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

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

Schematic view of possible errors 9 10 Schematic view of possible errors

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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

Example of a systematic error: metrology of a structure in quadrant (NDS4_vg2.5_thick) Error (microns) Average cell radius error: +0.0055 Aperture error: negligible

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

Example of random (?) errors: CLIC_VG1: RF measurements in KEK B Average phase advance per cell -119.943 degrees / cell Average phase advance per cell -120.424 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

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)

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 ?)

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

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

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

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

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