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Investigation of bunch gap effects for curing ion trapping

Investigation of bunch gap effects for curing ion trapping. Shogo Sakanaka KEK (High Energy Accelerator Research Organization). ERL07 Workshop, May 21-25, 2007, at Daresbury Lab. Outline. Introduction Stability of ions under bunch gaps Bunch-gap transient voltages

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Investigation of bunch gap effects for curing ion trapping

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  1. Investigation of bunch gap effectsfor curing ion trapping Shogo Sakanaka KEK (High Energy Accelerator Research Organization) ERL07 Workshop, May 21-25, 2007, at Daresbury Lab.

  2. Outline • Introduction • Stability of ions under bunch gaps • Bunch-gap transient voltages • Compensation of transients • Beam-size modulation • Summary

  3. 1. Introduction • Ion trapping may cause large betatron tune-shifts or fast ion instabilities in ERLs. • Preparation for possible cures is important. • Bunch gaps were investigated by Hoffstaetter and Liepe (Nucl. Instr. and Meth. A557 (2006) 205), by which it seemed not promising when the bunch-gaps are long (about 31 ms or 2ms). • We investigated the cases where bunch gaps are short (~50 ns). Example of the beam instability due to ions observed at the Photon Factory.

  4. 5-GeV ERL Test ERL Estimation of critical mass Critical mass (for y-direction):

  5. 2. Stability of ions under bunch gaps Linear focusing force: Drift: Transfer matrix for one period: Ions are stable if: np = Tp/Trf ng = Tg/Trf Illustration of bunch gap:

  6. Effect of bunch gaps for several repetitions (with 10% gap) 10 MHz 2 MHz 500 kHz 100 kHz

  7. Effect of bunch gaps with variable gap ratio(fixed repetition of 2 MHz) Gap 0% 5% 10% 20%

  8. Ultra-high vacuum will be important Bunch gaps cannot chase all kinds of ions, however: • Trapped ions suffer multiple ionizations, resulting in the change of their charge number (Z). • When the A/Z of ions come into the stopbands, ions are chased out of the beam. • Ion density is then determined by the equilibrium between the first and the second ionization processes in this case: • Low vacuum pressure is very important for reducing the ion density. Multiple ionizationof CO molecule.(P. A. Redhead: Can. J. Phys. 47 (1969) 2449.)

  9. 3. Bunch gap transients The bunch gaps introduce transient voltages in several components: • In the main linac  avoidable (see below) • In the injector • In the buncher cavity • In the high voltage of electron gun (C. Sinclair by way of G. Hoffstaetter) (Repetition freq. of bunch gap) = n(revolution frequency) (A. Hutton's idea; NIM A557 (2006) p. 211.)

  10. Bunch-gap transient in the injector RF voltage in the cavity: Beam induced voltagesat n-th bucket : Where

  11. Assumed parameters for injector cavities Assumptions: Five two-cell cavities,Rsh/Q  200 W/cavity (def.: Pc = Vc2/Rsh), beam current: I0 = 100 mA, total rf voltage: 5 MV, on crest acceleration (f = 0). * Per two-cell cavity

  12. Bunch-gap transients in the injector 2 MHz5% 2 MHz10% 2 MHz20% 100 kHz 10%

  13. Bunch gap transient (cont.) When ng, nt << Tfill/Tb , the bunch gap transient (peak-peak) is given by Brief summary: • Bun-gap transients in the injector: • DVc/Vc ~ 0.4% for 2 MHz, 10% gap • DVc/Vc ~ 8% for 100 kHz, 10% gap • Bunch-gap transients may be acceptable for high repetition case • The transient voltage can be compensated further using a feedforward compensation (see next slides). • In the buncher cavity, the bunch-gap transient will be severer.

  14. 4. Compensation of bunch-gap transients Planned feedforward compensation for the bunch-gap transients for the KEK B-factory (currently, not used). Cited from K. Akai, in Physics and Engineering of High-Performance Electron Storage Rings, World Scientific, 2002, p. 148.

  15. Equations for the cavity voltage On-crest acceleration: Generator powerrequired:

  16. Required generator power Pg (per cavity) Assumed: total voltage: Vc = 5 MV、Beam current: 100 mA、bunch-gap: np = 650, ng = 65

  17. Effect of limited bandwidth of the generator Cutting Fourier component below nc-th harmonic of gap repetition frequency: Cavity voltage Vc(t) per cavity Generator current ig(t) per cavity

  18. A possible way of increasing the bandwidth of the generator • Combination of a wide-band (but low power) and a narrow band (high power) generators using an asymmetric power combiner. • A similar 1:2 power divider was built for a 508-MHz application.(T. Takahashi et al., IEEE Trans. Nucl. Sci. 48 (2001) 1592.) S-matrix of asymmetric power combiner Realizable by a reciprocal, lossless device S-matrix is symmetric and unitary

  19. 5. Beam-size modulation -an alternative measure- • Consider to modulate beam sizes by modulating spot sizes of a drive laser. • No beam-loading variations. • Might be detrimental for user experiments, but beam-size modulations are under human control (i.e. we can supply gate signals for user's detectors). Illustration of the beam-size modulation.

  20. Effect of beam-size modulation Assumed 10% duty factor for beam-size modulation. Beam size mod.: 2, 2MHz Modulation: 3, 2MHz

  21. 6. Summary • Bunch gap can be a strong candidate for the cures for ion trapping if other problems can be resolved. • Low-vacuum pressures will be important for reducing ion densities. • Bunch-gap transients in injector may be acceptable for the high repetition cases: • DVc/Vc ~ 0.4% for the 2 MHz repetition, 10% gap case. • Bunch-gap transients can be reduced further by the feedforward compensation. • Required power increase: 100 kW  112 kW per cavity • Required bandwidth: 4 - 10 MHz or more (for a gap rep. of 2 MHz) • Transients in a buncher cavity will be severer and needs sophisticated countermeasures (e.g. energy-storage cavity or SC buncher). Transients in a gun high-voltage should be investigated as well. • Beam-size modulations may be an alternative solution, however, they may affect user's experiments.

  22. Some basic equations Critical mass (for y-direction): Ionization time: sx, sy : rms beam sizes sxi, syi : rms ion-cloud sizes li, -le : line-charge densities of ions and e- Limit of ion accumulation: Tune shift due to ions: In case of:

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