# Presentation: 471499

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

*Santa Cruz, July 27-August 2, 2008*  Seventh-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
*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

## 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.

## 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 + Δ*f into* TE111 mode,
_*output: *_19.992 GHz + 7Δ*f  *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.

## 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. 

- 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.

## 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 TE**711** 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

**Drive Cavity Design**

## Electric field

- Magnetic field

## 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

- 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
- (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.

## Theory of traveling wave coupling

*	**	**	**	**	**    *
*	**	**	**	**	**    **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***

## 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
Nwg | WG width 
b=27mm | WG width
b=28mm |
| --- | --- | --- |
| 6 |  9.35451 |   9.24736 |
| 7 | 10.45173 | 10.24586 |
| 8 | 12.36498 | 11.91907 |
| 9 | 16.68916 | 15.35814 |
| 10 | 57.00037 | 29.70131 |

- WG width for a=21mm (inner radius)

*a*

*b*

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

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

| Number of coupling
slots | Nwg
for Reverse wave  | Nwg
for Direct wave | Ratio D:R
(One slot is missing) | Ratio D:R
(Two slots are missing) |
| --- | --- | --- | --- | --- |
| 5 | 8 | 7 | 4:1 | 2:1 |
| 6 | 5 | 7 | 5:1 | 4:1 |
| 8 | 9 | 7 | 7:1 | 6:1.414 |
| 9 | 2 | 7 | 8:1 | 7:0.347 |
| 10 | 3 | 7 | 9:1 | 8:0.62 |
| 11 | 4 | 7 | 10:1 | 9:1.31 |
| 12 | 5 | 7 | 11:1 | 10:1.732 |
| 13 | 6 | 7 | 12:1 | 11:1.942 |
| 15 | 8 | 7 | 14:1 | 13:1.956 |
| 16 | 9 | 7 | 15:1 | 14:1.848 |
| 21 |  | 7 | 20:1 |  |
| 28 |  | 7 |  | 26:0  |

* **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

## 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:  Ncav-Nslot-Nwg

## Table: Waveguide dimensions for 7-8-9 configuration

| Inner radius, a
mm | Outer radius, b
mm | Waveguide Width
hwg,  mm |
| --- | --- | --- |
| 21 | 26 | 18.479 |
| 21 | 27 | 16.689 |
| 21 | 28 | 15.358 |
| 21 | 29 | 14.316 |
| 21 | 30 | 13.474  |

- 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)

- Configuration 7-8-9 (*HFSS simulations*)

- 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)

- 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

## Configuration 7-28-7

| Inner radius, a
mm | Outer radius, b
mm | Waveguide Width
hwg,  mm |
| --- | --- | --- |
| 21 | 24 | 11.217429 |
| 21 | 25 | 10.931234 |
| 21 | 26 | 10.678429 |
| 21 | 27 | 10.451725 |
| 21 | 28 | 10.245861 |
| 21 | 29 | 10.057099 |
| 21 | 30 | 9.882853 |

- 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*

## 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

**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:

- S11 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*

## General Layout of the output cavity in 7th harmonic converter 

- 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).*

## 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 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.