1. Tolerances: Origins, Requirements, Status and Feasibility
R. Zennaro
R. Zennaro CLIC meeting 27/04/07

2. Tolerances of the structures
4 kinds of tolerances:
Machining (Δx, Δy, Δz)
Assembly (Δx, Δy, Δz)
Alignment (Δx, Δy, Δz)
Operation [Cooling] (ΔT (t) water in, ΔT (z))
4 kinds of problems:
Beam induced transverse kick (wakefield)
RF induced transverse kick
RF matching (reflected power)
Phase error
2 kinds of technologies:
Structures in quadrants
Structures in disks
Predictable: operational temperature, longitudinal elongation, transverse elongation
Unpredictable: water temperature instability, RF power variation

3. Schematic view of possible errors9 10
Schematic view of possible errors

4. 10

5. CLIC_G Courtesy of A. Grudiev
Structure Shape
Dephasing:
Mismatching:
Beam dynamics: An error in the cell shape determines a wrong phase advance
Reflected power: in a structure a geometrical error introduces a reflection i.e. lower efficiency. Considering the last cell (narrowband; vg=0.83%) , the pass band at -30 dB is ~5 MHz and the computed tolerance (DB) to get S11< -30 dB is ~1.5 micron, if any tuning is applied. B D A P
The sensitivity of the phase advance to the main geometrical parameters has been computed for the different cells of the CLIC_G structure. Strong dependence on the group velocity: vg/c(%): 1.66 (first cell) 0.83 (last cell)
CLIC_G Courtesy of A. Grudiev

6. Example of a systematic error: metrology of a structure in quadrant (NDS4_vg2.5_thick)
Error (microns)
Average cell radius error:
Aperture error: negligible

7. Structure Shape (systematic error)
1 micron error, if systematic, gives a very large error on the average phase advance per cell (~11 deg).
Acceptable average phase error (Daniel): ~ 1 deg
dφ/dB= (dω/dB)/vg
Tuning is required
The phase error implies a variation on the effective accelerating field
Loaded
Unloaded

8. Example of random (?) errors: CLIC_VG1: RF measurements in KEKB
Average phase advance per cell
degrees / cell
Average phase advance per cell
degrees / cell
Single cell phase advance error up to 10 deg, sigma A~ 4.5 deg, sigma B~ 5.6 deg, average phase offset is less then 1 deg, D gradient A~0.3%, D gradient B~0.3% (calculated for syn. phase= 8deg)
Courtesy of T. Higo

9. Structure Shape (random error)
Gradient error generated by a Gaussian distribution of the phase; NO average phase error.
Acceptable average gradient error: sigma=2% (D. Schulte)
DB <17 microns (first cell); 9 microns (last cell)

10. Structure Shape: Tuning by deformation (push-pull)
The tuning is provided by deformation with the push/pull technique.
Very conservative approach (all the cells are tuned in one goal):
Assuming for the tuning screw a step of 0.5mm and a precision of 15o – 20o, the correction can compensate an error equivalent to DB~1 micron
Less conservative approach (cells tuned individually):
Tuning range determined by the tuning correction range (0.5 mm ?)

11. Negligible systematic error+ random errors < 1
Negligible systematic error+ random errors < 1.5 micron (for the matching)
No tuning required
Systematic error < 1 micron + random errors<1.5 micron
All the cells are tuned in one goal
Else
Individual tuning of each cell

12. Bookshelf or longitudinal misalignment of half-structure
Structure in quadrants
problem mainly for the machining and assembly Dz
Δz1 ≈ D/a* Δz
Δz1
Structure in disks
problem mainly for the brazing (assembly); probably easier to achieve

13. Bookshelf or longitudinal misalignment of half-structure
Direct kick calculation
Panofsky Wenzel (cross-check)
DVx/DVz~0.087*Dz computed
DVx/DVz=Dz/(4*a)=0.09*Dz
Prediction (Daniel)
Equivalent bookshelf angle: α=dz/2a
Middle cell of CLIC_G (a=2.75mm)
Tolerances: 1micron or 18 μrad

14. Thermal isotropic expansion
Assumption: isotropic dilatation for small variation of the temperature of the cooling water
Very conservative approach: same T variation for the full linac (?)
Dilatation has two effects on phase:
Elongation of the structure; 1D problem, negligible effect
Detuning and consequent phase error of each cell; 3D problem, dominant effect
requirement
The average gradient variation is “equivalent” to 0.2 deg phase jitter(*) (drive beam-main beam phase)
(*) In the case of synchronous phase = 8 deg

15. Conclusions Thanks to: R. Nousiainen, D. Schulte
RF mismatching, phasing errors and bookshelf are critical for structure tolerances
Tuning of the cells seems to be needed
Longitudinal precision in the alignment of the quadrant should be ~ 1 micron
Bookshelf for structures in disks requires equivalent tolerances (~ 180 μrad)
Variation of the cooling water temperature could generate beam energy variations; this should not be a problem (feedback system)
Thanks to: R. Nousiainen, D. Schulte