Strict control of rf field amplitude and phase must be maintained ... current beam and to prevent spilling of high energy particles within ... and the necessity for continuous control in the presence of beam loading ..... Fit of experimental phase response of the Mickey Mouse ...... The cellular structure is then utilized to express ...
,-. u
LA-3372
LOS ALAMOS
SCIENTIFIC LABORATORY of the University of California LOS ALAMOS
●
Analysis
NEW MEXICO
of a
Proton Linear Accelerator
RF
System
I
and Application
to RF Phase Control
—
FOR REFERENCE NOT TO BE TAKEN
FROM
THIS
ROOM
CAT. NO. 193s
I
I
L———
4
ATOMIC
UNITED STATES ENERGY COMMISSION
CONTRACT W-7405-ENG. 36
LEGAL
NOTICE
This report was prepared as anaccount of Government sponsored work. Neither the United States, nor tbe Commission, nor any person acting on behaif of the Commission: A. .Makes any warranty or representation, expressed or impiied. with respect to the accutheuse racy, completeness, or usefulness of the reformation contained in Utia report, or that of any Information, apparatus, method, or process dlscloaed in thhs report may not infringe privately owned rights: or . B. Assumes any liabllltles with respect to the uoe of, or for damages resulting from the uae of any Information. apparatus, method, or process disclosed in tttls report. As used in the above, “person acting on bebaif of the Commlaalon” Inciudea any empioyee or contractor of tbe Commission, or empioyee of such contractor, to tbe extent that such empioyee or contractor of “he Commission, or empioyee of such contractor prepares, disfiemlnateo, or provides access to. any information pursuant to ht.s employment or contract with ‘&e Commission, or his employment with such contractor.
Thts report expresses the opinions of the author or authors and does not necessarily reflectthe opinions or vfews of the Los Alamos ScientificLaboratory.
Printed in USA.
Price $7.00.
Available from the
Clearinghouse for Federal Scientific and Technical Information, National Bureau of Standards, U. S. Department of Commerce, Springfield, Virginia
LA-3372 UC-28, PARTICLE ACCELERATORS AND HIGH-VOLTAGE MACHINES TID-4500 (45thEd. )
LOS ALAMOS
SCIENTIFIC LABORATORY of the University of California LOS ALAMOS s NEW MEXICO
Report written: June 1965 Report distributed: November 8, 1965
Analysis
of a
Proton Linear Accelerator and Application
RF System
to RF Phase Control* by
Robert A. Jameson
*This reportwas takenfrom a thesissubmittedto the Universityof Colorado for the Degree of Doctor of Philosophy,Department of ElectricalEngineering.
i
.
ABSTRACT Strict control of rf field amplitude and phase must be maintained in the proton linear accelerator proposed for the LOS Alamos Meson Physics Facility to insure the quality of the 800 MeV, 1 m4 average “ current beam and to prevent spilling of high energy particles within the machine. The rf control problem is of particular importance in this linac because of the high beam intensity, the requirement for a frequency transition which effectively reduces particle acceptance, and the necessity for continuous control in the presence of beam loading transients. The general transient behavior of the accelerating structure ~ is derived using an equivalent circuit, and functions describing rf field phase and amplitude envelope responses are obtained for control system design. Experimental verification of the theory is presented. The combination of the accelerator structure and the rf amplifier which drives it through a long waveguide feed is analyzed. The magnitude of beam loading effects in the accelerator is discussed. The problem of providing a phase reference is examined, and the properties of direct comparison rf phase detectors and various microwave phase shifters are analyzed. The characteristics of these individual elements are combined in a study of the phase control system. Design criteria are established, and an example meeting these criteria is developed in detail. Digital computer programs were used in various parts of the work. Of particular importance to linear accelerator technology is the new understanding of the accelerator structure transient behavior, and the general conclusion that a practical, reliable phase control system meeting the strict accelerator specifications is feasible.
ACKNOWLEDGEMENTS This work was done under the auspices of the Atomic Energy Commission in Group MP-2 of the Meson Physics Division at the Los Alamos Scientific Laboratory, operated by the University of California at Los Alamos, New Mexico. The continued support and encouragement of Dr. D. E. Nagle, Associate MP Division Leader, are gratefully acknowledged. The author is especially indebted to Dr. Howard B. Demuth, LASL Group K-4, who directed this research at Los Alamos and served on the University of Colorado advisory committee. The supervision and guidance given by the Electrical Engineering Department of the University of Colorado, especially by Professor C. T. A. Johnk who acted as chairman of the PhD advisory committee, are sincerely appreciated.
iii
(
I
TABLE OF CONTENTS
I.
II.
Introduction A.
General Description of Accelerator
B.
General Description of the Accelerator RF Systems
c.
Background and Scope
D.
Summary and Outline of Some Possibilities for Future Work
Specifications for the Control of the RF System A.
III.
RF Phase and Amplitude Stability 1.
Introduction
2.
Calculations
3.
Control System Phase and Amplitude Tolerances
4.
Time Period of Phase and Amplitude Tolerances
B.
Frequency Tolerance
c.
Sequence of Events During RF Pulse
The 805 Mc Accelerating Structure A.
Equivalent Circuit Approach to the Transient Analysis of Cavities
B.
1.
Introduction
2.
Cavity-CircuitAnalogy
3.
Problems Involved in Analysis
Ceneral Transient Solution 1.
Derivation of General Transfer Function
2.
Discussion of General Transfer Function
3.
Example
4.
Discussion
v’
c.
D.
E.
IV.
Computer Solutions 1.
Ana log
2.
Iterative Solution of the Differential Equations
3.
Inverse Laplace Transform Solution
Phase and Amplitude Envelope Responses 1.
Introduction
2.
The General Envelope Function
3.
Envelope Responses to Certain Known Inputs
4.
Comparison of Results
5.
Small Signal Transfer Functions
6.
Sumary
Experimental Results 1.
Introduction
2.
The Accelerator Structure
3.
Amplitude Response to Amplitude Step in Drive
4.
Phase Response to Amplitude Step in Drive
5.
Amplitude Response to Phase Step in Drive
6.
Phase Response to Phase Step in Drive
7.
Other Results
8.
Summary
Characteristics of the “Controlled Elements” A.
The RF Amplifier 1.
Introduction
2.
General Description of Amplifier
3.
Intermediate Power Amplifier
4.
High Power Amplifier
vi
B.
The RF Amplifier - Waveguide Feed - Accelerator Tank Combination 1.
Introduction
2.
Transmission Line Equations
3.
Solution for Current at Load
4.
Solution for Non-Perfect Matching at the Load
5.
Conclusions
6.
Note:
Evaluation of Reflection Coefficients Using
Two Terms of Y(P) c.
v.
Beam Loading 1.
Introduction
2.
Basic Assumptions and Questions
3.
Steady-State Conditions
4.
Transient Considerations
5.
Conclusions
Characteristics of the “Controlling Elements” A.
Reference Frequency Generation and Signal-to-Noise Requirements
B.
1.
Specification
2.
The Phase Reference
3.
Phase Stability
4.
Application
5.
Conclusions
Phase Comparator 1.
Analysis of Direct Comparison Phase Detectors General vii
c.
VI.
2.
“Effect
of Input Sigml Amplitudes
3.
Effect of Changes in Detector Efficiencies
4.
Effect of Changes in Detector Law
5.
Sensitivity Near the Null
6.
Choice of Parameters
7.
A Practical Phase Detector
Phase Shifter 1.
General Requirements
2.
Survey of Phase Shifters
3.
Small-Signal Representation
Small-Signal Control Loop Study A.
Introduction
B.
Block Diagram 1.
Typical 805 Mc Tank Transfer Functions
2.
Transit Phase Changes in the HPA
3.
Beam Loading
4.
Phase Shifter
5. c.
‘Phase Comparator
Expected Inputs 1.
Random Disturbances
2.
Systematic Disturbances
D.
Performance Criteria
E.
Design Procedure 1.
Series Compensation
2.
Feedback Compensation
viii
F.
Example 1.
Block Diagram
2.
Frequency Domain Design
3.
Performance
4.
sulmnary
ix
—
.
LIST OF FIGURES
I-A-1.
Alvarez 201.25 Mc Accelerating Structure.
I-A-2.
Cloverleaf 805 Mc Accelerating Structure.
I-B-1.
Facility Block Diagram.
I-B-2.
Sector A Block Diagram, 201.25 Mc.
I-B-3.
Sectors B - F, Module Block Diagram,
I-c-1.
General Control System Block Diagram.
II-A-1.
Acceptance Change at Frequency Transition.
IS-A-2.
Probability density functions of phase emittance increase
805 Mc.
in an Alvarez lime due to random tank-to-tank phase and Phase errors chosen randomly
amplitude errors. a. between ~ 2°.
b. Amplitude errors chosen randomly
between & 2%. II-A-3.
Phase-amplitude error limit trade-off curve for an Alvarez linac with f)s= 30°.
II-C-1.
RF Pulse Structure.
III-A-1.
Equivalent Circuit for the 805 Mc Accelerating Structure.
III-B-1.
Dispersion curve for N coupled identical resonators.
III-B-2.
Dispersion curve for coupled resonators of alternating kinds.
III-C-1.
Response of Cell No. O to drive pulse. below pi-mode resomnce.
Frequency 100 Kc
The initial overshoot and the
momentary reinforcement which occurs after the drive is turned off are typical transient phenomena seen for off-resonance drives. The reinforcement, however, also occurs for on-resonance drives in cells far removed from the drive. See Fig. III-C-8. x
III-C-2.
Amplitude response of Cell No. O to drivo pulse.
Fre-
quency 50 Kc below pi-mode resonance. The “steady-state” part of the off-resonance drive response is characterized by scallops which result from beating between the drive frequency and the nearby mode frequencies. III-c-3.
Amplitude response of Cell No. O to drive pulse. Frequency - pi-mode resonance.
III-c-4
Amplitude response of Cell No. O to drive pulse. Frequency - 50 Kc above pi-mode resonance.
III-c-5.
Amplitude response of Cell No. O to drive pulse. Frequency - 100 Kc above pi-mode resonance.
III-c-6●
Amplitude response of Cell No. 19 to drive pulse. Frequency - 100 Kc below pi-mode resonance.
III-c-7.
Amplitude response of Cell No. 19 to drive pulse. Frequency - 50 Kc below pi-mode resonance.
III-c-8.
Amplitude response of Cell No. 19 to drive pulse at pimode resonance. Note momentary reinforcement which occurs after drive pulse is turned off.
This effect is
greater as the distance from the drive is increased. III-c-9.
Amplitude response of Cell No. 19 to drive pulse. Frequency - 50 Kc above pi-mode resonance.
III-C-1O. Amplitude response of Cell No. 19 to drive pulse. Frequency - 100 Kc above pi-mode resonance. III-C-11. Phase response of Cell No. O to drive pulse turn-on.
xi
III-C-12.
Phase response of Cell No. O to drive pulse turn-on, continued.
III-C-13.
Phase response of Cell No. 19 to drive pulse turn-on.
III-C-14.
Phase response of Cell No. 19 to drive pulse turn-on, continued.
ITS-C-15.
Amplitude and phase responses of Cell No. O to a +2% amplitude step applied to a steady-state, on-resonance pi-mode drive.
III-C-16.
Amplitude and phase responses of Cell No. 19 to a +2% amplitude step applied to a steady-state, on-resonance pi-mode drive.
III-C-17. Phase response of Cell No. O to a 180° phase step applied to a steady-state, on-resonance pi-mode drive. III-C-18. Amplitude response of Cell No. O to a 180° phase step applied to a steady-state, on-resonance pi-mode drive. III-C-19. Phase response of Cell No. 19 to a 180° phase step applied to a steady-state, on-resonance pi-mode drive. 111-C-20. Amplitude response of Cell No. 19 to a 180° phase step applied to a steady-state, on-resonance pi-mode drive. III-C-21. Phase and amplitude responses of Cell No. O to a +2° phase step applied to a steady-state, on-resonance pi-mode drive. III-c-22.
Phase and amplitude responses of Cell No. 19 to a +2° phase step applied to a steady-state, on-resonance pi-mode drive.
xii
III-D-l.
Exact and approximate computed envelope responses of the rf field amplitude and phase in a typical cell to a pulse of rf drive.
1X1-D-2.
Exact, approximate, and transfer function solutions for the rf amplitude and phase envelope responses in a typical cell to a 2% step increase in drive amplitude from steady-state.
III-D-3.
Exact and approximate computed rf amplitude and phase envelope responses in a typical cell to a 180° step phase change in the drive from steady-state.
III-D-4.
Exact, approximate, and transfer function solutions for the rf amplitude and phase envelope responses in a typical cell to a 2° step change in the drive phase from steady-state.
III-E-1.
The ‘?+iickey Mouse” - an experimental fi/2-moderesonantly coupled side-cavity structure.
III-E-2.
Dispersion curve for the experimental Mickey Mouse Structure.
III-E-3.
Experimental setup for amplitude response to amplitude step in drive.
III-E-4.
Experimental response
of rf field amplitude in the
Mickey Mouse Structure to a pulse of rf drive. III-E-5.
Experimental setup for phase response to amplitude step in drive.
III-E-6.
Qualitative experimental rf phase responses in the Mickey Mouse Structure to a pulse of rf drive.
xiii
a.
Drive 10 Kc
below x/2-mode resonance. b. c. III-E-7.
Drive at fi/2-moderesonance.
Drive 10 Kc above n/2-mode resonance.
Experimental rf phase response of the Mickey Mouse Structure to a pulse of rf drive at x/2-mode resonance.
III-E-8.
Fitting to the parameters ~ and SSPHI of the experiments1 rf phase response of the Mickey Mouse Structure to a pulse of rf drive.
III-E-9.
Experimental rf amplitude response of the Mickey Mouse structure to a 72° phase,step in the drive.
III-E-1O. Experimental rf amplitude response of the Mickey Mouse structure to a 72° phase step in the drive
(expanded) .
III-E-11. Amplitude disturbance in the Mickey Mouse structure due to a 72° step phase modulation in the drive shown on top of the main drive pulse. III-E-12. Experimental response of rf phase in the Mickey Mouse structure to a phase step of 130° in the drive. III-E-13. Fit of experimental phase response of the Mickey Mouse structure to a phase step of 130° in the drive to the theoretical phase response. III-E-14. Experimental rf phase response of the Mickey Mouse structure to a 20° phase step in the drive. III-E-15. Lissajous presentation of the Mickey Mouse structure phase response to a 20° phase step in the drive. III-E-16. a.
Input rf pulse to Cell No. 5 of an N = 10 iris-loaded
waveguide structure. b. Amplitude response of Cell No. 1 of anN=
10 iris-loaded waveguide structure to a pulse of rf
drive, showing slight reinforcement at pulse turn-off.
xiv
IV-A-I.
High power amplifier equivalent circuit.
IV-A-2.
Simplified HPA equivalent circuit.
IV-A-3.
HPA equivalent circuit from accelerator point of view.
IV-A-4.
Coaxitron Plate Modulator Circuit.
IV-A-5.
Coaxitron Plate Modulator Equivalent Circuit.
IV-B-1.
HPA equivalent circuit frcm accelerator point of view.
IV-B-2.
An eleanentdx of a transmission line.
Iv-B-3.
Transmission line reflection terms.
IV-C-1.
Equivalent circuit for a cavity driven by an rf amplifier with internal impedance, and beam loading represented by the perfect source VB.
Iv-c-2
.
IV-C-3.
Steady-state cavity field relations for beam loading of 40%. Steady-state relations showing changes in drive to compensate for beam loading of 40%.
IV-C-4.
Block diagram of beam loading equivalent which does not affect the power amplifier circuitry.
V-A-I.
General Phase Control System.
V-A-2.
Frequency Stability of Oscillators.
V-A-3.
Additive Noise Representation.
V-A-4.
Non-linear Noise Representation.
v-A-5.
Plots of maximum RMS fractional frequency deviation and maximum RMS phase deviation as a function of oample the for the S Mc output of Hewlett-Packard Models 107AR and 107BR Quartz Oscillators.
xv
v-A-6 .
Approximate maximum RMS fractioml frequency deviation and maximum RMS phase deviation as a function of sample time for the 805 Mc output of a Hewlett-Packard 8614A Signal Generator synchronized by a Dymec 2654A Oscillator Synchronizer to a Hewlett-Packard 107BR 5 Mc Quartz Oscillator.
V-B-1.
Input amplitude sensitivity of a two output phase detection system.
V-B-2.
Output of a phase bridge with detector efficiencies of 1.0 and detector laws of 1.3, as a function of the rf input signal amplitude ratio, K.
V-B-3.
Phase error resulting from interpreting AS = O as zero phase difference between inputs when detector efficiencies are unequal.
V-B-4.
Output of a phase bridge with detector efficiencies of 1.0 and 0.95, and detector laws of 1.3, as a function of the rf input signal amplitude ratio, K.
V-B-5.
Phase error resulting from interpreting zero bridge output as zero phase difference between the inputs when the detector laws are not equal.
v-B-6 ●
Output of a phase bridge with detector laws of 1.30 and 1.32, and equal detector efficiencies, as a function of the input rf signal amplitude ratio, K.
V-B-7.
Schematic of experimental phase bridge.
v-B-8.
Photograph of experimental phase bridge.
V-B-9.
Phase bridge schematic circuit.
V-B-1O.
Calibration curve for the experimental phase bridge.
xvi
v-c-l.
Phase shift,
insertion loss, and VSWR vs. DC bias voltage
characteristics for a Sanders Associates varactor phase shifter operating with 5 mw input at 805 Xc. VI-B-1.
General block diagram showi~ major components of the phase and amplitude control loops and interactions between loopsc
VI-B-2.
Frequency response of
●
typical 805 UC HPA and accelerator
tank combination. VI-B-3.
Phase response of a typical 805 Mc HPA-accelerator tank combination to a phase step of 20°.
VI-B-4.
Amplitude response of a typical 805 Mc HPA-accelerator tank combination to a phase step of 20°.
VI-B-50
Phase response of a typical 805 Mc HPA-accelerator tank combination to a 20% amplitude step.
VI-B-6*
Amplitude response of a typical 805 Mc HPA-accelerator tank combination to a 20% amplitude step.
VI-B-7.
Block diagram of phase and amplitude control loops for a typical LAMPF 805 Mc module.
VI-E-1.
Series ccnupensatedcontrol system wfth noise inputs.
n-E-2.
General block diagram of a control system with series or feedback compensation, with noise inputs.
,VI-F-1.
Example control system block diagram.
VI-F-2.
Frequency domain design curves for the example phase control system of Fig. VI-F-1.
VI-F-3c
Stabilizing network HI.
VI-F-4.
Frequency response of the minor loop open-loop gain
xvii
function, Am. VI-F-5.
Frequency response of the major loop open-loop gain function with the minor loop open, %“
VI-F-6.
u Frequency response of the major loop open-loop gain function with the minor loop closed, %“
VI-F-7.
Closed loop frequency response of A@/&.
VI-F-8.
Response of A#Ito a A@D step of 10°.
VI-F-9.
Response of AVB to a A$D step of 10°.
VI-F-1O.
Frequency response of A$/A6B.
VI-F-11.
Response of A@ to a A@B step of 10°.
VI-F-12.
Response of AVB to a AeB step of 10°.
VI-F-13.
Frequency response of A@/N.
VI-F-14.
Response of A@ to an N step of 10°.
VI-F-15.
Response of AVB to an N step of 10°.
VI-F-16●
Response of A@ to combined step disturbances of AE = 20% and AOB = 10°.
VI-F-17.
Response of AVB to combined step disturbances of AE=
VI-F-18.
20% and AOB = 10°.
Response of A@ to combined step disturbances of AE = 20% and A6B = 10° for the “beam-loaded” case.
VI-F-19.
Response of AVB to combined step disturbances of AE = 20% and he = 10° for the “beam-loaded” case. B
xviii
Introduction - Chapter 1
I-A-1
A.
~nera lM The
scrivtion of Accelerator
proposed Los Alamoa Meson Physics Facility (IAMPP) will be a
research tool for studies in nuclear physics, providing a primary high intensity beam of 800 MeV protons, lower intensity polarized proton beams fran a linear accelerator, and secondary beams of pions, muons, neutrons and neutrinos. The outstanding feature
of the facility is
the high average intensity of the accelerated beam, one milliampere average current. Existing proton linear accelerators have average * beam currents of about 0.02 pamps at 68 MeV. The accelerator is arranged as follows, in the order of beam passage. 1. 2. 3. 4. 5. 6.
Injectors Injector Beam Transport System “Alvarez” Section of the Linear Accelerator “Cloverleaf” Section of the Linear Accelerator Target Area Transport System Secondary-Beam Transport System
At the injector, protons are extracted from an electrical discharge in hydrogen gas in an ion source, and accelerated to an energy of 750 KeV by a steady DC field in a Cockcroft-Walton type accelerator. Both high intensity and polarized ion sources will be used. The injector beam transport system consists of focusing magnets and RP bunching cavities which manipulate the beam to the desired configuration for injection into the linear accelerator (linac). After entering the linac, the protons are accelerated to a final energy of about 800 MeV.
The acceleration is along a straight line,
as implied by the name linear accelerator. *
University of Minnesota Proton Linear Accelerator
I-A-2
The linac accelerating structures are of two types. From 0.75 MeV to about 175 MeV, the protons travel through five Alvarez-type tanks in series. An Alvarez tank is a cylindrical, electrically resonant cavity excited in the TMolo mode, at 201.25 Mc in the LAMPF case.
In
this mode, the axial electric field strength is independent of position along the axis. The electric field is a vector oscillating at the rf frequency, and thus is in the proper direction for beam acceleration only for a part of each cycle. Annular drift tubes are spaced along the axis such that the protons are in the gaps when the field direction is right for acceleration, and within the shielding drift tubes when the field is in the decelerating direction. The Alvarez tanks will be driven by five separate 201.25 Mc rf amplifiers.
I
SUPPORTING
[
pcl
II
STEMS
r’)m[p~ DRIFT
)(
“lAdL(
1[
TUBES
~ QUADRUPLE
MAGNETS ‘7
Fig. I-A-1. Alvarez 201.25 Mc Accelerating Structure Now, protons do not exhibit relativistic behavior until their energy is about 1 BeV.
Thus, the protons traveling through the LAMPF
linac will continuously gain velocity as well as mass - the velocity increasing from about 0.04 times the speed of light at injection to about 0.9 times the speed of light at the final energy of 800 MeV.
I-A-3
Because of the :hange in velocity, each section of the accelerating structure must ~e different. In the case of the Alvarez structure, the drift tubes must become progressively longer. Unfortunately, as the drift tubes become longer, the shunt impedance of the structure decreases. The efficiency with which an”accelerating structure Imparts energy to a beam decreases with a decrease in the shunt impedance which the structure presents to the rf drive; and the Alvarez structure is no longer practical at energies greater than about 175 MeV. Therefore, a transition is made after the fifth Alvarez tank to a second type of accelerating structure, called the “Cloverleaf”. In this section, the beam passes axially through 90 tanks in series. The tanks are standing wave, loaded waveguide structures - each is about 20 feet long and has 40 septums which form half-cells at the ends.
39 full cells and two
These tanks operate at 805 Mc, the fourth
harmonic of the frequency of the Alvarez tanks. The axial length of the cells is designed so that the protons traverse each cell in a time equal to one-half the period of the rf driving frequency. The tanks are driven at the pi-mode, that is, the electric field in each cell is arranged to be one-half cycle out of phase with its neighboring cells at any instant, so that the protons are successively accelcrated as they pass through each cell in turn. The name “Cloverleaf” comes from the physical cross-section of the cells. Four re-entrant lobes are used to shape the electric and magnetic fields in the cells. Coupling is accomplished through slots in the septums.
.
I
-A-4
Two 805 Mc tanks will be driven in parallel from a single 805 Mc rf power amplifier. The shunt impedance of the cloverleaf structure increases with beam energy, allowing a choice of crossover point from the Alvarez section. The design of the accelerating structures to insure acceleration of the particles in the axial direction is incompatible with maintaining simultaneous stability in the radial direction. Therefore, focusing systems of quadruple magnets are provided along the axis of the machine.
In the Alvarez section, the quadruples are fitted
within the drift tubes. In the cloverleaf section, the magnets are located in each gap between tanks. The target area and secondary-beam transport systems are arrangements of magnets and evacuated channels which guide the main proton beam to the target area.
They also guide the secondary beams which
are generated in the target to the various experimental areas.
.
I-A-5
1-B-1 ,
B.
General Description of the Accelerator RF Systems The basic function of the rf systems is to furnish power to the
accelerating structure. The following table lists the parameters which apply to the IAMPF accelerator and the rf power amplifiers. PF ACCELERATOR PARAMETERS1 Accelerated Proton Beam Intensity
1 ma (average) 20 ma (peak)
Accelerated Proton Beam Energy
800 MeV
Length of Linac
2324.3 ft
Accelerated Proton Beam Duty Factor
6.0%
Total RF Output Power
3.9 MW (average) 62 MW (peak)
RF Power Amplifier Duty Factor RF Pulse Length - 2100 vsec Pulse Repetition Rate - 30 pps
6.3%
No. of Alvarez Linac Tanks (201.25Mc Sector A)
5
No. of 201.25 Mc Amplifiers (one per tank)
5
No. of Modules - Sector A
5
Length of Sector A
440 ft
Nomiml RF Power Output per 201.25 MC Amplifier (except Module No. 1)
250 KW (average) 4MW (peak)
No. of Cloverleaf Linac Tanks (805 Mc Sectors B-F)
90
No. of 805 Mc Amplifiers (two tanks per amplifier)
45
No. of Modules per Sector
9
I-B-2
Nominal RF Power Output per 805 Mc Amplifier (each module Sectors B-F)
63 KW (operating average) 1.0 MW (operating peak) 1.25 MW (design peak)
The general block diagram of the rf system is shown in Fig. I-B-1. Sectors are established as outlined above for proper distribution of utilities power and cooling water. into modules.
The module
Each sector is broken
is the basic design unit and is intended
to be a self-contained, standardized unit.
The module layout for
Sector A is shown in Fig. I-B-2, and that for Sectors B - F in Fig. I-B-3. The rf drive system prwides
the basic reference frequency and
phase for the entire machine, based on a primary frequency standard at about 5 Mc. The timing system provides signals for synchronizing the injector, accelerator and experimental area operations. The reliability of the rf drive and amplifier system is of the greatest importance, since the loss of a single amplifier, except the last or last few, results in the shutdown of the entire machine. Improper operation of the rf control systems could result in loss of the high energy beam, with ensuing radiation and possible physical damage to the accelerator.
ml11-
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,—
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-4
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.
—
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I-c-l
co
Background and Scope The necessity for strict control of the rf field amplitude and
phase in the accelerator structure has been recognized as having fundamental significance since the beginning of design studies on high la3 intensity proton linacs. ‘ ‘ Simply stated, studies of proton beam dynamics show that tight tolerances must be placed on the field amplitude and phase in order that particles initially accepted and accelerated by the machine are not later “lost” inside the,accelerator because they have fallen out of step with the accelerating wave.
Lost
particles are not usually transported out of the accelerator, but collide with the walls of the structure. This is highly undesirable, because colliding protons with energies above about 8 MeV will cause radioactivity in the structure and will inflict physical damage if the intensity is high enough.
(The peak beam power of the 20ma,
800MeV proton beam in the IAMPF accelerator is 16 MW.)
It is esti-
mated that no more than 0.01% of the beam could be lost without incurring an unacceptably high radioactivity level. This problem has not been as important in linear accelerators built previously because their energy levels, currents and pulse * lengths are much lower.
These linacs are also short physically.
In the one tank linac,.the problem is reduced to staying on resonance, and in a three tank linac, the importance of tank-to-tank errors is reduced considerably because of the reduced interaction length. *
For example: Brookhaven Proton Linac - 50 MeV, 10 ma peak for 25 ~sec, 1 tank University of Minnesota Linac - 68 MeV, 2 ~a peak for 300 ~sec, 3 tanks Argonne Proton Linac Injector - 50 MeV, 5 ma peak for 500 psec, 1 tank
I-C-2
Even more significant frequency transition.
is
the fact that the LAMPF
requires a
linac
As will be explained in Sec. II, this is a
crucial point in the LAMPF machine in terms of phase tolerances. Thus a new consideration completely missing from older
~i.MCS
h
introduced. Many existing linear accelerators have employed amplitude control systems to regulate the rf amplifiers, and therefore the design of this system is not discussed in detail in this paper.
None,
however, have used a feedback phase control system capable of correcting short-term fluctuations during the rf pulse.
The University
Minnesota proton linac and the Stanford 2-mile electron
of
linac are
46
good examples of current practice.
‘
Both have slow speed automatic
phasing systems which drive mechanical
phase shifters.
The phasing
information is obtained during the steady-state portion of the pulse, and phasing cannot be accomplished
during the life of one pulse.
The LAMPF linac requires continuous phase and amplitude control during the pulse, primarily because the proton beam intensity is high enough to cause significant beam loading of the accelerator . the beam comes on and reaches a steady state. cause excessive variations
fields as
This effect would
in rf amplitude and phase and consequent
loss of particles during the transient period if uncorrected. In summary, it has never before been necessary to maintain continuous control of the rf field to the precision required by the proposed LAMPF 800 MeV accelerator. field must be carefully controlled
In particular,
the phase of the
in this application.
Because this problem had not been a pressing one on earlier
.-
______
-—
-
z -c-3
linacs, at the time when the
LOS
1962 and early 1963 no info~tion
Alamos
-s
design
studies began in late
available on the transient
behavior of a proton linac rf system. Indeed, the steady-state properties of loaded waveguide accelerating structures were just beginning to be applied to proton acceleration, using the results of groups at Harwell,e Rutherford,’and Yale,= and previous work by Chodorow and Craig on slow-wave amplifiers.s The codtrol problem was further complicated by questions concerning the performance of high power rf amplifiers required to drive high Q, resonant loads. The changing impedance presented to the amplifier by these loads during each pulse presented new and difficult problems in the design and control of rf transmitters, since most previous applications to phased array radar, electron linear accelerators and broadcasting systems have been designed around matched loads. To the author’s best knowledge, the work reported here is the first control system analysis of the transient behavior of a complete proton linear accelerator rf system. The following sections deal with the analysis of the 805 Mc portion of the IAMPF proton linear accelerator rf system, and the application of the results to the analysis and design of an 805 Mc phase control system. The 805 Mc rf amplitude control system is cwered
in lesser detail; however, the causes and effects of inter-
actions between phase and amplitude are investigated. The block diagram of the conceptual control system iS shown in Fig. I-C-1.
a : :
+ #
~
a
0
:
&
1-
w
”.-.-.-:
..+: y:. ......-
...... -.-+ --.:.:..:
.. ... ... ....“ -+ ..
.>:.....
-------..:. :.:..”.+:
.-.::. H a m
1 ::t:: :.--.: L.:*;3:+$ t . .A..:*:. ~.. ~ . .* .:I
.
I-C-4
t-l
H
Ii
v-l E.1
I-c-5
The transient behavior of the accelerating rf structure is developed in a general form to provide a firm basis for the control system de8ign. Experimental verification of the theory is presented. The remainder of the “controlled elements” - the rf amplifier, waveguide feed, and the combination of these with the accelerator are amlyzed
in terns of the specific system proposed for the IAMPF
accelerator. The “controlling elements” are then analyzed to determine their individual behavior. These are the reference frequency and phase generating devices, the phase comparator and the phase shifter. Design criteria for the rf phase and amplitude control systems are derived by translating the basic specifications in terms of the behavior of the components and estimations of the expected inputs, both desired and undesired. The combination of the elements in the phase control system is then studied on a small signal basis.
Compensation elements are
chosen to give the desired behavior. The resulting system is one of many that would work.
The derivation of an optimum system is
left for future work, as discussed in the next section. References, indicated by superscripts in the text, are listed by chapter in the bibliography, with superscripts restarted at one for each chapter. A list of general references is also given.
I-D-1
D.
Summary and Outline of Some possibilities for Future Work Considerable new understanding of the transient behavior of a
proton linear accelerator rf system has been obtained. In particular, the characteristics of the accelerator structure itself have been derived in general form. As a general conclusion, it appears that the construction and operation of a practical, reliable phase control system meeting the proton linac specifications is feasible. Several interesting problems remain, but they are not expected to influence the basic workability of the proposed system. Specifically, the following results have been obtained. In Section II, the basic specifications for the rf system phase and amplitude control are derived. The method consists of correlating phase emittance statistics at various points in the machine with the statistics of tank-to-tank amplitude and phase errors. A relation showing the trade-off between amplitude and phase errors is presented which shows how the tolerance on one kind of error is fixed when the other tolerance is chosen. The field error limits chosen for use in the remainder of the report are -&2°in phase, which fixes the amplitude tolerance at ~1.5%.
The equivalent phase control system speci-
fications are that the standard deviation of the random phase jitter in the entire system be less than or equal to ~ of the ptise tolerante and that the effects of all unwanted systematic inputs be attenuated to less than ~2°e A general theory for the transient behavior of coupled resonators is derived in Sec. III, in terms of a lumped parameter equivalent
I-D-2
circuit consisting of a chain of inductively coupled, identical series resonant cells. A general transfer function relating the field in any cell to a drive in any cell is obtained first. This transfer function describes the complete behavior of the circuit, including
,
the detailed rf structure. Since the control systems are concerned only with the envelopes of amplitude and phase during the pulse, the analysis is refined in order to express the form of these envelopes explicitly. The resulting expressions are simplified using a two component approximation. The approximate responses are shown to agree closely with the exact responses for several examples of both large and small signal types. The simplified expressions are then linearized and small-signal transfer functions are derived relating the amplitude and phase envelopes of the cell fields to drive phase and amplitude envelopes. This analysis has provided a thorough understanding of the transient behavior of a chain of identical coupled resonators. The method can be extended in a straight forward manner to chains of resonators of alternating kinds.
Such an extension has been useful
in determining the steady state characteristics of some of the more complicated waveguide structures such as the cloverleaf.g The use of effective parameters in the singly resonant theory also satisfactorily describes the transient behavior of doubly periodic structures, as discussed below. The transient theory was then tested experimentally. Various types of cavities were used, from a simple iris loaded waveguide,
I-D-3
which is adequately represented by the chain of identical cells, to more complicated structures whose design
is
based
on an understanding
of the doubly resonant chain. These experimental cavities have various types of errors due to mechanical tolerances. In all cases, the qualitative form of the transient responses observed agree with the results predicted by the singly r,esonanttheory. Quantitatively, the results for the responses strongly characterized by the driven mode agree withiq measurement error. It is shown how the effects observed in responses strongly dependent on cavity modes other than the driven mode can be easily attributed to ckracteristics of the coupling cells, and how equivalent parameters are assigned in the theoretical expressions to match the experimental data. These results demonstrate that the singly resonant theory, with effective parameters assigned where appropriate, adequately represents the transient behavior of the proposed accelerator structure. The transfer functions derived for small-signal control studies are simple and accurate. In Sec. IV, equivalent circuits for the rf power amplifiers and the combination of the amplifiers, the waveguide feed, and the accelerator load are derived and analyzed. The primary concern here was the effect of reflections with a long transmission line between amplifier and load. It is shown that the effect should be negligible for the T.AMPFcase if the waveguide is nA/2 long. Beam loading is discussed at the end of this section. The steady-state effects of a 40% beam load are shown, and estimates of the transient behavior of the rf system when beam loading is applied are discussed. The
~
I-D-4
transient aspects are not answered; the discussion serves to point out several of the questions and paradoxes which arise in a consideration of this subject. Section V discusses the phase reference, sensing, and shifting devices. It is shown that random noise in the phase control system is negligible if the signal-to-noise ratio is greater than 40 db throughout. The characteristics of reference sources are investigated,and it is concluded that rf references having phase stabilities with standard deviation of less than one degree are feasible for periods up to 2 msec. A direct-comparison phase bridge is chosen for the phase detector because of its simplicity. Its properties are analyzed in detail in Sec. V-B.
The results from an experimental bridge are presented,
showing good agreement with the theory. Various types of phase shifters are discussed qualitatively. The foremost contender for the IAMPF at present is a varactor phase shifter operating at low power levels. In the final section, the small-signal design of a phase control system is studied. The expected disturbances are reviewed and it is concluded that the linearized system will adequately describe normal operation. Detailed block diagrams for a typical accelerator section are presented, and the phase control loop design criteria are sumnMrized. Series and feedback compensation designs of general form are discussed briefly in terms of their ability to reduce the effects of intra-loop disturbances at the output. The feedback methods are
I-D-5
shown to have several advantages. An example is developed in detail, illustrating the design procedures. The system responses to reference changes and unwanted “noise” inputs are shown, demonstrating compliance with the design criteria. These results show that a conservatively designed phase control system for the LAMPF accelerator is indeed feasible. Portiops of this work have been published as the work progressed.l”,11,12 The author was also concurrently involved in a study of the application of real-time computer control to the entire IAMPF complex.13 The results indicate the desirability of such control. These results were published at the 1965 Washington Conference on Particle Accelerators. 14 There are many opportunities for future work on the control system. The non-linear aspects should be studied, both to understand more about the basic stability and suitability of the design for larger inputs, and to ascertain whether desirable characteristics could be obtained by the exploitation of inherent or introduced nonlinearities. It would also be desirable to attempt to optimize the system in one or more ways.
The most obvious optimization would
be to minimize the output response to the “noise” inputs. ‘I’he time wasted during filling at the start of the pulse could be minimized. The sensitivity to elements which prove troublesome in a practical realization could possibly be minimized. The transient beam loading problem is one of the most interesting possibilities for future work.
It is important because the
beam is the quantity being controlled, either directly or indirectly, and beam loading is one of the major inputs to the control system. The problem is to find in detail how the beam affects the entire rf system, not just the cavity, and to derive a suitable mathematical model which can be incorporated into the equivalent circuits derived for the amplifier and accelerator.
Specification
SPECIFICATIONS FOR THE CONTROL OF THE RF SYSTEM
- Chapter II
II-A-1
A.
RF Phase and Amplitude Stability 1.
Introduction The phase and amplitude of the rf field determine proton
motion in the accelerator. Thus, the basic specifications for the rf system come directly from the study of beam dynamics in the machine. The accelerator structure is designed so that a “reference”, or “synchronous”s Particle is exposed in each gap to the proper field gradient at a constant angle, called the synchronous angle, @s, ahead of the crest of the rf wave.
The machine will accept and
accelerate protons which are injected at phases from -2$s to +$
s
relative to the synchronous angle, for a total “acceptance” of about 3@s.
Particles injected at other phase angles are not accel-
erated and are lost after a few cycles, mainly by collision with the structure walls.
The accepted particles bunch around the synchronous
angle as they are accelerated, since lagging protons will see a higher field, and vice versa.
This damping of the phase spread is
rapid in the low energy sections.12, At the transition between the 201.25 Mc and the 805 Mc sections, the effective acceptance is quartered, as illustrated in Fig. II-A-1. Thus, the important criterion for the Alvarez section is that the final phase spread, or “phase emittance”, of the beam as it makes the transition must be sufficiently reduced to insure that the bunch is totally accepted into the 805 Mc “bucket”. Protons at energies higher than about 8 MeV would cause radioactivity in the structure if they were lost and hit the walls. .
II-A-2
Therefore, “total” acceptance means literally that. The radioactivity would become unacceptably high if even a small fraction of one percent of the beam were lost anywhere in the machine above the 8 Mev point.
+.-300
--&
AHEAD
\
OF
CREST
ACCEPTANCE s3+~=90”AT
1
I--ACC =3 I
I
PTANCE ~~90.AT
$
BUT =22.5”
REGION 201,25 MC
REGION 805 Mc REFERRED
TO 201.25MC
Fig. II-A-1. Acceptance Change at the Frequency Transition. The frequency transition will be the most difficult point in this respect. Of course, practically, some particles will be lost, and a statement of an allowable limit can be used as a guide in setting the tolerances on various machine parameters. At the start of the 805 Mc section, the phase spread has increased by a factor of four. During the remainder of the acceleration to 800 Mev, the phase spread is reduced by only about 25%.
II-A-3
Thus, the phase “bucket” is always relatively full in the 805 Mc section. The criterion in this section is that the tank phase and amplitude errors be SUM1l enough to prevent the bunch from wandering to the edge of the phase acceptance region and losing particles from the bucket. There are, of course, many other machine parameters which interact to cause reductions in phase acceptance. Some of the most important of these are radial-phase oscillation coupling effects, quadruple alignment errors, and physical tolerances on the machine components. The errors which will remain constant for long periods of time, such as machining and alignment errors, are assumed to be independent of fluctuations in the operating parameters and are studied separately. We are primarily concerned with the effects of short term fluctuations in the operating parameters such as the rf amplitudes and phases, and it is from beam dynamics calculations that a set of tolerances on these quantities is derived. The result of specification studies must be a set of compromises allowing so much error in the rf amplitudes and phases, so much in the alignment, and so on. 2.
Calculations In the beam dynamics calculations performed at Los Alamos,3Y4z5j6
random phase and amplitude errors from a uniform probability density between two limits are imposed on the cell-to-cell and average tankto-tank fields. Certain known error distributions were also used. Our concern in dealing with the rf system is with the tank-to-tank errors, since it is planned to feed each tank or set of tanks from
II-A-4
one point. The motion of a group of particles distributed in an appropriate manner in phase and energy space is calculated through the machine, and the resultant phase and energy spread at various points in the machine are obtained. Since the transition region is so crucial, the majority of the work done to date has been concerned with errors in the Alvarez section. Numer6us computations have been made using complete solutions of the non-linear beam dynamic equations, including error terms> to obtain emittance statistics.5 This procedure has been checked and extended by Butler,3 who has devised analytical procedures using matrix methods on the linearized beam dynamics equations to find the statistical uncertainties directly. The results of the linearized calculations check with the non-linear results very closely for errors within the range of the approximations. The effect of the errors is to cause the synchronous particle to become “non-synchronous”, i.e. to seek a new synchronism, and thus describe small oscillations in phase space. This is because the quantity E cos ~~, where E is the gradient, must remain constant. Tank-to-tank errors are far more serious than cell-to-cell errors, because they are in effect over a longer length. Positive or negative errors are equally probable, and the error probability density function is even.
For convenience, we shall speak
in terms of the positive errors. Based on the work described above, the half-width phase emittance of a particle distribution injected from an ideal buncher and accelerated through an errorless Alvarez ,gectionis about 3°. The emittance will always increase if errors
II-A-5
are present.= Figure II-A-2 shows the probability distribution of the increase in phase emittance at the end of an Alvarez linac compiled from 20 computer runs for a) errors in tank-to-tank phase randomly chosen from a uniform probability density between+
2° and -2°, and
b) errors in tank-to-tank amplitudes randomly chosen from a uniform density betmen + 2% and -2%.
(A new set of errors is chosen for each
run, and phase and amplitude errors are treated independently.) The phase spread at 50% is shown on each of the curves. These phase spreads are close to the standard deviations of the densities, and will be used as such in the following discussion. Since the linear theory permits extrapolation within the bounds of its approximations, we may interpret the standard deviations as “the standard deviation per unit limit on the input error density.” Then the standard deviation for phase errors is about .66°/10, and about 1.58°/1% for amplitude errors. When both kinds of errors are present, the combined standard deviation is the rms of the individual values, assuming the errors are independent. The limits on the uniform input error densities are set by the following specification. 3“ + 3[Z(X.3.]=]* n
2 if we define
III-B‘4
In order to make Eq. (6)Laplace transformable with respect to h, interpolate the points of l~(s,h)l by a jump function starting at h=
O, designated rl~(s,h)l.
Transforming with respect to h, let Zh [j=(~h)l] =
E ~s,u)
where P(w) = < transform for the unit pulse =
1 e
J
-5X ~x
~
1;S
0
Letting p = ew, the characteristic equation is
Expanding into partial fractions: I (P-p&
-p2)
p-%Q (p-plxp-pz)
=
= +
“
pl!pz
‘(
I
JwL. ( p-p,
@,oY p,-pa
-
p-pz
p-yz
)
p’-pl
(
+
w
)
=+ pl-pz
PI C“-p*
J.L. ( P-b
em P (u) )
L p-pz )
III-B-5
-1
For pr a constant:
d[ tb)
e@P(ti) ‘* - pr
= ]1
P:
(11)
Performing the inverse transformation:
Using Eq. (10) and considering only integral values of h, the jump notation may be dropped: \e(s, h)l
=
I=(s,])sinh
h(3
- l=(s,o)ls~nh(h-t)$
●
(12)
Substituting Eq. (12) into Eq. (5) and simplifying, we obtain the condition: Sinh N
P
=0
(13)
(14)
where c is an arbitrary integer And x.
=
Z cosh
e
(15)
III-B-6
The characteristic equations for the chain are then:
The proper sign is determined by investigating the h~ogeneous equation for the general cell: ~ (sOn](sz
+- ~
S +
0.2
) + -$ s=[l(s,n-t)+I@,n+\
)]=0
(17)
This equation is satisfied if the plus sign is chosen in the characteristic equation, and the currents have an n-dependence as follows: I(s,
rI.1) +
I(s,
n+l)
= Zcos+
I@, n)
(18)
This latter dependence is also necessary to satisfy the inhomogeneous equation, as we shall soon see. Then the characteristic equation for this case is: (19)
It is seen that the characteristic equation does not depend on n or d. We now return to Eq. (4). The information gained about the characteristic solutions will be worked into the equation for I(s,n) to obtain a form which will be useful in working with the inhomogeneous equations.
(20)
III-B-7
Superposition with respect to the drives holds, so we will work th cell, If there is only one drive, in the dl
With one drive only. then .
F(s,
d)
+
()
=0 Id,(%n)
and ,
if
d=
if
d+d,
d,
AQ(s, n,d,)
= :
(21)
F(s9
S2 i+kcosT~)+&S X’” [(
d,)
(22) +cJez]
Substituting Eqs. (21) and (22) into the general inhomogeneous equation:
(23)
This equation will be satisfied if the following two conditions are
met:
A%(s,n-l,d,)
*Aq(s,n+l,d,)
= 2cos~A3(s,n,d,)
(24)
which is the same as Eq. (18).
;0A+n,d,)
=
e
(25)
I
To find a form of Aq(s,n,d) which meets these requirements, first try to separate the functional dependence of Aq(s,n,d) as follows: Aq(s,n,d,) v
s
~q(s,d,) 9
G(n)
(26)
III-B-8
Then Eq. (24) reduces to:
G(t’1+1)
+ G(n-1) .
ZCOSw~
=
(27)
G(n)
This is a difference equation in the same form as Eq. (6), yielding: G(l)sin~ G(n)
G(o) sin w.
-
=
j
sin ~
Y=O,..,N
(28)
G(0) and G(1) are found from the equation for the first cell:
S2(1+
&*L&2
kcos~~)+
=
G(o)(szt~s+Q~)
+ G(l)ks2
(29)
Thus
G(0)
=
I
G(I)
=
COS~
G(n)
=
Ws
; ~=O,.. -,N
=+
(30)
The remaining condition, Eq. (25), will now be satisfied to give an explicit form for Aq(s,d).
F(s,d)
=
fAyCOSm+
Eq. (23) simplifies to:
F(s, d,)
(31)
1=0 where the functional notation of Aq(s,d) has been dropped for blevity The Aq’s may be found using the orthogonality relation for the chain of coupled cells:14
where Wl(n) =
~
I
“,~+ 3n,N t I
III-B-9
The summation over n = O,..., N here means a sumation over all the cells in the chain. Multiplying Eq. (31) by #ewl(n)
cos
=
‘+r
F(s,
&W,(n)cOs n)
IsK:* N
= (33)
2
n=o
f_At
w, (n) cos ‘*”
F(s,
COST%
d,)
f=o
Rearranging the order of the summations on the right side, using Eq. (21) on the left side, performing the summations over n, and invoking Eq. (32):
~
Wl(d,)cos
*#
‘
~
‘~
[
a2N,($+r)
+
h,($+r)
t
‘o,($-r)
~
(34)
7’0
Performing the summation over q:
+dl(dl)cosw~r
,N
=
Ar + AN61-,N+
&&r,o
(35)
Changing variables back to q:
‘1
*
=
~
Wl(d,)Wl(q)cos
‘~
(36)
Argument of F(s,d) on left side can be changed to F(s,n) at will since n and d run over the same index and are used only as a convenience in keeping track of cells and drives.
III-B-1O
The complete solution for I(s,n) is then:
(37)
The transfer function relating the current in the n
th
cell to a
th “ cell is: drivinz voltage in the d N
“I(s,n) E(s,d)
=
Y@, n,d~
= z ,G 1
2cosT*cosT+wl @L)f’4
S2 l+kc~smfl [(
(q) ~ )%$
s S+ti:
(38)
1
This transfer function will be called the “general transfer function” for the system of coupled cells. 2.
Discussion of the General Transfer Function. Et!. (38) a.
If E(s,d) = 2L is substituted in Eq. (38~ the result
is the normalized Laplace transform of the impulse response of the circuit. Thus the transfer function reveals the unforced, or “natural”, behavior of the system. It is seen that the natural resonances occur whenever the characteristic equation Sz(l+kcosT~)
is satisfied.
+ $&
+ tioz = O
(39)
; l= O’”””N
The solutions are:
(40)
XII-B-11
Each term of the frequency dependent part of the transfer function is characterized by a zero at the origin of the s-plane, and a pair of . conjugate poles. b.
The vector representation of the n and d dependence is use-
ful in understanding the modal characteristics of the system:
(41)
For instance, the e
jmq/N
term contributes both a magnitude and
a Phase term to the current in each cell for each of the q modes. The mode of primary interest in this application is that in which there is a phase difference of pi radians in the instantaneous rf electric fields in adjacent cells of the accelerating structure. This condition is met if the structure is driven at w
q
=WN.
Thus
the terms “pi-mode” and “q = N mode” are synonymous. The condition for resonance is seen to be met physically by the fact that at resomnce, the total phase shift from one end of the structure to the other and back is always an integral multiple of 2firadians, insuring a reinforcement condition. nq/N c. A plot of the angle ej versus the natural frequencies Wq gives the Brillouin diagram, or dispersion curve, for the circuit. For the finite chain of N cells, there will be N discrete points on the curve. The bandwidth of the structure is seen to be related to the coupling coefficient k:6
III-B-12
Fig. III-B-1. Dispersion curve for N coupled identical resonators.
The slope of the dispersion curve is zero at the pi-mode. The frequency separation between the pi-mode and the next (N-1) mode is given for k
i“zE=+
[
-110.6
=
(s+
.333)
1[
S
[(s+.333)2
da rad. ‘1
57.3
(lo). d=gre~s
+(3.4&)~3
volt
The frequency response of Eq. (7) is shown in Fig. VI-B-2. responses of &$ and K
The
to a phase step Ml = 20° are shown in Figs.
VI-B-3 and 4, respectively. The maximum &
for this case is about
8.3% of B. i
The responses of ~
and AG to an amplitude step AE = .2, or 20%,
are shown in Figs. VI-B-5 and 6, respectively. The maximum &$ is o about 2.85 .
.
VI-B-5
00
●
r
.
● ✎ ●
-lao
-t?, -“
Fig. VI-B-2. Frequency response of a typical 805 Mc HPA and accelerator tank combination.
vI-B-6
3.0
2.4
(n Ill w a a Ill n uUI
a
1.8
I.2
z a
.6
0
-o
12
6
TIME,
18
24
MICROSECONDS
Fig. VI-B-3. Phase response of a typical 805 Mc HPAaccelerator tank combination to a phase step of 20°.
30
VI-B-7
.9
.8
.7
.6
.s
.4
.3
.2
.1
0
-.1 0
6
12 TIME,
la
24
MICROSECONDS
Fig. VI-B-4. Amplitude response of a typical 805 Mc HPAaccelerator tank combination to a phase step of 20°.
30
VI-B-8
1.0
0
03 IJl
w
-1.0
E
u n
-2.0
I
I
I
I
I
I
I
1
[
I
1
I
I
I
1
I
I
I
I
I 1 1 1 I
-3.0
-4.0 0
12
6 TIME,
la
24
MICROSECONDS
Fig. VI-B-5. Phase response of a typical 805 Mc HPAaccelerator tank combination to a 20% amplitude step.
30
VI-B-9
2
I
I
0
6
12
TIME,
18
24
MICROSECONDS
Fig. VI-B-6. Amplitude response of a typical 805 Mc HPA accelerator tank combination to a 207.amplitude step.
30
VI-B-10
These transfer functions and those which follow are shown on the example block diagram, Fig. VI-B-7. Note that A$/At7and llG/AE form a part of the forward path in their respective loops, while inputs through l@/AE and AG/~0 act as load disturbances. 2.
Transit Phase Chanzes in the HPA The change in transit phase through the HPA per percent
change in the HPA modulator voltage, for the IAMPF case as discussed in Sec. IV-A, is; Ae z Zir=
0.5percent
vottag~
(11)
change
This effect occurs ahead of the accelerator
tank
and thus adds
ahead of the A$/A6 block in Fig. VI-B-7. In the following, disturbances AE will be considered as open loop outputs of the amplitude
system;
that
is, closed loop interactions
between the systems will not be discussed. 3.
Beam Loading The beam loading equivalents discussed in Sec. IV-C-4a.
add load disturbances to the phase loop as shown in Fig. IV-C-4 and by the solid lines in Fig. VI-B-1. In these cases, Q/Af3Bw
iS
equal to &$/AQ derived with a = .166 or .333. However, since the transient nature of beam loading is not well defined, AeBw
will be
treated for design purposes as a step disturbance, modified only by
4
* --l 2
1-
VI-B-11
~-13-12
which modifies the leading edge of the A(3BW step to an exponential rise with a rise-time of 0.5 psec.
This modification merely insures
the physical realizeability of the beam disturbance. A beam transient of this form is more severe than anything actually expected.
Thus its
use leads to conservative design. Should beam loading affect the time constant of @/LW, as discussed in Sec. IV-C-4b, the situation becomes more complicated because the system is no longer time-invariant. This is implied by the dotted lines on Fig. VI-B-1. It is believed that this representation can be adequately handled in this stage of the design work by requiring that the loop criteria be met with or without the presence of the beam. control loop must be relatively insensitive to c%
In other words, the The assumption here
is that the transition between states is “smooth” enough that stability and conformance to the design criteria are maintained.
The study of
the actual behavior during such a transition is left for future work. In summary, beam loading in the following small-signal design will be considered as follows. a.
The design criteria must be met by the unloaded system
described in Eqs. (7) - (10), and also by a beam loaded system in which ~ is increasedup tO 40%. The transfer function l@Ae
1.025 [(S+.34)2+ (2.35)2]
A+ Ae
for the loaded case is
beam Ioadad
=
(S+.466)[(S+.466)%
+(3.4L)ZJ
(13)
VI-B-13
b. by the A$/A6BW
A(3BW will be treated as a step disturbance, modified of Eq. (12), and imposed as a load disturbance on
both the loaded and unloaded systems. 4.
Phase Shifter The phase shifter transfer function is taken from the linear
region of Fig. V-C-l.,
A(3, KB =
1 radian volt
= 57.3
degrees volt
(14)
The linearity of this element is affected in two ways. At large negative bias voltages, a saturation effect occurs. voltages drive the diodes into the forward region.
Positive bias This is an unde-
sirable effect and should not be allowed to occur. Therefore, the following restriction is placed on the loop performance. a.
The phase shifter must operate in a ~ 1 volt range
centered at -1.0 volt.
Transient or steady-state bias changes from
-1 volt which occur in closed loop operation may not exceed these limits. 5.
Phase Comparator A reasonable sensitivity for a practical phase shifter
operating near the null as indicated by Eq. (24),
Sec. V-B., is 10
millivolts per degree. In addition, the differential amplifier which forms the error signal is assumed to have a bandwidth of about 80 Kc, with a roll-off of 20 db/decade at higher frequencies. Then:
4$%=
.005 S+,5
(15)
VI-c-l
c.
Expected Inputs 1.
Random Disturbances Random phase jitter will be negligible if the signal-to-noise
ratio in the system is greater than 40 db.
This is assumed to be true
here. 2.
Systematic Disturbances The major disturbances are due to beam loading effects, and
they are felt during every pulse. A 40% beam load will of itself cause a phase change of about 8° in the accelerator, as shown in Fig. IV-C-2. The amplitude correction occurring in the amplitude loop results in two inputs to the phase loop. The first is due to transit phase change in the HPA.
AE will be
about 20%, so the phase change, using A6!/AE, will be about 10°, in the same direction as the beam load error. The second is due to amplitude-phase interaction in the accelerator. Fig. VI-B-5 shows that the maximum phase excursion for AE = 20% is about -2.85°, and that this maximum is the first maximum. Each of these inputs lie well within the valid range of the linearized small-signal theory. The largest phase excursions in the closed loop can be expected to occur at A(3,,since the phase shifter is allowed to swing ~ 57°. However, a comparison of accelerator responses to step phase inputs using the exact driven mode expression, Eq. (53), Sec. III-D, and the linearized expression, Eq. (54), Sec. III-D, shows that the inequality
VI-C-2
Q > I
c
%, G,
T=
I +G,GZ
ZIG,
~
ZIG, =
(19)
{ +- AM=
(20) A~=
L< 1
i5,G, AM=
(21) AM= >> I
VIE-2
‘hereq
c
istheopen-loop
gainofthe
corrected major loop.*
Equations (16)-(21) indicate that C/Q and C/N are minimized by aslarge as possible over as large a bandwidth as possible, c and that this should be done by making G2 >> G1 if possible.
ma~ing~
A number of series compensators using lead networks in conjunction with one or two integrators were investigated. None looked promising, for the following reasons: a.
The crossover frequency, where l%
\ = 1, had to be c raised very high in order to get enough attenuation, particularly in C/Q .
This was undesirable in two respects. 1)
The crossover frequency is so high that the phase
comparator and phase shifter bandwidths probably should be considered in the model. 2)
The system becomes more vulnerable to changes in
R, since 2= R
G,Ga I+G,G=
=
AM. I + AM=
~
1
IAM=Z~
i
IA~=c
> I
(30)
(31) Equation (30) is especially interesting in that it shows how the minor loop can be used to provide attenuation even after the corrected major loop is cut off.
This means that useful correction
VI-E-5
of intra-loop disturbances is possible without increasing the sensitivity to errors in the reference, R. It is also seen that making El, E2, HI and H2 large will help reduce both C/Q and C/N. Further, it can be shown that sensitivity to G1 and G2 can be reduced by concentrating gain in E
1
and E . 2
It is evident that this approach is very flexible and affords many possibilities for optimization. We content ourselves at this point, pending further experimental verification of the model, with an example which shows the feasibility of meeting the performance criteria and serves to illustrate the above considerations.
VI-F-1
F.
Example 1.
Block Diapram The example chosen for illustration is a Type 1 system* with
frequency sensitive minor-loop feedback and unity major-loop feedback. The block diagram is shown in Fig. VI-F-1. PHASE COMPARATOR
PHA8E SHIFTER
— )+ .
\
I I
(NoRMALIZED
To E=l)
I
~2
I
L
(s+.02 )(9+.03)
Fig. VI-F-1. Example control system block diagram. L.
Frequency Domain Design The system design resulting in the above is carried out in
the frequency domain as shown in Fig. VI-F-2. 1~1 is drawn first. u The minor loop exerts control when Am > 1. Thus the system will and% for Aml,
tend to follow ~
*
as indicated by
c
A Type 1 system contains one integrator in the forward loop and is capable of following a step change in R with zero steady-state error. As may be seen from Eq. (26), an integrator in E2 also allows correction of a step input Q or N to zero steady-state error. The Type 1 system will follow a ramp (velocity) input at R with a constant, finite steady-state error, but cannot follow an acceleration input.
.
80 ‘XJfUlN9VUU
0.
0
co
VI-F-2
.
●
s’ In) El
.+-l
VI-F-3 The shape of the minor loop then follows directly from the shaping of~tothe desired form. Here ~ has been broken down sharply at a c c fairly low frequency, then leveled off to a -1 slope which continues through the crossover, and then increased to a -2 slope again to the intersection with
%“
This intersection is allowed to occur at a
u rather high frequency. This shape is chosen for the -1 slope some distance before and after crossover to insure stable operation, and for a reasonably low cut-off for L@/&$D, which decreases the sensitivity to reference changes. At the same time, the resulting shape of Am is advantageous. The full attenuation of ~
is in effect up tow ~ 0.05, as shown by u Eq. (29). At this point, Am takes over (Eq. (30)) and is in control over a wide range of frequencies. The feedback function HI can be synthesized from passive RC elements, as shown in Fig. VI-F-3.
FTmOuT Transfer Function: _EIN Eeur
T,T=
.
T,T=s2+[T,(\
‘1 = ‘Icl ‘2
= ‘2C2
GO=O G=l co
Fig. VI-F-3. Stabilizing network H1.2
S2
+~#T2]s
+ \
VI-F-4 Performance
3.
a.
Open Loop Frequency Responses Figures VI-F-4 - 6 show the actual frequency responses of
‘m’%u ‘n” M”c
These and the following responses were found using the
INLAP computer code.3 Notice that ~
has a phase margin of 51° at crossc
over. b.
@/@D-
Response to a change in the reference
Fig. VI-F-7 shows the closed loop frequency response of response of 4$1to a step &$D demand of 10° is shown in Fig. VI-F-8, and the corresponding AVB excursions in Fig. VI-F-9. @
overshoots about 32%at
the first peak.
This is in accordance
with thephase margin of~and the ratio of the peak amplitude to the DC c amplitude, M $ ‘f l@@Dl~ ‘iich ‘n this case is 1.175. M values between 1.3
and 1.5 are common design practice if overshoot is not undesirable for
other reasons. The overshoot is considered acceptable here for several reasons. 1)
The phase margin is adequate for good stability.
2)
The bandwidth of @/@D
is small, which minimizes the
sensitivity of the output to undesired, rapid changes in the reference. 3)
Reference changes will be made using a motor driven
phase shifter in the reference arm.
Thus demand changes will be slow and
the loop will track without the overshoot seen for a step demand. If ~he overshoot should prove undesirable, it could be reduced or eliminated by repositioning the poles and gain of the minor loop. This should be possible without compromising the attenuation of intra-loop disturbances to any appreciable extent.
VI-F-5
● 9O
00
-i#O
nAo#scc
Fig. VI-F-4. Frequency response of the minor loop open-loop gain function, A . m
VI-F-6
.0s0
● OO
I
I
I
I
I I Ilm
,
,
I
,
I , I ~~wli
● ☞ ●
-,Ta
-“
Fig. VI-F-5. Frequency response of the major loop openloop gain function with the minor loop open, %“
u
● OS
00
●
.
-1#0
2.56(s (s+.5~s+ -*70-Ica. os ,,
1
-01
,
*
,
4s
,
~l! #
10-0’
, 2
, , , , , ~11 46
I
,
10””’
,
c
,
,
,
,
4
,
%,+”
1
,
1
1
1
{
:
MM #see
Fig. VI-F-6. Frequency response of the major loop open-loop gain function with the minor loop closed ‘% “ c
I I
w
VI-F-8
●
c , ● ● ●
-1s0
-rr#
-’
Fig. VI-F-7. Closed loop frequency response of A$J/C$D.
VI-F-9
15
12
9
6
3
0 0
20
40 TIME,
60
80
MICROSECONDS
Fig. VI-F-8. Response of q
to a A@D step of 10°.
100
VI-F-1O
o
20
40 TIME,
Fig. VI-F-9.
80
80
MICROSECONDS
Response of AVB to a &$D step of 10°.
100
VI-F-11
c.
AC$/AOB - Attenuation of Load Disturbances Figures VI-F-1O - 12 show the frequency response of
&$/A6B, the response of A@ to a AOB step of 10°, and the corresponding AVB excursions, respectively. . The attenuation is at least 15 db at all frequencies of interest. o The maximum phase error is 0.6 , and the maximum AV~ iS -0.6 volts. d.
@N
- Attenuation of disturbances introduced after the
phase shifter. Figures VI-F-13 - 15 show respectively the frequency response of @/N,
the response of @
to an N step of 10°, and the corresponding
AVB excursions. The attenuation is at least 33 db.
The maximum phase error is
0.18°, and the maximum AVB is - 0.175 volts. Notice that the zeros of A$/AEJ,which is acting as Gl, Eq. (28), effectively cancel the poles which caused the oscillations in the response to A6B, Fig. VI-F-11. e.
Response to Combined Disturbances Af3Band AE. Fig. VI-F-16 shows the ~
response to combined disturb-
antes of AE = 20% and AeB = 10°. The maximum phase error is 0.64°. The corresponding AVB response is shown in Fig. VI-F-17, with a maximum of -0.62 volts. f.
Sensitivity to ~. The insensitivity of the system to ~ is easily seen by
studying how the use of Eq. (13) instead of Eq. (7) for @A6
affects
the asymptotic design curves of Fig. VI-F-2. The responses of @ and AVB to combined disturbances of AE = 20% and AEJB= 10° for the
VI-F-12
llbeam-l~adedll case are shown in Figs. VI-F-18 and 19 respectively. These correspond to Figs. VI-F-16 and 17 for the unloaded case. maximum phase error is 0.52°, and the ~xim~
The
AV is - 0.5 volts. B
The
added damping reduces the errors, as would be expected. 4.
Summarv The feasibility of phase control of the TAMPF rf system to
the specifications written down in Chapter II has been demonstrated by the example of this section. This example is, in fact, overdesigned in the following respects. The accelerator transfer functions result in somewhat more violent oscillations than do the exact functions,
as
shown in Sec. III-D.
Also, the beam load is imposed”as a step, rather than through the expected filtering of the accelerator tank. Thus the responses shown are somewhat pessimistic. Additional work is planned in the near future on
a
prototype
system. Further experimental verification of the model and implementation of a system such as the one described in this section should be done first. Subsequent investigation should include the non-linear effects and optimization studies. Eventually, the setting of reference levels and collection of phase and amplitude data must be integrated into the overall computer control system which will supervise, and in some areas directly control the entire linear accelerator.
I
VI -F -13
.,0
00
●
M 4
-*o
s-
0
c . ●
. ●
A@
—=
Aee
2.0 S(S+.02)(S+.03XS+ (S+ Z)(S+51.6)(S+.387
.333)(S+.5)L(S+ )(S+.01?)[(S+.048)Z+
.333>2
+ (3.46)2]
(.048 )2][(S+.3>2
Fig. VI-F-1O. Frequency response of A$/AO . B
+ (2. [)2]
n-F-14
2.0
1.6
I.2
.8
.4
0
-.4
-. 8
-1.2
-1.6
-2.0 0
12
6
TIME,
18
24
MICROSECONDS
Fig. VI-F-11. Response of @
to a Ae step of 10°0 B
30
VI-F-15
I
co
IJ o >
o
6
12 TIME,
18
24
MICROSECONDS
Fig. VI-F-12. Response of AVB to a A6B step of 10°.
30
VI-F-16
00
●
M
a s c
-80
0 B ●
●
.
●
-l#o
I
(A4
1.765S(S+.02~S+.03)(S+ .5)[(S+. ZZ8)2 + (2.1)21
—= N
-*?9
-:s#.mm
(S+2XS+51.6~s+.3S7 XS+.b17)[(St.0!8 )2+(.048)2]~S+.3 )2+(Z.l)2] 1
fmttutm HIIIIIm 1
1
,
46
,
1,-”
c
t
,
46
Illllm
#
:8’” t
46
#ABt9cc
Fig. VI-F-13. Frequency response of &$/N.
mm
911”’’,
,,,
VI-F-17
2.0
1.6
I.2
.8
co : a
.4
C9
0
-. 4
-.8
-1.2
-1.6
-2.0 0
6
12
TIME,
18
24
MICROSECONDS
Fig. VI-F-14. Response of A@ to an N step of 10°.
30
VI-F-18
I .0
.8
.6
4
.2
o
~ 0 > “
-.2
2“ -. 4
-. 6
-. 8
-1.0 0
6
12 TIME,
18
24
MICROSECONDS
Fig. VI-F-15. Response of AVB to an N step of 10°.
30
VI-F-19
2.0
[.6
1.2
.8
.4
0
-. 4
-. 8
-[.2
-1.6
-2.0
0
20
40
TIME,
Fig. VI-F-16.
60
80
MICROSECONDS
Response of A@ to combined step disturbances of AE = 20% and AC3B= 10o.
100
vI-F-20
02 ~
o > “
m
z
o
12
6
TIME,
Fig. VI-F-17.
18
24
MICROSECONDS
Response of AV to combined step disturbances of AE = 20% an!3 A~B = 10°.
30
v-i-l? -21
2.0
I .6
I .2
.8
.4
0
-.4
-.8
I .2
1.6
ttmt
2,01
‘
I I t 1 I I I I 1 I I I I [ I I I I 1 I I I I
o
20
40
TIME,
Fig. VI-F-18.
60
80
100
MICROSECONDS
Response of @ to combined step disturbances of AE= 20% and AOB = 10° for the “beam-loaded” case.
vI-F-22
u)
!i
o > . m
z
o
6
12 TIME,
Fig. VI-F-19.
18
24
MICROSECONDS
Response of AV to combined step disturbances of AE = 20% and A~B = 10° for the “beam-loaded” case.
30
R-1
KU! ’JT!JU$NL.WS
1.
-
WUWIEK
1
Preliminary proposal for a Meson Facility at Los Alamos, LOS Alamos Scientific Laboratory of the University of California, December 28,
1962 and attachment:
Accelerators
for the Production of Pi and Mu Mesons
University
“Comparison of Particle for the
of California Los Alamos Scientific Laboratory”,
William B. Brobeck Associates,
Report No. 45OO-104-1-R1,
PP. 15, 18, 24, 25. 2.
Minutes
of the Conference on Proton Linear Accelerators
University,
at Yale
October 21-25, 1963, pp. 29-48, 131-152, 171-189,
190-195, 311-320. 3.
Yale Study on High Intensity Proton Accelerators,
Internal
Report Y-6, Yale University Physics Department, October 30, 1962, pp. 11-5-8. 4.
University
of Minnesota Linear Accelerator
Progress Reports MINN-LA-67,
Laboratory, Annual
1963, pp. 8-9, and MINN-LA-70,
1964,
pp. 10-14. 5.
C. Brian Williams,
“Design Report - Automatic
Phasing System for
High Power Klystrons,” SLAC, 1963. 6.
P. D. Dunn, C. S. Sahel, and D. J. Thompson, “Coupling of Resonant Cavities by Resonant Coupling Devices,” AER.E (Harwell) Report GP/R 1966, December 1956.
7.
A. Carrie, “Crossbar and Cloverleaf Structures at Rutherford,” Proc. of the Yale Conference on Proton Linear Accelerators,
8.
M. Chodorow and R. A. Craig, Proc. I.R.E. Q,
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1963.
R-2
9.
E. A. Knapp, Appendix II, “A Proposal for a High-Flux Meson Facility at Los Alamos, ” Los Alamos Scientific Laboratory, September,
10.
1964.
R. A. Jameson, “Rf Phase and Amplitude
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1964 MURA Conference on Proton Linear Accelerators,
of the
July 20-24,
1964. 11.
R. A. Jameson, “Rf Phase and Amplitude
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111
of “A Proposal for a High-Flux Meson Facility at Los Alamos, New Mexico,” Los Alamos Scientific Laboratory, 12.
R. A. Jameson, T. F. Turner, and N. A. Lindsay, “ksign Rf Phase and Amplitude Accelerator,” Washington,
presented at the Particle Accelerator
D. C., March
10-12, 1965.
Abstract
of the
Conference,
published
in the
Physical Society, paper to be published
in the summer issue of the IEEE Transactions
on Nuclear Science.
“Preliminary Design Study Report, Los Alamos Meson Physics Facility Controls System,” Edgerton, Germeshausen Tech.
14.
1964.
Control System for a Proton Linear
Bulletin of the American
13.
September,
Report No. 675, 28 August
and Grier, Inc.,
1964, EGG 1183-1069.
T. M. Putnam, R. A. Jameson, and T. M. Schultheis,
“The Applica-
tion of a Digital Computer to the Control and Monitoring Proton Linear Accelerator,” Conference, Washington,
of a
presented at the Particle Accelerator
D. C., March
in same manner as No. 12 above.
10-12, 1965.
To be published
R-3
REFERENCES
1.
-
CHAPTER 11
Lloyd Smith, “Linear Accelerators”
Handbuch der Physik, Band
XLIV, pp. 341-389. 2.
Livingston and Blewett, “Particle Accelerators,!! McGraw-Hill, 1962, Chapters 9 and 10.
3.
H. S. Butler, “Linac Error Analysis by Matrix Methods,” APS Meeting, Washington,
D. C., April
1965.
4.
H. S. Butler, Los Alarnos Scientific Laboratory,
5.
M. Rich, “Beam Dynamical Calculations with Realistic Fields in a Drift Tube Linear Accelerator,” Conference, Washington,
Washington
D. C., March
unpublished work.
Particle Accelerator
10-12, 1965.
To be published
in summer 1965 issue of IEEE Trans. on Nuclear Science. 6.
M. Jakobson and W. M. Visscher, “A Numerical Study of Radial and Phase Stability LASL P-n
7.
in a High-Energy
Proton Linear Accelerator,”
Internal Memo.
W. W. Harman, “Principles of the Statistical Theory of Communication,” McGraw-Hill,
1963, Chapter 7.
R-4
REFERENCES
1.
- CHAPTER III
A. Carrie, “Crossbar and Cloverleaf Structures at Rutherford,” Proc. of the Yale Conference on Proton Linear Accelerators, 1963, p. 104.
2.
E. A. Knapp, “Accelerating Structure Research at Los Alamos,” Proc. of the Yale Conference on Proton Linear Accelerators, 1963, p. 131.
3.
11800MeV RF Structures$ “ Proc. of the MURA Confer-
E. A. Kmpp,
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4.
M. Chodorow and R. A. Craig, Iisme New Circuits for High-power Traveling-Wave
5.
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M. Jakobson, “Some Calculations Wave Linear Accelerator, IIWSL
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1964, P. 31.
E. A. Knapp, Appendix
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E. A. Knapp, “Design, Construction and Testing of RF Structures for a Proton Linear Accelerator,” Conference, Washington, published
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D. C., March
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10-12, 1965.
To be
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B. C. Knapp, E. A. Knapp, G. J. Lucas, D. E. Nagle and J. M. Potter, “Electrical Behavior of Long Linac Tanks and a New Tank-Coupling Washington, No. 7 above.
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D. C., March
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10-12, 1965.
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R-5
9.
J. M. Potter, B. C. Knapp, E. A. Knapp and G. J. Lucas, “Resonantly Coupled Accelerating Linacs, ” Washington D. C., March
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10-12, 1965.
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To be published as in No. 7 above.
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S later, “Microwave Electronics,”
11.
Chodorow and Susskind, “Fundamentals McGraw-Hill,
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D. Van Nostrand, of Microwave
1950. Electronics,”
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12.
Gi.nzton, “Microwave Measurements,” McGraw-Hill,
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Gardner and Barnes, “Transients
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D. E. Nagle, IASL P-11 Internal Memo.
15.
O. A. Farmer, TAF Program, L4SL Group N-4, Los Alamos Scientific Laboratory.
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T. E. Springer, INLAP Program, IASL Internal Office Memos, 20 July 1961, 14 May 1963; modified by R. A. Jameson for the STRETCH computer to handle the precision requirements of this problem, Los Alamos Scientific Laboratory.
17.
T. L. Martin, Jr., “Electronic Circuits,” Prentice-Hall,
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R-6
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“Vacuum Tubes”, McGraw-Hill,
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1.
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F. E. Terman, “Radio Engineer’s Handbook”, McGraw-Hill,
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W. G.
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Slater, “Microwave Electronics”,
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D. Van Nostrand, of Microwave
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W. M. Visscher, Los Alamos Scientific Laboratory,
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C. H. ‘M. Turner, “Theoretical Analysis istics of the Power Amplifier,
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●
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F. J. Kriegler, F. E. Mills, J. van Bladel, “Fields Excited by Periodic Beam Currents in a Cavity-Loaded Phys. —35, 1721-1726
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“Beam Loading Effects
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R-7
REFERENCES
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- CHAPTER V
K. H. Sann, “Phase Stability of Oscillators”, February
Proc. I.R.E.,
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A. Hund, “Frequency Modulation”, McGraw-Hill,
3.
Based on information on a 107-2654A combination with a differ-
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L. B. Mullett,
“A Matrix Treatment of Four-Arm Bridges”, A.E.R.E.
(Harwell), Report No. GP/R 1578, 1955. 5.
J. Dobson and M. Lee, “The Beam Induction Technique of Phasing Linear Electron Accelerators
Over Large Ranges of Beam Current”,
TN-63-70, SLAC, December 1963. 6.
G. E. Schaefer, “Mismatch Errors in Microwave Measurements”, November
7.
I.R.E. Trans. on Microwave
C. B. Williams, “Design Report - Automatic
Phasing System for
SLAC, 1963.
J. B. Brinton, Jr., “Electronically Product Survey, Microwaves,
9.
Theory and Techniques,
1960, p. 617.
High Power Klystrons”, 8.
Phase Shift
Controlled Phase Shifters”,
December 1964, p. 72.
P. R. McIsaac and L. F. Eastman, “Studies of Phase Stability in Linear Beam Tubes”, Cornell University School of Elec. Engr’g., RADC-TDR 61-289, 20 October 1961.
10.
M. E. Malchow,
“Precision Measurement
of Short Term Frequency
Stability”, RCA Report No. EM-61-421-17,
July 1961.
R-8
REFERENCES
1.
J. L. Bower and P. M. Schultheiss, ‘ of Servomechanisms”,
2.
- CHAPTER VI
“Introduction
to the Design
Wiley, 1958, Chapter 8.
H. Chestnut and R. W. Mayer, “Servomechanism
and Regulating
System Design”, Vol. II, Wiley, 1958, p. 124. 3.
T. E. Springer, INIAP Program, LASL Office Memos
20 July 1961
and 14 May 1963, Los Alamos Scientific Laboratory.
R-9
GENERAL REFERENCES
General 1.
Minutes of the 1964 Conference on Proton Linear Accelerators held at Midwestern
Universities Research Association,
July
20-24, 1964, MURA-714, Edited by Mills, Curtis, Swenson and Young. 2.
Minutes of the Conference on Proton Linear Accelerators
at Yale
University, October 21-25, 1963, Edited by Knowles. 3.
Los Alamos Physics Facility Title I Design Study, 2 Vols., prepared by Giffels and Rosseti, Inc. Architects-Engineers, and Wm. M. Brobeck and Assoc., Consultants,
for the U.S.A.E.C.,
Los Alamos Area Office, Contract AT(29-1)1772. 4.
SLAC Quarterly
Progress Reports,
Stanford Linear Accelerator 5.
Alvarez,
1963,
Center.
et al, “Berkeley Proton Linac”, Review of Scientific
Instruments, February 6.
1 July 1962 - 30 September
1955.
C. R. Wylie, Jr., “Advanced Engineering Mathematics”,
McGraw-Hill,
1960. 7.
Y. W. Lee, “Statistical Theory of Communication”,
Accelerator 10
Wiley, 1960.
Structures
E. V. Bohn, “The Transform Analysis
of Linear Systems”, Addison-
Wesley 1963. 2.
S. Ramo and J. R. Whinnery, “Fields and Waves in Modern Radio”, Wiley, 1953.
3.
H. J. Reich, et al, “Microwave Principles”, D. Van Nostrand,
1957.
RF Amplifier
1.
Engineering
Study and Cost Estimate for Fifty 805 Mc Power
Iunplifiers, prepared by LTV Continental Electronics Continental Electronics Mfg. Co., for University
Division,
of California,
Los Alamos Scientific Laboratory, under P. O. LY-16005-1. 2.
Study Report - Los Alamos Meson Physics Facility Radio Frequency Power Equipment, prepared by Radio Corporation Defense Electronics
of America,
Products, Missile and Surface Radar Division,
for Los Alamos Scientific Laboratory,
University
of California,
under P.O. LY-16004-1. 3.
R. Graham, Jr., “TRADEX, The Second Generation UHF Transmitters”,
of Super-Power
presented at the 1963 PGMTT National Symposium,
May 20, 1963, Santa Monica, California. 4.
M. C. Jones, “Grounded Grid Radio Frequency Voltage Amplifiers”, Proc. I.R.E., July 1944, p. 423.
5.
Radio Corporation of America,
Defense Electronics
Products,
Missile and Surface Radar Division, Tradex Transmitter Memoranda TTDM-(u)-(92), 6.
7 September
1961, and TTDM-L-174,
I. E. Martin, et al, ‘\Technical and Experimental RF-Phase Stability in Grid-Controlled
15 December
1961.
Review of
Tube Amplifiers”,
RCA
Report No. 962-45. 7.
J. W. Rush, “The Use of Gridded Ceramic Vacuum Tubes in Phased Array Long Pulse UHF Radars”, The Microwave
Journal, May
1963, p.88.
R-II
Phase Detectors
1.
“phase Measurements
on a High Power Pulsed Microwave Amplifier”,
Tech. Proposal No. 134, Electronic Systems, Inc., Acton, Mass., September 2.
1964.
P. Lacy, “Automated Measurement Characteristics
of the Phase and Transmission
of Microwave Amplifiers”,
presented at the 1963
IEEE International Conv., New York City, March 25-28, 1963. 3.
N. P. Weinhouse,
!lp~se Measurement
Equipment Accuracy AmlYsis”s
Rantec Tech. Memo No. PM-1, Rantec Corp., Calabasas, California, 30 October 1962. 4.
R. A. Sparks, “Microwave Phase Measurements”, uary 1963.
5.
B. O. Pedersen, “Phase-Sensitive
S. B. Cohn and N. P. Weinhouse, Measurement
Jan-
Includes extensive bibliography. Detection with Multiple Fre-
quencies”, I.R.E. Trans. on Instrumentation, 6.
Microwaves,
December
1960, p. 349.
“An Automatic Microwave
System”, The Microwave
Journal, February
Phase
1964,
vol. 7, p. 49. 7.
R. A. Jameson, “Note on 4-Arm Bridge Phase Detectors”, LASL P-n Internal Memo, Los Alamos Scientific Laboratory.
8.
R. P. Featherstone,
“Further Note on 4-Arm Bridge Phase
Detectors”, LASL P-n
Internal Memo, Los Alamos Scientific
Laboratory. 9.
R. F. Koontz, “Microwave Phase Measurement Transmitter Systems”,
10.
1962 WESCON Conv., August 21-24, 1962.
R. A. White, “Swept Frequency Measurement of a Pulsed Microwave Amplifier”, Meas., June-September
of Dispersed Pulse
1964, p. 81.
of Phase Shift and Gain
IEEE Trans. on Instr. and
R-12 Phase Shifters
1.
C. M. Johnson, “Ferrite Phase Shifter for the UHF Region”, I.R.E. Trans. MTT, January 1959, p. 27.
2.
D. D. King, C. M. Barrack, C. M. Johnson, “Precise Control of Ferrite Phase Shifters”, I.R.E. Trans. MTT, April
3.
A. Clavin, “Reciprocal Ferrite Phase Shifters”, T,.R.E. Trans M’IT, March
4.
1959, p. 229.
1960, Correspondence,
C. F. Augustine
p. 254.
and J. Cheal, “The Design and Measurement
of Two
Broad-Band Coaxial Phase Shifters”, I.R.E. Trans MTT, July 1960, p. 398. 5.
A. S. Boxer, et al, “A High-Power Coaxial Ferrite Phase Shifter”, I.R.E. Trans MTT, December 1961, Correspondence,
6.
p. 577.
W. J. Robertson and J. R. Copeland, “A Proposed Lossless Electronic Phase Shifter”, I.R.E. Trans. MTT, September
1962, Correspondence,
p. 394. 7.
M. Cohn and A. F. Eikenberg,
“Ferroelectric
VHF and UHF”, I.R.E. Trans. MTT, November 8.
R. H. Hardin, et al, “Electronically
Phase Shifters for
1962, p. 536.
Variable Phase Shifters
Utilizing Variable Capacitance Diodes”, Proc. I.R.E., May 1960, Correspondence, 9.
H. N. Davirs and W. G. Swarner, “A Very Fast Voltage-Controlled Microwave
10.
p. 944.
Phase Shifter”, The Microwave
Journal, June 1962, p. 990
P. Penfield and R. P. Rafuse, “Varactor Applications”, Press, 1962.
The M.I.T.
R-13
Controls 1.
J. L. Bower and P. M. Schultheiss, of Servomechanisms”,
2.
“Introduction
to the Design
Wiley, 1958.
Seifert and Steeg, “Control Systems Engineering”,
McGraw-Hill,
1960. 3.
A. S. Jackson, “Analog Computation”, McGraw-Hill,
4.
H. Chestnut and R. W. Mayer,
“Servomechanism
1960.
and Regulating
System Design”, Vols. I and II, Wiley, 1959. 5.
Newton, Gould and Kaiser, “Analytical Design of Linear Feedback Controls”, Wiley, 1957.
