1. HOMs in high-energy part of the Project-X linac. V. Yakovlev, N. Solyak, J.-F. Ostiguy Friday 26 June 2009

2. Motivation: HOM dampers are an expensive and complicated part of SC acceleration structure (problems – multipactoring; additional hardware – cables, feedthrough, connectors, loads; leaks) SNS SC linac experience show that HOM dampers may cause cavity performance degradation during long - term operation; SNS linac experience doesn’t show necessity of the HOM couplers; For another hand, analysis of the BBU in SNS linac does not show critical influence of the HOMs on the beam dynamics; Low- energy part of the Project X linac does not contain HOM dampers; Our goal is to understand the HOM influence on the beam dynamics in Project X in order to decide whether we need the HPM dampers in high energy part of the linac and in the low energy part as well. From other side, in ILC HOM dampers are necessary. All ILC cavities are equipped by HOM couplers, that work successfully at DESY. In the case of future upgrade Project X couplers may become necessary.

3.  Project X is an intense proton source that provides beam for various physics programs.  The source consists of an 8 GeV H - superconducting linac that injects into the Fermilab Recycler where H - are converted to protons.  Protons are provided to the Main Injector and accelerated to desired energy (in the range 60 - 120 GeV) or extracted from the Recycler for the 8 GeV program.  The 8 GeV linac consists of a low energy front end possibly based on superconducting technology and a high energy end composed of ILC-like cryomodules.

6. High Energy Linac Overview - Nagaitsev 6 ILC RF Unit  Some 650 units of this type will be required for the ILC and about 15 for Project -X ILC RF Unit: 24-26 Cavities, 3 CM, klystron, Modulator, LLRF

8. ILC-type HOM coupler Loop Antenna Choke Output

10. Collective effects:  Frequency spread is essential;  Initial conditions, i.e., chopping, charge and timing jitter, etc, are critical (no feedback)

11.  1.2 msec beam pulse has the average current of 20 mA.  It has 33% chopping at 53 MHz and 6% chopping at 89 kHz.  The bunch sequence frequency is 325 MHz. The beam current spectrum.

12.  R.m.s. spread of the resonance frequencies is 6-9 MHz depending on the pass band according to DESY measurement statistics*.  “Dangerous” modes: 1. The dipole mode of the 2d pass band with the frequency of 1734.9±6 MHz and transverse impedance of 15 Ohm/cm 2. The mode frequency domain contains the second side frequency of the 325 MHz harmonic, or 1731 MHz that has the normalized amplitude of 0.5. 2. The mode of the 3d pass band with the frequency of 2579±9 MHz and transverse impedance 25 Ohm/cm 2. It’s distance to the 325 MHz harmonic 2600 MHz is 21 MHz, or 1.75 r.m.s. frequency spread. The most “dangerous mode!” * J. Sekutowicz, HOM damping,” ILC Workshop, KEK, November 13-15, 2004. Transverse dynamics: HOM spectrum.

13. The dipole mode spectrum vs. the beam current spectrum. Transverse dynamics: HOM spectrum:

14. BBU estimations for High Energy part of the Project – X linac: Simple model:  No synchrotron motion;  Short bunches;  Homogeneous focusing;  Similar types of the cavities over the linac;  Random transverse misalignment of the cavities;  Model: (P-W) Parameters:  Beam current: 32 mA;  Pulse: 1 msec;  Chopping: 33% at 59 MHz and 6% at 89 kHz  Bunch frequency: 325 MHz;  r.m.s cavity off-set: 0.5 mm;  Beta-function: 25 m.  HOM frequency: 2579 MHz;  HOM frequency  r.m.s. spread: 9 MHz;  R || (1) : 25 Ohm/cm 2 ;  Q HOM : 10 8 Transverse dynamics.

15. Bunch deflection versus HOM frequency spread for different HOM central frequencies. (Average is taken over 10 Monte Carlo linacs). Transverse dynamics.

16. Bunch deflection versus HOM central frequency for different HOM frequency r.m.s. spread. Transverse dynamics.

17. HOM voltage distribution over the linac for different HOM r.m.s. frequency spread. Transverse dynamics.

18. Deviation versus the bunch number for different HOM frequency spread. Transverse dynamics.

19. The bunch deviation versus the beam current for HOM central frequency of 2579 MHz and HOM frequency r.m.s. spread of 9 MHz. No significant influence of HOMs on the beam transverse dynamics for Project-X parameters. Transverse dynamics.

20. The monopole mode spectrum vs. the beam current spectrum. “Dangerous” modes: f=2451 and 2457 MHz having (R/Q)=160 Ohms. The modes are far of any high harmonic side frequencies. The normalized current spectrum line amplitude is only 0.02. HOM r.m.s. freq. spread is 9 MHz. Longitudinal dynamics. Monopole HOMs

21. The voltage exited by the beam in the end of the pulse is equal to and the power dissipation in the cavity walls (all excited field is dissipated in the cavity) is equal to Power losses in the cavity caused by HOM excitation: For operating mode U=30 MV, and P = 0.5 W! ( f rep =5 Hz) Longitudinal dynamics.

22. Longitudinal dynamics:  J. Tuckmantel graciously provided his simulation code to us.  Parameters: F HOM = 2.450 GHz; HOM frequency r.m.s. spread is 9 MHz; Q=1.e 10 ; R/Q=160 Ohms; Current: 32 mA; Pulse length: 1 msec.

23. R.m.s. emittance is inversely proportional to σ f 2. Central frequency is 2451 MHz. Average is taken over 10 Monte Carlo linacs.. Longitudinal dynamics.

24. Relative energy spread is inversely proportional to σ f. HOM central frequency is 2451 MHz. Longitudinal dynamics.

25. Longitudinal emittance versus frequency. R.m.s HOM frequency spread is 9 MHz. HOM central frequency is 2451 MHz. One can see the resonance at 2275 MHz (bunch frequency harmonic).

26. Energy spread for different HOM frequency r.m.s. spread (central frequency is f bunch  7=2275 MHz). For frequency spread 1 MHz and higher The energy spread is negligible; For the spread of 100 kHz part of the beam is lost. 1 MHz 10 MHz 100 kHz

27. The bunch longitudinal emittance versus the beam current for HOM central frequency of f bunch  7=2275 MHz, and for HOM frequency r.m.s. spread of 9 MHz. No significant influence of HOMs on the beam transverse dynamics for Project-X parameters..

28. Low – beta section (400 MeV-1200 MeV, simulations): Monopole mode spectrum. Dipole mode spectrum. For  =0.81 11-cell structure HOM spectrum does not coinside to the spectrum of ILC structure; No HOMs close to the bunch frequency harmonics of side lines. Longitudinal dynamics.

29. BBU for SNS compared to Project-X Project- X: 1.Pulse current: 20 mA; 2.Operating frequency: 1.3 GHz; 3.Pulse width: 1.2 msec SNS: 1.Pulse current: 38 mA; 2.Operating frequency: 805 MHz 3.Pulse width: 1 msec NO evidence of BBU even after some HOM dampers was reported.

30. TRANSVERSE BEAM BREAK-UP STUDY OF SNS SC LINAC*, PAC2001 D. Jeon† and J. Wei, SNS/ORNL, P.O.Box 2008, Oak Ridge, TN37830, USA L. Merminga, G. Krafft, B. Yunn, R. Sundelin, and J. Delayen, JLab, Newport News, VA23606 Effect of the HOM frequency spread is essential. For JLab cavities the HOM frequency from cavity to cavity ranges from 5 MHz to 30 MHz 3.0MHz Half-Width-Half-Maximum Lorentzian HOM frequency spread makes linac operation possible even for 500-mA beam current under most severe resonant condition. CONCLUSION “Study indicates that HOM beam break-up is not a concern even for a pulsed mode operation of SNS superconducting linac. This is mainly due to the HOM frequency spread of cavities due to manufacturing tolerances. Heat load does not seem to be a concern up to Q=10 8 with ±1.0MHz uniform f HOM spread.” BBU for SNS compared to Project-X

31. Alternative option of the Project X:

32. Initial energy: 400 MeV; Final energy: 2 GeV Beam current: 10 mA; Pulse: CW; Chopping: 10% at 2 MHz; Average current: 1 mA; Bunch frequency:325 MHz; Operating frequency: 1.3 GHz r.m.s cavity off-set: 0.5 mm; Beta-function: 25 m. Dipole HOM frequency: 2579 MHz; Dipole HOM freq. r.m.s. spread: 9 MHz; R || (1) : 25 Ohm/cm 2 ; Q HOM : 10 9 Monopole HOM frequency: 2451 MHz; Monopole HOM freq. spread: 9 MHz. (R/Q): 160 Ohms; 2 GeV CW linac parameters: Alternative option of the Project X:

33. Alternative Project versus basic Project (HE parts): Alternative Project Basic Project: Pulse length: CW > 1 msec Current: 1 mA < 20 mA Length: ~100m < ~ 300m BBU and longitudinal instability are under considerations. Alternative option of the Project X:

34. Summary:  For high-energy part of the basic version of Project – X linac HOM influence on the beam dynamics (longitudinal and transverse) may be not an issue mainly because of high HOM frequency spread over the linac cavities. Heat load does not seem to be a concern as well.  Estimation of HOM influence on the beam dynamics in the low energy part is the next step.  HOMs may be more important in the Alternative CW project (under investigation now).