1. HS, CTC 1-9-2009 Progress on beam-feedback? Proposal to study electromagnetic correction coils for the September 2009 module review

2. HS, CTC 1-9-2009 Background (1/2) 4000 MB quads, need about 80 correctors close to quads for beam-based feedback (BBF); Pre-choice of 80 locations impossible?  equip all 4000 quads with correctors Frequency range covered by BBF: sub-Hz to 1 Hz In order to - have some feedback gain at f_cl=1 Hz (f_cl = f_s/gain) - to average over several BPM readings the BBF will run at f_s=50 Hz; requested settling time of corrections is 5 ms; i.e. in-between 2 beam pulses

3. HS, CTC 1-9-2009 Background (2/2) Baseline in 2008: - additional windings onto quad jokes in order to produce “a sort of dipole correction field” Choice of 1 st option for MB quad late 2008: Non-laminated quads (considered best for stabilization) excludes correction coil (bandwidth problem) Present baseline: Extend dynamic range of stabilization actuators by 100 ! hence make BBF corrections by displacing the MB quads.

4. HS, CTC 1-9-2009 Problems with present baseline Actuator dynamics, in particular for the (long) heavy magnets Absolute displacement of quads not precisely known (no position sensor; “only” velocity or accelerometer type sensors; non-linearities of piezos; slow drifts…) BPMs (50 nm required resolution) will move with quad. Needs sophisticated bookkeeping of past displacements. BPM close to “zero” and for longer elongations non- linear (monopole and quadrupole mode signals) Machine protection: non-energized position of quad (vertical) is max.down, not middle; might need interlocks.

5. HS, CTC 1-9-2009 …following 3 slides taken from a presentation of J.Pfingstner (June 2009)

6. CERN, BE-ABP (Accelerators and Beam Physics group) Jürgen Pfingstner Piezo actuators as orbit correctors Scaling piezo behavior for heavy magnet 1.) Resonance frequency of a piezo actuator The eigenfrequency can be calculated [3] as: … Spring constant of the piezo P-225.40 (high load) … Effective mass of the piezo … Biggest CLIC QP (1.9m) on 3 actuators 2.) Damping factor of a piezo actuator According to PI for all actuators between 0.2 and 0.1 Assumed to be the same as for the laboratory model P-753: 3.) Piezo amplifier According to PI similar than the one in the labratory Could probably be improved by R&D effort (‘just’ cost) Assumed to be the same as in laboratory: E- 503

7. CERN, BE-ABP (Accelerators and Beam Physics group) Jürgen Pfingstner Piezo actuators as orbit correctors Performance of the final strategy With feed forward strategy, the specifications can be meet, if the sensor signal represents the ground motion well enough. Interestingly enough the measured signal y the controller acts on has completely different form than the controlled variable x.

8. CERN, BE-ABP (Accelerators and Beam Physics group) Jürgen Pfingstner Piezo actuators as orbit correctors Conclusions The use of a piezo actuated quadrupole as an orbit corrector is possible with the following assumptions made: The scaling of the small to the big is valid (it is according to piezo company PI). The ground motion can be accurately measured not only as an acceleration but a displacement in real time (biggest assumption). The piezo amplifier should maybe have a bigger input output range to be able to act on fast control action resulting in big actuating signals. But optimization can still be done. A first design is made which should be further tested and improved (maybe state controller approach is better). The following influences have not been included in the simulation yet: Other disturbances than ground motion, that act on the quadrupole directly (sound, electromagnetic fields, cooling water) Support structure (since no reliable model is available yet)

9. HS, CTC 1-9-2009 Proposal to prepare for module review Required corrector strength (Bdl): 200 T/m *10 um * 2m (@ 1.5 TeV) = 4 mT * m = 0,4 T * 1 cm 1 cm long 0.4 T magnet - end-field problems? - will create synchrotron radiation? (200 times higher bending radius)

10. HS, CTC 1-9-2009 First thoughts on integration Shorten MB quads type 1..4 by about 5 cm and use space for dipole corrector This will reduce the strength of the quads, so start earlier as energy increases with type 2, type 3, type 4. At the very end a 5 cm shorter type 4 might still be OK? Overall cost in extra linac length to be calculated.

11. HS, CTC 1-9-2009 Appendix …slides of A.Lunin (FNAL) on BPM design

12. July 2009 A. Lunin, Fermilab 1.General idea: - low Q-factors - monopole modes decoupling BPM parameters: - Cavity length - Waveguide dimensions - Coupling slot - Coaxial transition 3. Parasitic signals: - monopole modes - quadruple modes 5. Tolerances calculation: - coupling slots - waveguide to cavity - cavity to pipe Cavity spectrum calculations: - Frequency - R/Q, Q - TM11 output voltage Cavity BPM design steps 4. Cross coupling: - waveguide tuning - 2 ports vs 4 ports loop 1 1 1 1 1

13. July 2009 A. Lunin, Fermilab R4 R12.05 2 1 7 2 14 20 25 BPM Geometrical Dimensions

14. July 2009 A. Lunin, Fermilab HFSS EigenMode Calculation (II) Bunch trajectories (I) Matched Impedance, P_coax HFSS Data: W - Stored Energy P_coax - Exited RF Power Ez - E-field along bunch path g sym - Symmetry coefficient Cavity BPM spectrum calculation Scale Factor: Output Power: r e-e- Estimated Sensitivity (q 0 = 1nQ): V/nQ/mm

15. July 2009 A. Lunin, Fermilab Waveguide to coaxial transition 5.05 5

16. July 2009 A. Lunin, Fermilab 1 - Stainless steel material was used 2 - Dipole and quadruple modes values were normalized to 1mm off axis shift 3 - Signals are from a single coaxial output at resonance frequency. Cavity BPM spectrum calculation

17. July 2009 A. Lunin, Fermilab BPM Cavity Modes Mode TM 01 Mode TM 02 Mode TM 21 Mode TM 11

18. July 2009 A. Lunin, Fermilab Waveguide Low-Q resonances Mode WG_TM 11 Mode WG_TM 21

19. July 2009 A. Lunin, Fermilab Multi-bunch Regime Rejection Single Bunch Signals : TM 11 signal TM 01 signal TM 21 signal Rejection: Multi-bunch regime (2 GHz) TM 01, TM 11, TM 21 Time, [s]

20. July 2009 A. Lunin, Fermilab Monopole Mode Coupling due to Mechanical Errors Slot RotationSlot Shift HφHφ HzHz ∆α∆α Strong Magnetic Coupling ~∆α x ∆x∆x HφHφ HzHz Slot TiltWeak Electric CouplingWeak Magnetic Coupling + 2.Slot tilt causes the non zero projection of TM 01 azimuth magnetic (H φ ) and longitudinal electric (E z ) filelds components in the cavity to a transverse (H x ) and vertical (E y ) components of TE 10 mode in the waveguide. Because both H x and E y are close to zero near the waveguide wall tilt error causes the weak electric and weak magnetic coupling of monopole mode to waveguide. ∆θ∆θ HφHφ EyEy EyEy HxHx 1.Slot rotation causes the non zero projection of TM01 azimuth magnetic field component (Hφ) in the cavity to a longitudinal one (Hz) of TE10 mode in the waveguide. Small slot shift is equivalent to rotation with angle: α x ~ arctan(Δx/Rslot). Therefore both slot rotation and shift cause strong magnetic coupling of monopole mode to waveguide.

21. July 2009 A. Lunin, Fermilab TM 01 Mode Leak (tolerances calculations) ∆x a) ∆α∆α c) Slot RotationSlot Shift TM 01 normalized signals ∆θ∆θ Waveguide Tilt

22. July 2009 A. Lunin, Fermilab Multi-bunch Regime The sum of TM 11, TM 01, TM 21 output voltages 1 - Stainless steel material was used 2 - Sum of the signals from two opposite coaxial outputs at resonance frequency. Vout, [V] Time, [s] Vout, [V] 100 μm off-axis beam shift 0.1 μm off-axis beam shift

23. July 2009 A. Lunin, Fermilab Port 1 Port 2 Cavity&Waveguide couplings (nominal geometry) a) b)b) c) a)Vertical Waveguide coupling with slots b)Vertical Waveguide coupling, no slots c)Horizontal Waveguide coupling, no slots Crosscoupling

24. July 2009 A. Lunin, Fermilab Cavity&Waveguide Couplings (geometry with errors) Port 1 Port 2 a) b)b) c) Vertical Waveguide coupling with slots (case a) has the lesser TM 11 mode cross coupling due to geometry errors.

25. July 2009 A. Lunin, Fermilab Cavity&Waveguide Couplings (geometry with errors) Port 1 Port 2 a) b)b) c) Vertical Waveguide coupling with slots (case a) has the lesser TM 01 mode leakage due to geometry errors.

26. July 2009 A. Lunin, Fermilab Port 1Port 2 Port 4Port 3 a) b) c) TM 11 Modes X&Y Cross Coupling

27. July 2009 A. Lunin, Fermilab Port 1Port 2 Port 4Port 3 a) b) c) BPM Mechanical Tolerances There is no visual advantage of particular scheme of coaxial layout (a, b, c) The most sensitive to mechanical errors part of the BPM is a coupling slot. The required mechanical tolerances of a cavity with coupling slots: Mechanical Tolerances 1,2 Cross Coupling -40 dB Cross Coupling -30 dB Cross Coupling -20 dB Slot Rotation, [deg]< 0.05< 0.2< 0.6 Slot Shift, [μm]< 5< 15< 40 Other, [μm]< 50 Max Dynamic Range, [μm] 1002510 1 - In-phase signals reflection (worse case) is taken into account. 2 – The reflection from LLRF part is assumed less than -20 dB.