1. 13 th Advanced Accelerator Concepts Workshop. Santa Cruz, July 27-August 2, 2008 Seventh-Harmonic Multi-MW K-band Frequency Multiplier: Rf Source for for High-Gradient Tests* N.A. Solyak 1,2, V.P. Yakovlev 1,2, S.Yu. Kazakov 1,3, and J.L. Hirshfield 1,4 1 Omega-P, Inc., New Haven, CT 06511, USA 2 Fermi National Accelerator Laboratory, Batavia, IL, USA 3 High Energy Accelerator Research Organization (KEK), Tsukuba, Japan 4 Physics Department, Yale University, New Haven, CT 06520, USA *Work supported by the U.S. Department of Energy

2. Motivation: ● In order to investigate the frequency scaling of breakdown, high power tests are necessary at frequencies from X-band upwards. ● Key elements for these tests are high power, 0.5-1  sec pulsed RF sources. ● A“ quick-and-cheap” high-power RF source, an Harmonic Multiplier, is proposed for this application and described in this talk.

3. Seventh-harmonic 20 GHz harmonic multiplier: ● Simple two-cavity structure, with room-temperature solenoid ● Uses hardware available at Yale Beam Lab.  the gun built for the CARA accelerator,  the SLAC XK-5 S-band klystron as the RF driver  modulators driver: 2.856 GHz + Δf into TE111 mode, output: 19.992 GHz + 7Δf out in TE711 mode. Note that phase stability is comparable to that of the 2.856 GHz klystron driver, and that technology (gun, modulator) is already proven.

4. XK5 S-band klystron and overhead WR-284 evacuated transmission line with variable amplitude and phase splitters in the Yale Beam Physics Laboratory. Also seen is the 300-kV gun modulator and gun tank. Gun tank, portion of magnetic system, and quadrature WR-284 feeds into CARA accelerator in the Yale Beam Physics Laboratory that can be available for the proposed harmonic multiplier. 65-MW modulator that powers the S-band XK-5 klystron in the Yale Beam Physics Laboratory. Klystron and gun modulator are visible in the background.

5. 20 GHz, waveguide 7 th harmonic multiplier [J.L. Hirshfield, et al, 2000]:

6. Sketch of the proposed two-cavity 7 nd harmonic frequency multiplier based on the S-band SLAC: Drive frequency: 2.856 GHz Output frequency: 19.992 GHz Drive power: 8.5-10 MW Output power: 4-4.7 MW Multiplication efficiency: 47% Beam power: 5 MW Beam voltage: 250 kV Beam current: 20 A Operating mode TE 111 (drive cavity) Operating mode TE 711 (output cavity)

7. Two-gap gun: The electron gun is a 100 kV, 10 -6 A –V-3/2, Pierce type diode gun with a 200 kV post-acceleration stage. The ratio of the cathode voltage to the intermediate anode voltage can be varied by approximately 10% to allow flexibility in the voltage/current characteristics of the output beam (i.e. the beam current is not entirely determined by the terminal voltage). Beam power: 5 MW Beam voltage: 250 kV Beam current: 20 A Beam perveance 0.16 ×10-6 A–V -3/2 Cathode diameter 50.8 mm Beam diameter in the drive section 2.5 mm Beam transverse compression ratio: 400:1

8. Magnetic circuit configuration, with 5 coils and 4 iron pole pieces. Plot at top shows the magnetic field profile generated by this circuit. Drawing at bottom shows drive cavity (left) and output cavity (right). Beam particle energies (blue) and radial excursions (red) with the TE 711 mode output cavity tuned to 19.992 GHz. Cavity outlines are also shown.

9. The drive cavity: Operating frequency - 2.856 GHz Operating mode - rotating TE 111 Loaded Q - 150 Maximal electric field - 58 kV/cm. Rotating TE 111 wave is excited by two standard waveguides placed by 90 deg of each other in azimuthal direction. Two compensating protrusions to restore field symmetry Drive Cavity Design

10. Electric field Magnetic field

11. Output Cavity Cavity parameters: –Operating frequency, GHz – 19.992 (7x2.856 GHz); –Operating mode - rotating TE711 –Loaded Q - 900 –Maximal electric field -175 kV/cm.

12. Concept of output cavity coupler At least two waveguide are necessary to load both polarizations. Unfortunately, such a scheme doesn’t work for the modes with high azimuthal index: Large perturbation of field due to coupling slots Coupling to other modes Problem of power input / output from the cavity with rotating wave is important for many high power devices for accelerator applications Solution is well-known* – azimuthally distributed coupling waveguide runs around cavity and coupled through many slots Wave phase velocity in WG and azimuthal location of coupling slots have to be chosen accordingly to azimuthal index in cavity to excite travelling wave *Suggested by N. Solyak at 1985 for 7 GHz, 60 MW gyrotron.

13. High power RF devices based on such approach: Output cavity of the 7GHz, 60 MW Gyrocon (frequency multiplier) (BINP,1985, N.Solyak) Pulse compressors ● 11.4 GHz, 135 MW (BINP/KEK, 1991) ● 3 GHz, 80 MW (CERN,1998,I.Syrachev) Klystron Proposal for CLIC 937 MHz, 50 MW MBK design (CERN, 2005, I.Syrachev et al.,) 1-RF cavity; 2-collector 3-collector; 4-coupling holes. The output cavity with incorporated mini-windows.

14. Rotating TE 711 mode in output cavity is coupled thru the series of coupling slots to waveguide. The amplitude of rotating mode in cavity is equal: N cav – cavity azimuthal index  - azimuthal coordinate (angle). Each coupling slot will excite waveguide with the amplitude:  - coupling between cavity and WG  i =2  i/N slot - angular position of each slot In waveguide two waves are excited: direct wave D (running in the same direction as rotating mode in cavity) and reverse wave R (opposite directions). The amplitudes of these modes are as follow: N wg - WG azimuthal index N slot - number of slots Theory of traveling wave coupling

15. Waveguide dimensions Waveguide dimensions is defined from equation: 0 =c/f – free space wavelength, c - critical wavelength in coaxial waveguide, which is defined from the equation: Here a,b – waveguide radial dimensions, k=N wg – azimuthal index. Index N wg WG width b=27mm WG width b=28mm 6 9.35451 9.24736 7 10.4517310.24586 8 12.3649811.91907 9 16.6891615.35814 10 57.0003729.70131 WG width for a=21mm (inner radius) a b (gradient limit) 6 < N wg < 10 (dispersion)

16. Number of coupling slots N wg for Reverse wave N wg for Direct wave Ratio D:R (One slot is missing) Ratio D:R (Two slots are missing) 5874:12:1 6575:14:1 8977:16:1.414 9278:17:0.347 10379:18:0.62 114710:19:1.31 125711:110:1.732 136712:111:1.942 158714:113:1.956 169715:114:1.848 21720:1 28726:0 D - amplitude of a direct wave R - amplitude of a reverse wave. Ncav = 7 (Considering 6 < Nwg < 10 only) Parameters for excitation Direct or Reverse traveling Waves

17. Two configurations: 7-8-9 and 7-28-7 CASE 1: Configuration 7-8-9 Traveling waves in Cavity and Waveguide are rotating in opposite directions CASE 2: Configuration 7-28-7 Direction of rotating of TW in cavity and waveguide are the same Configuration: N cav -N slot -N wg

18. Inner radius, a mm Outer radius, b mm Waveguide Width h wg, mm 212618.479 212716.689 212815.358 212914.316 213013.474 Table: Waveguide dimensions for 7-8-9 configuration Red line shows dimensions, which are close to standard waveguide - WR51: width x height = 12.954 x 6.477 mm. It will be easy to mach them.

19. Eight slots, size = 15.358 mm x 2 degrees; Frequency = 20 GHz, Q=400 (over-coupling) Configuration 7-8-9 ( HFSS simulations ) Good directivity (Small amplitude of direct wave) Some transformation to quadrupole mode, which is not trapped in cavity

20. Magnitude of electric field in cavity and waveguide at 0 phase. Case 7-8-9: HFSS simulations (2) Slot/2= 6 mm x 3º. Freq = 20 GHz. Source : WG port #1. Half-cavity with the magnetic boundary conditions on plane of symmetry. Ports on the waveguide radiation boundary conditions at the end of beam-pipe Dipole mode

21. Configuration 7-28-7 Inner radius, a mm Outer radius, b mm Waveguide Width h wg, mm 212411.217429 212510.931234 212610.678429 212710.451725 212810.245861 212910.057099 21309.882853 Waveguide dimensions for 7-28-7 configuration WR51: 0.51”x 0.255” = 12.954 mm x 6.477 mm. WR42: 0.42” x 0.17” = 10.688 mm x 4.318 mm

22. Configuration 7-28-7: Cavity parameters Frequency = 19.995 GHz Q_ext = 909 Waveguide dimensions: R min = 21 mm R max = 27 mm Width = 10.45 mm Slot size = 4mm x 2  Fig. shows half-cavity Cavity is exited by port#1. Complex amplitude of the electric field Good quality of traveling wave Compensating Coupling protrusions slots No propagating modes!

23. Waveguide matching to standard WR51 a = (0.1, 27.762); b = (5.536, 20.284); c = (9.603, 25.228); d = (6.578, 28.953) Dimensions of matching section in mm: S 11 was matched at the level of 0.03 at the broad band WR51: 0.51”x 0.255” = 12.954 mm x 6.477 mm

24. Layout #1 of the output cavity inside magnetic system. General Layout of the output cavity in 7 th harmonic converter Layout#2 Waveguides are penetrating through the gap between magnetic (blue-magnetic coil, grey – cavity, red – beampipe, magenta – waveguide).

25. Conclusions ● Through use of 8.5-10 MW S-band drive power from SLAC XK-5 klystron and the beam from the CARA gun, preliminary simulation results indicate that a simple two-cavity 7 th harmonic multiplier can be designed and built to furnish ~4-5 MW of phase-stable RF power at 20 GHz for use in high gradient accelerator R&D. ● Theory is developed of the azimuthally-distributed coupling of the cavity with rotating whispering-gallery mode to the rectangular waveguide. Basing on this theory, the design of the output cavity with 28 coupling slots for the 7 th harmonic multiplier is developed. ● The preliminary design of the 7 th harmonic multiplier is made.