# Presentation: 407862

## Liling Xiao, Zenghai Li

_**Advanced Computations Department, SLAC**_

- Presented at LARP-CM11, FNAL, Oct. 27-28, 2008

**Notes:**
Graeme reported the waveguide coupler design for the LHC crab cavity.
We had proposed another coupler schemes we named it the coax-to-coax coupler and coax-to-waveguide coupler. They utilize a coax coupler or waveguide coupler feeding into a short coaxial beampipe. They should give strong damping in a compact structure. Today I will update the progress on the coax-to-coax coupler design for the LHC crab cavity.

## Outline

**Cell Shape Optimization**
**Optimum Squash Ratio**
**LOM/SOM Coupler Design**
**HOM Coupler Design**
**Cavity Configuration Considerations**
**Summary**

## Cell Shape Optimization

- _400MHz Cavity Design, __Courtesy  Rama Calaga's _

**Cell Shape Optimization**

- Maximum kick gradient limited by Bpeak
- Optimize disk parameters for optimal Epeak and Bpeak
- Cell_l=187.5mm, R_disk=70mm

- TM110-pi

- _Without Squashed, __Courtesy Rama Calaga_

- 800MHz crab cavity design

## Optimum Squash Ratio

- Fc=1.2GHz@R_beampipe=70mm

*Squash ratio is chosen to optimize mode separation.*
*Max Dx is limited by available horizontal space*

- Dx

**Optimum Squash Ratio**

- Dy

## 800MHz Crab Cavity RF Parameters

**800MHz Crab Cavity RF Parameters**

- E-field

- B-field

- TM110-pi mode

## Damping Requirements

**High R/Q LOM and SOM modes need to be strongly damped.**

**Qext for LOM<200**

- _Courtesy F. Zimmermann, R. Calaga_

**Damping Requirements**

## LOM/SOM Damping Schemes

**LOM/SOM Damping Schemes**

- Symmetric Waveguide

- Shorted Waveguide

- Coax

- Coax-to-coax

- Coax-to-waveguide

- Hook type coax

- Other coupler ideas (BNL, JLAB, LBNL, FNAL, ANL, UK ...)

## LOM/SOM Coax-to-Coax Coupler Design 

**LOM/SOM Coax-to-Coax Coupler Design **

- LOM/SOM

- gap

- R_disk=70mm

- R_beampipe=60mm

**Give strong damping on unwanted modes in a compact structure because no cutoff for TEM mode in the coax**
**Is more flexible to achieve the required damping by adjusting the location of the beampipe tube and the intrusion of the coupler probe **

- d

- Gap=10mm

***There are two additional LOM modes due to the coupling of the cavity modes to the shorted coaxial beampipe TEM modes.***

## LOM/SOM damping results meet the requirements! Qext<100

***LOM/SOM damping results meet the requirements! Qext<100***

## HOM Coupler Design  

***df/dgap=0.4MHz/micron***

- HOM coupler: damp the dipole modes in the horizontal plane
-                         reject the operating TM110 mode at 800MHz.

- HOM notch filter transmission curve

- A two-stub antenna instead of the coupling loop is proposed.
- This can simplify the model and remove the narrow gap between the loop and the outer cylinder which is prone to multipacting.

**Notes:**
Next we will work on the HOM coupler with filter. It is under progress.
There are many possible options on the arrangement about the FPC/HOM/LOM/SOM couplers. Here is one concept design for the whole LHC crab cavity.
Once the impedance budget and other constraints are confirmed, we can chose one of them.
So far the max transverse dimension in the 800 MHz cavity is about 237mm that is larger than the beam-to-beam separation of 200mm. One possible option which was suggested before is to turn the cavity to use the high frequency TM110-pi mode as operating mode.  

## Cavity Configuration Considerations

**Cavity Configuration Considerations**

- LOM/SOM

- HOM

***Option 2: LOM mode may shift to one side due to asymmetry, may result in ineffective damping***

- FPC

- LOM/SOM couplers use the electric node to reject operating mode, and symmetry is very important in cavity-coupler integration.

- LOM/SOM

**Notes:**
Next we will work on the HOM coupler with filter. It is under progress.
There are many possible options on the arrangement about the FPC/HOM/LOM/SOM couplers. Here is one concept design for the whole LHC crab cavity.
Once the impedance budget and other constraints are confirmed, we can chose one of them.
So far the max transverse dimension in the 800 MHz cavity is about 237mm that is larger than the beam-to-beam separation of 200mm. One possible option which was suggested before is to turn the cavity to use the high frequency TM110-pi mode as operating mode.  

## cell_l

***Option 3: Power coupler and HOM couplers in between of the two cells***
- Maintain field symmetry in LOM/SOM coupler regions
- Avoid cross coupling between power coupler and LOM/SOM couplers

| Modes | R/Q& (R/Q)T (ohm/cavity) | Qext |
| --- | --- | --- |
| LOM: TM010-pi (~600MHz) | 94 | 80 |
| LOM: TM010-0 (~600MHz) | 130 | 80 |
| Operating Mode TM110-0 (800MHz) | 110 | 106 @ FPC |
| SOM: TM110-0 (890MHz)  | 80 | 50 |

**Further HOM coupler optimization is needed. Waveguide coupler can also be considered as HOM coupler.  **

- FPC

## Summary

**Summary**

- Thanks all the members of LHC Crab Cavity Collaboration for valuable discussions.

- Significant progresses have been made for the 800MHz crab cavity design for LHC
- Strong damping achieved using coaxial-beampipe to coax LOM/SOM couplers, Qext of high R/Q modes below 100
- HOM coupler optimization is underway
- Multipacting simulations in cavity/couplers are in progress
- Further simulations planed to analyze RF/thermal/mechanical effects