RF-kick in the CLIC accelerating structures Andrea Latina (CERN) Alexej Grudiev (CERN) A. Latina LCWS11,September 29th, 2011

Outline Multipole kicks in TD26_CC Comparison with the strength of the main linac quadrupoles Phase dependence of the kick Beam dynamics in TD26_CC Impact on a perfect main linac Impact on a misaligned main linac Alternative coupler design: TD26_CCSF Additional kicks in this design Uncompensated case vs. alternating pattern Beam dynamics in TD26_CCSF Conclusions and future steps A. Latina LCWS11,September 29th, 2011

Multipole expansion for TD26_CC Quadrupole Starting from the field maps, the electric field has been reconstructed added the contribution of the magnetic field (Lorentz force) applied the beam loading scaled the input power from Pin=4 W to the nominal value Pnominal=61.3 MW A multipole expansion of the reconstructed field has been computed over the aperture disk for the quadrupolar component over the a radius R=1 mm for the octupolar component The integrated strengths have been calculated in 2 locations: Input, Output for the quadrupole component 1 location: Average for the octupole component The plots show the equivalent magnetic gradient in T/mn for the on-crest particle. Octupole A. Latina LCWS11,September 29th, 2011

Accelerating cavity model Standard CLIC module layout Multipole kicks considered: Input C AS Output C TD26_CC K1 K3 TD26_CCSF K0, K1, K2 K0=dipole, K1=quadrupole, K2=sextupole, K3=octupole, … 216.6 mm 6.7 mm Accelerating Structure Input Coupler Output Coupler A. Latina LCWS11,September 29th, 2011

Transverse kick strength in TD26_CC What matters is the integrated strength, that we express in GeV/mn-1. In these units, the transverse kicks for the on-crest particle are: Symbol Input C Acc Structure Output C Units Quadrupole S2 0.002 - -0.001 GeV/m Octupole S4 59.7 GeV/m3 Couplers strength / Main linac quads strengths These kicks are very small if compared with the main linac quadrupole strength. A. Latina LCWS11,September 29th, 2011

Phase dependence of the kick The EM field depends on the phase, by , and so do the transverse kicks. In CLIC, the beam is accelerated off-crest, at two phases: 8 and 30 degrees. The bunch length, 44 microm, accounts for 0.63 degrees phase difference. Quadrupole Octupole At phi=30 degrees the octupolar component is magnified by a factor ~70 w.r.t. the on-crest particle. A. Latina LCWS11,September 29th, 2011

Impact of TD26 couplers on the emittance in a perfect machine Emittance growth in a perfect 3 TeV CLIC main linac PLACET Simulation Single-bunch wakefield effects are taken into account Horizontal axis Vertical axis The impact is negligible even if magnified by a factor 100 A. Latina LCWS11,September 29th, 2011

Impact of TD26 couplers on the emittance with misaligned cavities Cavity misalignment The RMS transverse misalignment of the accelerating cavities is assumed to be ~10 microm Horizontal axis Vertical axis The impact is negligible even if magnified by a factor 10 The results are the average of 100 random seeds A. Latina LCWS11,September 29th, 2011

Single feed couplers: TD26_CCSF An alternative design to TD26_CC exists: single feed compact couplers (CCSF) Despite their advantages, CCSF couplers give also a dipole horizontal kick a sextupole transverse kick Integrated strength for the dipole kick: Integrated strength for the sextupole kick: A. Latina LCWS11,September 29th, 2011

TD26_CCSF dipole kick compensation To compensate the dipole kick, an alternative configuration is being studied Notation: CCSF1: uncompensated case CCSF2: 1st order cancellation of the dipole kick Uncompensated configuration: TD26_CCSF1 1st order compensation of the kick: TD26_CCSF2 A. Latina LCWS11,September 29th, 2011

Impact of TD26_CCSF on the emittance Emittance growth induced by the couplers in a perfect 3 TeV CLIC main linac Horizontal axis CCSF1 CCSF2 Vertical axis CCSF1 CCSF2 Horizontal blow up is largely reduced in CCSF2. Vertical is negligible in both cases. A. Latina LCWS11,September 29th, 2011

Dipole kick correction in TD26_CCSF To correct for the horizontal kick, we apply 1-to-1 correction CCSF1 CCSF2 1:1 correction largely reduces the impact of the dipole kick Still, the huge emittance growth induced by CCSF1 prevents the operability of the uncorrected machine. CCSF2 configuration (or better solution) has to be chosen. A. Latina LCWS11,September 29th, 2011

Cavity misalignment on CCSF2 Impact of 10 um RMS cavity misalignment. Horizontal axis. 1:1 Corrected Uncorrected The emittance growth in the uncorrected machine is about 5%. The correction cancels any effect of the couplers The results are the average of 100 random seeds A. Latina LCWS11,September 29th, 2011

Cavity misalignment on CCSF2 Vertical axis Uncorrected The impact of the couplers on the vertical axis is negligible The results are the average of 100 random seeds A. Latina LCWS11,September 29th, 2011

Partial conclusions and future steps… Multipole moments have been calculated for baseline design TD26_CC, and also for the alternative design TD26_CCSF Beam dynamics simulations have shown that the impact of baseline design couplers TD26_CC is very small, as it consists of weak quadrupole and octupole components TD26_CCSF design, that seems appealing from several points of view, presents a dipole moment that greatly harms the beam, if not counteracted A first 1st order cancellation of the dipole mode, called TD26_CCSF2, where the cavities are installed with alternate orientation, showed a significant improvement Other configurations, like a second-order cancellation schema, where cavities are oriented along the following pattern is being tested. Multi-bunch effects must be evaluated. Perceived kick Beam energy A. Latina LCWS11,September 29th, 2011

Spare slides A. Latina LCWS11,September 29th, 2011

Multipole coefficients in various units A. Latina LCWS11,September 29th, 2011