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Dynamics of Ion Instability and Tune Shift in Particle Accelerators

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This study examines the intricate dynamics of ion instability and tune shifts in particle accelerators, emphasizing the effects of CO+ and H+ ions. It highlights variations in growth rates based on machine design, such as different accelerator types (DAS, TESLA, etc.), bunch spacing, and vacuum conditions. The findings indicate that CO+ induces significant tune shifts compared to H+, revealing the necessity for feedback mechanisms and defining optimal gap lengths to stabilize ion behavior. Understanding these factors is crucial for improving accelerator performance and efficiency.

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Dynamics of Ion Instability and Tune Shift in Particle Accelerators

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  1. Wi =Length_element/ Length_section Wi=0 if ion is unstable Both growth rate and tune-shift are small if there is a • Smaller (vertical) beta function • Long bunch spacing

  2. Peak growth rate of FII for CO+ Pwiggler=2.0nTorr; Plong_straight=0.1nTorr P_arc=0.5nTorr Growth time is less than 1 turn! Peak growth rate of FII for H+ The growth time is 100 times longer than CO+!! (H+ has small cross section and it is likely unstable after several damping time) 17km ring has a longer growth time Shorter average growth time • TESLA; DAS; MCH; OTW; OCS; BRU;PPA

  3. Tune-shift H+ CO+ The Tune shift caused by CO+ is 30~100 times larger than H+!!

  4. Ion yield Aluminium Copper H+ is dominant component!

  5. Incoherent vertical tune shift-strongly optics dependent Larger tune shift • OTW; DAS; TESLA; MCH; PPA; BRU; OCS • OCS has the longest ARC • OTW has the shortest ARC and small beta at ARC! • DAS, MCH and TESLA has a long bunch spacing!! (ion is Not easy to be trapped)

  6. A smaller beta function help in two aspects! OTW OCS

  7. ATF Nbunch=20, P=10nTorr, 20% is CO+ Radiation damping time 30ms Close to the experiment Tune shift is very small

  8. PLS • Ions are not trapped at some location with the equilibrium emittance, especially in Wiggler • Long straight section PLS(P=5nTorr) • Energy 2.0GeV • Lsep=2ns • x=12.1nm • y=0.12nm • N=1.1681010 • Nbunch=180 • rad=16ms ILC P=5nTorr • Energy 5.0GeV • Lsep=4~20ns • x=0.5nm • y=0.002nm • N=21010 • Nbunch=2820 >100s scaling>21s Calculation (don’t know the optics) 0.9 ms for 100% CO+ 5ms for 100% H+

  9. B-factories KEKB(P=1nTorr) • Energy 8.0GeV • Lsep=2.4m • x=24nm • y=0.4nm • N=5.61010 • Nbunch=1389 • feedback=0.5ms PEPII(P=1nTorr) • Energy 8.0GeV • Lsep=1.26m • x=50nm • y=1nm • N=4.61010 • Nbunch=1732 • cal=0.23ms • Qcal=0.008 scaling_ILC>1s There is no FII observed in usual operation of B-factories except at the beginning of the operation after long shutdown (suppressed by Feedback?) ILC has a faster FII than B-factories

  10. Gaps T Stable Zone with gap (linear model) tgap • Long term motion of ions are likely unstable; (multi-turn trapping is difficult) Trapping time(0.1MHz for 6km ring)

  11. Decay of ion-cloud during the train-gap The decay time of ion-cloud is about 1 times of the ion oscillation period: Wiggler section need a short gap Light ion need a short gap. Gap in KEKB HER: 69.38m(230ns) Gap in PEPII HER: 40m(130ns) (Tco+=110ns; TH+=30ns)

  12. Co+ oscillation period TESLA OCS Damping ring is different from B-factories & Light source The required gap varies with time!

  13. Gap effect on stable zone (OCS) Gap=8 bunch spacing=49.2ns Trapping location varies with time

  14. Summary • The instability/tune shift is dominated by CO+ if it is more than 10% in the vacuum • 17km rings has longer growth time (factor 5~10 better than 6km and 3km rings) • Scaling with the present machines is NOT easy! The shorter growth time is around 100 s (scale with PLS) • Feedback is certainly necessary • Necessary gap is around 1.2 times of ion oscillation period (PEPII). It varies with the time (emittance) and Optics. We need to define the necessary gap for a certain time.

  15. Conclusion • Both DAS and TESLA have longer growth time and small tune shift • Feedback is necessary • Necessary gap is about 1 period of ion oscillation period. 17km ring need a longer train gap Peak growth rate of FII and tune shift with CO+

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