# Presentation: 886351

## ML Quad	Requirements 	and Specs	

- Nikolay  Solyak

## Latest changes in ML

**CCR#24a**: Change of the cryomodule (CM) layout driven by each of the 10MW klystron RF unit. Previously, the basic linac cryomodule ‘cell’ consisted of two 8-cavity cryomodules without a magnet and one 8-cavity cryomodule with a magnet (8-8-8). Implementation of this change request will result in a cell of two 9-cavity CM without a magnet and one 8-cavity with a magnet (9-8-9). Thus, 26 cavities are to be driven by one 10MW klystron rather than the previous 24.
**CCR#24b**: Elimination of RF unit overhead. Previously, 3.5%. Now, 0%. However, the conventional facilities, including the tunnels, are to be maintained to accommodate the missing 3.5% worth of RF systems if/when determined needed.
**CCR#24c: **Elimination of the uncertainty factor in the cryogenic static heat load. Previously, 50%. Now, 0%. This allows lowering the cryogenic capacity by 13%.
**CCR#24d**: To modify the baseline parameters.  Operation with these parameters would result in a luminosity of 2.1 × 1034, in spite of a small reduction in total charge and average current, through reduction of horizontal β* at the IP.
**2. CCB recommends that the EC: **
**	****A. To accept CCR#24a. **
**	****B. To accept CCR#24b. **
**	****C. To reject CCR#24c.**** **
**	****D. To accept CCR#24d.**** **

## ML 9-8-9 Lattice

**37.956**

| Tolerances | Vertical (y) plane |
| --- | --- |
| BPM Offset  w.r.t. Cryostat | 300 μm |
| Quad offset w.r.t. Cryostat | 300 μm |
| Quad Rotation w.r.t. Cryostat | 300 μrad |
| Structure Offset w.r.t. Cryostat | 300 μm |
| Cryostat Offset w.r.t. Survey Line | 200 μm |
| Structure Pitch w.r.t. Cryostat | 300 μrad |
| Cryostat Pitch w.r.t. Survey Line | 20 μrad |
| BPM Resolution | 1.0 μm |

## Number of quads

| Main  linac (15-250 GeV) | # CM | # Quad |
| --- | --- | --- |
| Electron Linac* | 846  | 282 |
| Positron Linac | 834 | 278 |
| Overhead (3.5%) | 30+30 | 10+10 |
| Total | 1680+60 | 560+20 |

- *Includes 12 CMs to recover 3 GeV energy losses in undulator
- Not included CM and quads in RTML system (same design)

## Main Linac Cryomodule

**Quadrupole and Corrector**

**BPM**

**SCRF**

**300 mm pipe**

**Central support**

**SCRF**

- TESLA TDR

- ILC

- Combined or stand alone correctors ?  

## Quad package in Separate cryostat option?

- Benefits: Independent from CM, better alignment, vibration stability, easy upgrade to 1TeV.
- But ...Not in RDR baseline design. R&D postponed.

- Not in RDR document

## ILC2006e (8-8-8) Lattice. Curved linac

- MAD

- Dispersion

- Beam Trajectory

- Undulator

- 1Quad/3CM (9-8-9) Lattice
- Spacing ~38m
- x/y phase advance = 75°/60°
- ~10% strength variation in matching sections

## Energy Upgrade path

- _HE Linac  (250-500 GeV)_
- Same layout 1Q/3CM
- Same Quad strength
- Half-phase advance, 30deg
- Stronger Correctors (~10% if the same curvature)

## Quads in Matching sections (8-8-8)

- ! match FODO cell
- Kf :=   0.050639379596
- Kd := - 0.045468508059
- ! Match at the end of linac
- QML184 : K1=-0.046873933156
- QML185 :  K1= 0.053475880256
- QML186 : K1=-0.050814879351
- QML187 :  K1= 0.057532693993
- QML188 : K1=-0.056273098368

- ! match between cryo strings
-  KML001 :=  0.051534217418
-  KML002 := -0.047121431874
-  KML003 :=  0.05256226055
-  KML004 := -0.045999875653
- ! match between cryo segments
-   KML013 :=  0.050223631804
-   KML014 := -0.042933511963
-   KML015 :=  0.043435434262
-   KML016 := -0.040256932375
-   KML017 :=  0.04189803359
-   KML018 := -0.041137076483
-   KML019 :=  0.046355757702
-   KML020 := -0.044726545476
- ! match between cryo units
-   KML064 := -0.038574388805
-   KML065 :=  0.0399426354
-   KML066 := -0.043070513254
-   KML067 :=  0.046690240896
-   KML068 := -0.044216847834
-   KML069 :=  0.051250690772

- Needs ~10% higher Quad Strength for Matching section

- 250 GeV, K=0.058  B’ =48 T/m

## Quadrupole Strength

- 	Integrated Quad strength is defined by quad spacing, required phase advance and beam energy.
- Quad spacing for 1Q/3CM Lattice ***s = 38 m *** (9-8-9 cavities in RF unit)
- Designed phase advance (*********x************y***) = 75°/ 60°. For flexibility quad should provide optics with phase advance *********= 90°*** up to E=250 GeV.
- L (effective) =  0.626m

- Add  20% for matching (10%) and uncertainty

## Correctors

- Corrector will bend beam in vertical plane to transport beam along earth curvature  and correct beam offset ***y** *
- 			*where ****s - ****quad spacing****, R = 6400 km - ****Earth radius.** *
- RMS Quad alignment offset:   0.3 mm;   3  0.9 mm;
- Correction coil max field to correct 1.5 mm beam offset at 250 GeV
- Corrector strength to deflect beam in vertical plane along earth surface is  <10 % of strength needed for beam/quad offset correction.
- There is one correction coil for vertical beam deflection in every magnet package and one for horizontal beam deflection in every second package.

## Quad specs

***Dimensions: ***
- Beam pipe* *diameter = 78 mm
- Quad total length (z- slot) ~ 0.66m  (TESLA - 0.666 m)
***Integrated gradient:***  (if L=0.66 m) *scales with energy*
** **B'*L < 31 T (B' < 50 T/m)  - 1Q/3CM lattice at 250 GeV
***Max current:*** (at 250 GeV) = 100A
***Stability*****:**
- faster than orbit correction (<1 ms)  < 2.e-5
- slower than orbit correction (>0.2 s) < 1.e-3
***Higher harmonic tolerance***: not studied yet
- Skew quad        < 3.e-4   (at reference radius 5mm)
- High harmonics < 1.e-3   (at r=5mm)
- Field in cavity region <10 T (at r=35mm, z~650 mm from quad center. Cavity has magnetic shielding)

## Quad (cont.)	

***Alignment (installation) tolerances:  ***
*X/Y Position <* 0.3 mm *(rms)*
- Pitch, yaw, roll : < 0.3 mrad
**Reference: TDR alignment (angle) < 0.1 mrad (~5um@ 50mm)**
- Roll tolerance are tight, needs built-in skew corrector (?)
***Field changes:***
- 20% of nominal for quad shunting (finding BPM-Quad offset),
- 100% for ballistic alignment
- Within a few seconds
- Center motion:  below 2 um / 20%
***Upgrade Path (500GeV/linac):***
- twice weaker lattice at high energy (>250GeV)

## Dipole Correctors

***Maximum integrated strength***
- (at 250 GeV to correct  1.5 mm beam offset)
- 0.05 [T•m]  integral strength or 0.074 T (L=0.66m) for 1Q/3CM lattice
- <10% of strength needs to deflect beam along the Earth curvature
***Max current:*** (at 250 GeV) = 40A
***Stability:*** same as for quads.
- Field change: by a few percent in 0.2 s, every 0.2 s
- Change step: (~1m of quadrupole motion)
** ****2.e-6 T*m at  15 GeV**
** ****3.e-5 T*m at 250 GeV **

## Specifications

| Quad 
 | Beam pipe diameter 
Inner coil diameter 
Coil Length
Gradient, max
Operating T
Nominal Current
Max Field at conductor
N turns/pole
Inductance | 78
90
626 
60
2 
100
3.6 
1007* 
~3.2* | mm
mm
 mm
T/m
K
A
T

H |
| --- | --- | --- | --- |
| Field quality
 | Skew quadrupole
Higher harmonics* 
Alignment error (angle)  | 3.e-4
1.e-3 
0.1 | 

mrad (rms)  |
| Dipole coil | Length (if separate) 
Max Current
Max Field at conductor
Max Field at axis
Inductance | 350
40
3.6
0.074
~29* | mm
A
T
T
mH |

**	****( Some specs are copied from TESLA TDR as a reference)**
- *Tolerances for higher harmonics are probably looser. Need to check.

## Magnet strength errors (K.Kubo) 

*** ******Vertical position change due to magnet strength error.****** ***
***Relative magnet strength*** < 2.10-5  0.14 rms beam offset
- (Random 0.14  offset of each beam will make average position offset 0.2 
- between two beams at IP, which will decrease luminosity about 3%, without
- beam-beam force.)
-  Very tight but relevant only for **fast jitter**, faster than orbit feedback
***2. Emittance increase due to magnet strength error.***
***	***
***Relative magnet strength*** < 2*10-3   /0 less than 0.063
- (Emittance increase by 0.063 will decrease luminosity about 3%, without beam-beam force.)
***Stability*** slower than orbit correction

- Magnet strength errors (K.Kubo)
- (quad and dipole correctors)

## Summary of preliminary magnet studies

- Design work started. Magnet design review April 5, 2007.
- R&D and prototyping are needed to confirm the specified performance and efficiency
_*Main issues:*_
-   - Optimal quadrupole configuration
-   - Integrated field range (high:low)
-   - Magnetic center stability during –20% field change
-   - Combined or stand alone correctors ?
-   - Fringing fields in SCRF areas from magnet package
-   - Effective current leads