
br
ISTART
0.3155E+01
0.2984E+01
0.2862E+01
0.2781E+01
0,2735E+01
0.2721E+01
0.2739E+01
0.2789E+Ot
0. 2873E+01
0.2997E+01
0.3169E+01
0.3401E+01
0.371 4E+01
0.4140E+01
0.4733E+01
0.5594E+01
0.6928E+01
0.9223E+01
0.1401E+02
0.2974E+02
0.5504E+01
0.5492E+01
0. 1465E+03
0.1730E+02
0.9847E+01
0.7300E+01
0.6113E+01
0.5515E+01
0.5249E+01
0.5209E+01
0.5357E+01
0.5688E+01
0.6224E+01
0.7015E+01
0.8150E+01
0.9778E+01
0. 1216E+02
0. 1577E+02
0.2155E+02
0.3161E+02
0.5175E+02
0.1050E+03
0.'5480E+01
0.5468E+01
0.5456E+01
0.5444E+01
0.5432E+01
0.5420E+01
0.5408E+01
0.5396E+01
0.5384E+01
0.5372E+01
0.5360E+01
0.5348E+01
0.5336E+01
0.5324E+01
0.5313E+01
0.5301E+01
0.5289E+01
0.5277E+01
-12-
C. Terminal Output (continued)
br
ISTART
0. 5S12E+01
0.5497E+01
0.5482E+01
0.5467E+01
0.5453E+01
0.5438E+01
0.5423E+01
0.5408E+01
0.5393E+01
0.5379E+01
0.5364E+01
0.5349E+01
0.5334E+01
0.53i9E+01
0.5304E+01
0.5290E+01
0.5275E+01
045260E+01
0.5245E+01
0.5230E+01
0.3672E+02
0.4108E+01
0.2340E+01
0.1744E+01
0.1472E+01
0. 1343E+01
0. 1296E+01
0.1308E+01
0. 1372E+01
0.1490E+01
0. 1674E+01
0. 1943E+01
0.2334E+01
0.2906E+01
0.3767E+01
0.5118E+01
0.7368E+01
0.1147E+02
0.2015E+02
0,.4474E+02
0. 5730E+01
0*5723E+01
0.5715E+01
0.5708E+01
0.5701E+01
0,5693E+01
0.5686E+01
0.5679E+01
0.5671E+01
0.5664E+01
0.5657E+01
0.5649E+01
0.5642E+01
0.5634E+01
0.5627E+01
0.5620E+01
0.5612E+01
0.5605E+01
0.5598E+01
0.5590E+01
Select output foroiat: (integer)
(1)Table
(2)Graphics
(3)Neither
r 11:32 12.899
90
0.230E+02
0.200E+01
mo= 0.230E+02
a . 0.200E+01
mo= 0.230E+02
a = 0.100E+01
ISTARI
br
ISTART
0. 1652E+02
0.9316E+01
0.6624E+01
0.5250E+01
0.4443E+01
0.3935E+01
0.3611E+01
0.3410E+01
0.3303E+01
0.3276E+01
0.3324E+01
0.3450E+01
0.3671E+01
0.4015E+01
0.4536E+01
0.5341E+01
0.6659E+01
0.9082E+01
0.1473E+02
0.4092E+02
0.5387F+01
0.5377E+01
0.5367E+01
0.5358E+01
0.5348E+01
0.3338E+01
0.5328E+01
0.5318E+01
0.5308E+01
0.5298E+01
0.5289E+01
0.5279E+01
0.5269E+01
0.5259E+01
0.5249E+01
0.5239E+01
0.5230E+01
0,5220E+01
0.5210E+01
0.5200E+01
0.4064E+03
0.2895E+02
0. 1588E+02
0,1146E+02
0*9329E+01
0.8156E+01
0.7487E+01
0.7130E+01
0.6996E+01
0.7042E+01
0.7249E+01
0.7621E+01
0.8171E+01
0,8933E+01
0.9958E+01
0. 1133E+02
0.131.6E+02
0. 1564E+02
0. 1909E+02
0.2402E+02
-13-
IV.
PROGRAM LISTING
-14-
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