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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

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13th Advanced Accelerator Concepts Workshop.

Santa Cruz, July 27-August 2, 2008Seventh-Harmonic Multi-MW K-band Frequency Multiplier: Rf Source for for  High-Gradient Tests*

N.A. Solyak1,2, V.P. Yakovlev1,2, S.Yu. Kazakov1,3, and J.L. Hirshfield1,4

1Omega-P, Inc., New Haven, CT 06511, USA

2Fermi National Accelerator Laboratory, Batavia, IL, USA

3High Energy Accelerator Research Organization (KEK), Tsukuba, Japan

4Physics Department, Yale University, New Haven, CT 06520, USA

*Work supported by the U.S. Department of Energy


● 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.

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.
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.

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.

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.

20 GHz, waveguide 7th harmonic multiplier

[J.L. Hirshfield, et al, 2000]:

Sketch of the proposed two-cavity 7nd 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 TE111 (drive cavity)

Operating mode TE711 (output cavity)

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
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 TE711 mode output cavity tuned to 19.992 GHz. Cavity outlines are also shown.

Drive Cavity Design
  • The drive cavity:
  • Operating frequency - 2.856 GHz
  • Operating mode - rotating TE111
  • Loaded Q - 150
  • Maximal electric field - 58 kV/cm.
  • Rotating TE111 wave is excited by two standard waveguides placed by 90 deg of each other in azimuthal direction.
  • Two compensating protrusions to restore field symmetry
electric field
Electric field

Magnetic field

output cavity
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.
concept of output cavity coupler
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.

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



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.

Theory of traveling wave coupling
  • Rotating TE711 mode in output cavity is coupled thru the series of coupling slots to waveguide. The amplitude of rotating mode in cavity is equal:
  • Ncav – cavity azimuthal index
  • - azimuthal coordinate (angle).
  • Each coupling slot will excite waveguide with the amplitude:
          •  - coupling between cavity and WGi =2i/Nslot - 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:
  • Nwg - WG azimuthal index
  • Nslot - number of slots
waveguide dimensions
Waveguide dimensions

WG width for a=21mm (inner radius)



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=Nwg – azimuthal index.

(gradient limit) 6 < Nwg < 10 (dispersion)

Parameters for excitation Direct or Reverse traveling Waves

Ncav = 7(Considering 6 < Nwg < 10 only)

D - amplitude of a direct wave

R - amplitude of a reverse wave.

two configurations 7 8 9 and 7 28 7
Two configurations: 7-8-9 and 7-28-7

Configuration: Ncav-Nslot-Nwg

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

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.

Configuration 7-8-9 (HFSS simulations)
  • Eight slots, size = 15.358 mm x 2 degrees; Frequency = 20 GHz, Q=400 (over-coupling)
  • Good directivity (Small amplitude of direct wave)
  • Some transformation to quadrupole mode, which is not trapped in cavity
Case 7-8-9: HFSS simulations (2)
  • Half-cavity with the magnetic boundary conditions on plane of symmetry.
  • Ports on the waveguide
  • radiation boundary conditions at the end of beam-pipe

Slot/2= 6 mm x 3º.

Freq = 20 GHz.

Source :

WG port #1.

Dipole mode

Magnitude of electric field in cavity and waveguide at 0 phase.

configuration 7 28 7
Configuration 7-28-7

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

configuration 7 28 7 cavity parameters
Configuration 7-28-7: Cavity parameters
  • Frequency = 19.995 GHz
  • Q_ext = 909
  • Waveguide dimensions:
    • Rmin= 21 mm
    • Rmax= 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!

waveguide matching to standard wr51
Waveguide matching to standard WR51

WR51: 0.51”x 0.255” = 12.954 mm x 6.477 mm

Dimensions of matching

section in mm:

a = (0.1, 27.762); b = (5.536, 20.284);

c = (9.603, 25.228);

d = (6.578, 28.953)

S11 was matched at the level of 0.03 at the broad band

General Layout of the output cavity in 7th harmonic converter


Waveguides are penetrating through the gap between magnetic

Layout #1 of the output cavity inside magnetic system.

(blue-magnetic coil, grey – cavity, red – beampipe, magenta – waveguide).


● 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 7th 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 7th harmonic multiplier is developed.

● The preliminary design of the 7th harmonic multiplier is made.