# Presentation: 941488

##  325 MHZ RFQ for the FNAL proton driver

- P.N. Ostroumov, A.A. Kolomiets and V.N. Aseev
- Physics Division, Argonne National Laboratory

- November 28, 2005

## Basic RFQ Parameters

| Average radius R0, cm | 0.340 |
| --- | --- |
| Vane curvature radius Re, cm | 0.255 |
| Voltage Ul, kV | 90.45 |
| Length   (cm) | 302.71951 |
| Modulation factor | 1 – 1.98 |
| Synchronous phase, degree | -90,  -30 |
| Transverse phase advance, 0/45mA, degree | 45/32 |
| Transverse acceptance norm.,  cm mrad | 0.289 |
| Peak surface field, kV/cm | 330 |
| Peak surface field, Kilpatrick units | 1.8 |

***R******0*** is constant along RFQ
***R******e****** ***= 0.75 ***R******0 ***along RFQ
***U******l*** is constant along RFQ
- Modulation factor profile is given in  file **FNAL 325 RFQ.xls**
- Synchronous phase profile is given in file **FNAL 325 RFQ.xls**

## Peak surface field

- 	The RFQ design procedure maintains peak surface field ***E*****max** constant along the structure. The peak surface field was calculated using the empirical expressions:
- 	where

***A***10 – coefficient of field expansion (see PARMTEQ or TRACK manuals). The Kilpatrick limit ***E******s  ***[kV/cm] has been found from the equation

- Where ***f ***[MHz]– operational frequency, ***g*** [cm] – minimum distance between unmodulated RFQ electrodes and is defined as

- (1)

## Peak surface field

- Recently the validity of above mentioned formula we have confirmed by EMS software. EMS simulations produces about 2-3%  higher  peak surface fields compared with the estimations using simple formula (1) on previous page.

|  | EM simulation | Expression (1) |
| --- | --- | --- |
| Cell number | 233 | 233 |
| Cell length, cm | 1.744 | 1.744 |
| Modulation | 1.98 | 1.98 |
| Maximum field, kV/cm | 334.7 | 329 |
| Maximum field, Kilpatric limits | 1.83 | 1.8 |

**EM Studio model of ANL design electrodes**

**Peak Field on the Vertical  Electrode along a cell**

- Distance (cm)

- Emax (kV/cm)

- Example

## Main section of the RFQ

**2R****e**

**2ma**

**2a**

**2R****0**

**L****c**

**Cross section with exact **
**quadrupole symmetry**

**Geometry of electrodes**

- Modulation of electrodes is sinusoidal with constant radius of vane tip curvature. Distance from axis to the electrode surface along ***i***-th cell is

***R******0*** – distance from the axis to the electrode at cross section with exact quadrupole symmetry
***m*** – modulation factor

***L******c*** – cell length. For constant synchronous phase

- Here
****** – relative velocity of the synchronous particle,
******** ****- **wave length of rf field

- Modulation and cell length of electrodes for each cell has been calculated with DESRFQ code and are given in the file **FNAL** **325 RFQ.xls.**
- In the regular bunching-accelerating sections of the RFQ electric field has been presented by 8 terms of Fourier-Bessel expansion. These terms are the same as in PARMTEQ code.

- for vertical plane,

- for horizontal plane.

*z *is the longitudinal coordinate along the vanes.
- Z*i** *= is the longitudinal coordinate of the beginning of the *i-th *regular
- cell. The beginning of the cell is the point with exact quadrupole
- symmetry.

## Vanes

- Geometry of electrodes Is given in the file **vanes.xls**

## Input Radial Matcher 

**Input Radial Matcher **

| Beam current, mA |  | 0 | 10 | 20 | 30 | 45 |
| --- | --- | --- | --- | --- | --- | --- |
| Twiss 
parameters |  | 1.10 | 1.15 | 1.20 | 1.26 | 1.33 |
|  | , cm/rad | 3.30 | 3.38 | 3.47 | 3.56 | 3.69 |
| Matching coefficient |  | 1.018 | 1.019 | 1.019 | 1.020 | 1.022 |

**Input Matcher Electrode Profile**

- Distance (cm)

- Radius (cm)

- Distance ***r*** from the RFQ axis to the electrode in the input radial matcher is given by the expression

**Calculated Initial Matched Beam Parameters**

- Here ***R******0*** is average radius, ***R******0*** = 0.34 cm
***L******c*** – cell length

**EM Studio Model of Input Matcher**

- Here ***N*** – number of cells, ***N***=6
******in – relative velocity of injected beam,
- - rf field wavelength.
- For TRACK simulations 3D field distribution is calculated with EM Studio has been used.

## Output Radial Matcher

**EM Studio Model of output Matcher**

- Distance ***r*** from the axis to  the electrode in the output radial matcher is given by the expression

- Here ***L******1****** = ***2.2168 cm***,  D=***12.5664** **cm
***L******2*** = 13.7779 cm is the length of the output matcher. These parameters are optimized to provide similar Twiss parameters in both H- and V-planes.
- In the TRACK simulations we have used  3D field distribution calculated with EM Studio

**Output Matcher Electrode Profile**

- z (cm)

- r (cm)

## Slide 9

## Slide 10

## Slide 11

## Slide 12

## TRACK Window

**TRACK Window**

## TRACK Simulation

|  | 2 term | 8 term |
| --- | --- | --- |
| Output energy, MeV/u | 2.4936 | 2.4934 |
| Transverse emittance, 4 rms, in/out,  cm mrad  | 0.100/0.103 | 0.100/0.107 |
| Transverse emittance, 99.5%, in/out,  cm mrad  | 0.140/0.209 | 0.140/0.213 |
| Long. emittance, 4 rms,  keV/u nsec | 4.61 | 4.41 |
| Long. emittance, 99.5%, keV/u nsec | 13.81 | 13.76 |
| Acceleration efficiency, % | 96.7 | 96.5 |
| Particle losses inside the RFQ, % | 1.3 | 1.8 |

**TRACK  Simulation Results**

- Energy (MeV)

**Particle Losses**

- Lost particles (%)

- For H-minus beam the kinetic energy is equal to
- 2.4936*1.00838=2.514 MeV

- Two colors represent simulations with 2-term and 8-term potential

## Phase Space Plots at the RFQ end

**Phase Space Plots at the RFQ end**

**Longitudinal**

**Transverse**

- Emittance (keV/u nsec)

- 1-N/N0

- 1-N/N0

- Emittance ( cm mrad)

- Phase (deg)

- dW/W (%)

- X (cm)

- dX/X (mrad)