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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

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

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