This document discusses optimizing the charging of superconducting cavities to minimize reflected energy. It presents that the optimal charging profile can be determined by finding the charging curve that minimizes the reflected energy, which is treated as an effective Lagrangian. Simulations show that using the optimal profile requires more power from the RF source but reduces reflected energy compared to step charging. Accounting for practical sources like klystrons and their efficiency variations is also important to determine the best charging strategy.

1. Optimal Charging of Accelerating
Superconducting Cavities
For Reflected Energy Minimization
Anirban (Krish)na Bhattacharyya
FREIA / HIGH ENERGY PHYSICS
Uppsala University
June 10, 2015

2. Outline
• ESS and MAX-lab
• FREIA @ Uppsala University capabilities and activities
• Reflected energy minimization
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3. Large accelerator projects in Sweden
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MAX IV
ESS

4. Large accelerator projects in Sweden
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MAX IV
ESS
Two storage rings
3 and 1.5 GeV
Hard and soft X-ray/VUV
A 3 GeV linac
Undulators for 100 fs.

5. ESS
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Courtesy Matts Lindroos (ESS)

6. Cavity Parameters
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7. FREIA
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8. 6/10/2015 Anirban Krishna Bhattacharyya 7
FREIA
UU-ESS-IPNO-CERN &
Industry Collaboration
(Thales, Electrosys, DB Elettronica,
Siemens, NXP, ESRF, CERN)RF Source Development
(vacuum tube amplifier, solid-
state amplifier, SSA module &
combiner optimization)
High-power Spoke Cavity Testing
(tuning system, dynamic load, electron
emission, mechanical parameters and
multipacting)
Digital LLRF
Combined THz/X-ray
source
Future
• Acceptance testing of spoke
cryomodule
• Test of prototype spoke
cryomodule valve box
• Testing of crab cavities for
LHC upgrade
• ESS neutrino super beam.

9. FREIA
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Spoke Cavity
(super - conducting)
Courtesy of P. Duthil

10. FREIA
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Cryogens

11. FREIA
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Spoke Cavity
(super - conducting)
Courtesy of P. Duthil
Horizontal Cryostat

12. FREIA
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RF power /LLRF
CERN RF Station

13. FREIA
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Bunker
Spoke Cavity
(super - conducting)
Courtesy of P. Duthil
Horizontal Cryostat

14. FREIA
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30 mm 500 mm
output coupler connected to 3-1/8 inch coaxial line
7/16 inch input connector

15. FREIA
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16. Step Charging
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RF
Source
Circulator
Cavity
Load
Spoke Cavity
(super - conducting)
Courtesy of P. Duthil

17. Step Charging
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RF
Source
Circulator
Cavity
Load
Charging time
Spoke Cavity
(super - conducting)
Courtesy of P. Duthil
Beam injection

18. Step Charging
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RF
Source
Circulator Cavity
Load
Spoke Cavity
(super - conducting)
Courtesy of P. Duthil

19. Step Charging (Frequency domain)
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(MHz)

20. Optimal Charging
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• Instantaneous cavity voltage
Ib
Ig
Ir
Filling time
(Natural time
scale)
Loaded
Quality
factor
Generator
current
Loaded
cavity
impedance
(Nominal cavity voltage)

21. Optimal Charging
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• Instantaneous cavity voltage
• Reflected current
Ib
Ig
Ir
Filling time
(Natural time
scale)
Loaded
Quality
factor
Generator
current
Loaded
cavity
impedance
External
Quality factor
Bare cavity
Quality factor

22. Optimal Charging
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• Instantaneous cavity voltage
• Reflected current
• Reflected energy
Filling time Loaded Q Generator
current
Loaded
impedance
External Q Bare cavity Q

23. Optimal Charging
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• Reflected energy, , is the effective Lagrangian
• The concept of minimum action,
Optimal charging profile
Find optimal
and such
that is
minimum.

24. Optimal Charging
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• Reflected energy, , is the effective Lagrangian
• The concept of minimum action,
Optimal charging profile
Free parameter

25. Effect of Optimal filling
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Step filling Optimal filling

26. Effect of Optimal filling
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Step filling Optimal filling
No free lunch!!!

27. Effect of Optimal filling
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Step filling Optimal filling
More power needed

28. Effect of charging time ( )
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Peak generator powerReflected energy

29. Practical sources
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Gain characteristics Efficiency characteristics
/ IOT / IOT

30. Practical sources
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Efficiency characteristics
Klystron !!!!
/ IOT
W. Doherty, A new high efficiency power amplifier for modulated waves,
Radio Engineers, Proceedings of the Institute of 24 (9) (1936) 1163–1182.
doi:10.1109/JRPROC.1936.228468.
B. Kim, J. Kim, I. Kim, J. Cha, The doherty power amplifier, Microwave
Magazine, IEEE 7 (5) (2006) 42–50. doi:10.1109/MW-M.2006.247914.
R. Pengelly, N-way rf power amplifier with increased backoff power and
power added efficiency, wO Patent App. PCT/US2003/002,365 (Aug. 7
2003).
URL http://www.google.com/patents/WO2003065573A1?cl=en
P. Colantonio, F. Giannini, R. Giofr, L. Piazzon, The doherty power ampli
fier, INTERNATIONAL JOURNAL OF MICROWAVE AND OPTICAL
TECHNOLOGY 5 (6) (2010) 419–430.
G. Ahn, M. su Kim, H. chul Park, S. chan Jung, J. ho Van, H. Cho,
S. wook Kwon, J.-H. Jeong, K. hoon Lim, J. Y. Kim, S. C. Song, C.-S.
Park, Y. Yang, Design of a high-efficiency and high-power inverted doherty
amplifier, Microwave Theory and Techniques, IEEE Transactions on 55 (6)
(2007) 1105–1111. doi:10.1109/TMTT.2007.896807.
NXP Semiconductors, AN10967 BLF578 demo for 352 MHz 1kW CW
power, 2nd Edition, application note (November 2012).
D. Rees, D. Keffeler, W. Roybal, P. Tallerico, Characterization of a
Klystrode as a RF Source for High-Average-Power Accelerators, Conf.Proc.
C950501 (1995) 1521.
E. Montesinos, Tetrode power amplifiers, in: TIARA Workshop on RF
Power Generation for Accelerators, Uppsala University, A˙ ngstr¨om Laboratory,
2013.
N. Pupeter, Significant increase of efficiency of solid state amplifiers due
to improved ac/dc conversion and adaption of p1 point to actual operating
power, in: EnEfficient RF Sources, Cockcroft Institute, 2014.

31. Practical sources
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Source efficiency during filling
RF
Gain
Source
loss

32. Practical sources
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33. Effect of Transit time factor
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Variation Along Spoke LINAC

34. Effect of Transit time factor
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Peak power Charging time
Beam injection time,

35. Effect of Transit time factor
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ESS operation: 14 Hz pulse rate
140 J/sec saved
per cavity
Assuming 8000 hours of
operation 1.12 MWhrs
saved per cavity
10 J/pulse

36. Cryogenic considerations
• Losses on cavity surface
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Surface field Cavity voltage

37. Cryogenic considerations
• Losses on cavity surface
• Ratio of energy loss
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Surface field Cavity voltage

38. THANK YOU
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39. ESS
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40. Simulation Block Diagram
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Ʃ
Power
Amplifier
Cavity AntennaRF Controller Ʃ
Open Loop Set point
(Driving voltage to
source)
Cavity Voltage
set point
ƩBeam
-
Tuner Loop
Cavity
Phase
Ʃ
Power Output
Phase
-

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Source with and without saturation

42. Effect of charging time
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Supplied energy

43. Equations
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