Beam Dynamics and Instabilities in MEIC Collider Rings

1. Beam Dynamics and Instabilities in MEIC Collider Rings Byung C Yunn Jefferson Lab Newport News, Virginia, USA

2. Outline • MEIC e-ring • Impedances • Single-bunch instabilities • Coupled-bunch instabilities • Intrabeam scattering and Touschek scattering • Beam-gas scattering, ion trapping • MEIC p-ring • Single- and coupled-bunch instabilities • Intrabeam scattering and Touschek scattering • Beam-gas scattering • Electron clouds • Summary

3. Impedances • For the overall longitudinal broadband impedance of the MEIC e-ring, is assumed. This is equivalent to assuming roughly the same amount of impedance in e-ring as in PEPII ring. • Transverse impedance is estimated to be about 1 MΩ/m from • With the help of existing B-factory designs with comparable beam parameters a first cut on impedance budgeting has been made. Estimation of the total inductive component of impedance at MEIC e-ring is 0.2 Ω. where b is beam pipe radius, c the light velocity.

4. The MEIC inductive impedance budget

5. Total loss factor in e-ring is estimated to be 25 V/pC. • The beam power lost to higher order modes (i.e. HOM loss) is given by where kB is the total number of bunches and f0 is the revolution frequency in the ring. Note that HOM loss will be less with more bunches for a fixed amount of total charge in the ring. • The total HOM loss for 5 GeV electron beam at the design current of 3 Ampere is only 150 kW.

6. Single bunch instabilities • e-ring parameters • Longitudinal microwave instability limits the bunch peak current. For the Gaussian bunch the threshold current is given by

7. Single-bunch instabilities • For the broadband impedance seen by the short MEIC bunch the Spear scaling law is assumed. • With 3 cm of beam pipe radius assumed longitudinal microwave instability threshold bunch current is estimated to be 3.1 mA for MEIC e-ring.

8. Transversely the mode coupling instability is to limit the single bunch current. The threshold current is estimated to be 4.2 mA from • The average beta function of 20 meter has been assumed. • MEIC e-ring is not expected to suffer from single bunch instabilities. This was expected because the bunch current is rather low considering very large beam current in the ring by filling every bucket at 1.5 GHz RF frequency. Broad band impedance requirements in MEIC e-ring are less demanding compared to other existing and/or proposed rings of comparable beam parameters.

9. Coupled-bunch instabilities • Narrow band impedance in a storage ring, typically from the higher order modes of RF cavities can induce coupled bunch instabilities as wakefields generated by a bunch ring long enough to interact with the following bunches. • In MEIC effectively all HOMs of CEBAF cavity can cause the coupling of successive bunches leading to a possible instability problem. Damping for a HOM Q may be estimated from Q of only about 10 will make inter-bunch interaction possible for MEIC. • For N bunches in the ring there are N coupled bunch modes. A coherent mode is specified by one index specifying the phase shift between bunches and another index describing its motion in synchrotron phase space.

10. Instabilities are counteracted by Landau damping from the synchrotron frequency spread within the bunch. • Longitudinally a growing mode is Landau damped when • Transversely a growing mode is Landau damped when • For MEIC e-ring longitudinal Landau damping condition will be satisfied if the longitudinal impedance is less than 7.1 mΩ. Therefore, it is not likely to get a help from Landau damping. Situation is similar in transverse oscillations.

11. The total number of particles in e-ring is 6.25 1013 (to be compared with 9.8 1013 in PEPII LER). MEIC will be expected to suffer from coupled-bunch instabilities as these instabilities are driven by this total charge in the ring and cavity impedance is much higher presently compared to PEPII . • Calculations of ZAP with CEBAF cavity data show unstable longitudinal modes (from Shahid Ahmed)

12. Coupled-bunch instabilities induced particularly by cavity resonances will limit the total current in MEIC e-ring both in longitudinal and transverse phase spaces. In storage ring these instabilities are routinely controlled by the feedback system. Obviously, damping of higher order modes of CEBAF cavity for use at MEIC rings would require a major R&D effort in controlling resonant modes. A detailed study on the design of the feedback system will be required with upgraded cavity modes.

13. Intrabeam scattering and Touschek scattering • Multiple small-angle Coulomb scattering causes diffusion in both longitudinal and transverse phase space resulting in a degradation of beam emittances in both spaces. The intrabeam scattering growth rates of emittances depend on beam parameters as follows • Compared to PEPII transverse phase space volume is about 10 times smaller. But the number of electrons in a bunch is smaller by a factor of 5. Consequently, IBS growth rate is expected to be worse by a factor of 2 for the same energy electron. PEPII design study concluded that no significant emittance growth from intrabeam scattering was to be expected even for the 2.5 GeV beam operation in the low energy ring. It is safe to say that intrabeam scattering will not be a problem at MEIC for the 5 GeV beam. • One needs to confirm this conclusion with a detailed numerical study when the design of MEIC optics is advanced sufficiently to allow such a study.

14. Large-angle single scattering events during intrabeam collisions can change the momentum sufficiently to make it fall outside the momentum acceptance of a ring. The momentum acceptance may come from the RF system or by the dynamic and physical aperture of the accelerator. •  Touschek half-lifetime for a flat beam is given by • where F is a very slow varying function of its argument. For the 5 GeV electron beam the momentum acceptance from the RF system is 0.42 %. With this RF aperture I have estimated the half-lifetime of MEIC electron beam to be 12 hours. The momentum acceptance associated with dynamic aperture is also needed to complete. Currently MEIC design team is studying the dynamic aperture of the machine with several optics codes.

15. Beam-gas scattering, ion trapping • Electron beam-gas scattering with residual gas nuclei results in the loss of beam particle either from the excitation of betatron oscillation or from a momentum change exceeding the dynamic and/or the momentum acceptance of the ring. Two processes of particular interest are elastic scattering on nuclei and the bremsstrahlung on nuclei of which the latter is more dominant for the 5 GeV electron beam in MEIC. • The total cross section for the bremsstrahlung is given by where Z is the atomic number of the residual gas species. • The lifetime (hour) is related to the gas pressure P (N2 equivalent). I get 43/P (nTorr) hours for the MEIC electron beam. The beam lifetime from beam-gas scattering is about 8 and a half hours at a gas pressure of the 5 nTorr. • The overall beam lifetime from gas and Touschek scattering is 4 hours.

16. The trapped ions resulted from beam interactions with residual gas molecules in the vacuum chamber degrade the performance of electron storage rings. For any ring there exists a critical mass Ac such that ions with mass greater than the critical value. An expression for the critical mass from linear theory is given by • Critical masses are much less than one with MEIC design beam parameters. In other words all ion species will be trapped and stable. In order to avoid ion trapping there will be a gap (or several gaps) in the MEIC electron bunch train and the total length of the gap will be about 5 to 10% of the ring circumference. Note that clearing electrodes are also necessary in addition to the gap.

17. Single turn ions though unstable can affect the beam. They can produce a betatron tune spread between bunches and also induce a two beam instability known as the fast beam-ion instability, for example. The growth rate for the beam-ion instability is given by the linear model as (Lsep is the bunch spacing) • The strength of this instability is about the same as that of B-factories when the machine is operated under a similar vacuum pressure. MEIC may need a feedback system like those used at B-factories.

18. Outline • MEIC p-ring • Single- and coupled-bunch instabilities • Intrabeam scattering and Touschek scattering • Beam-gas scattering • Electron clouds • Summary

19. MEIC p-ring • MEIC ion complex consists of several rings and instability issues only in the final proton storage ring are discussed here. • It is assumed that for the overall broadband longitudinal impedance of the MEIC p-ring. A detailed impedance counting is yet to be carried out. • This implies

20. Single- and coupled-bunch instabilities • p-ring parameters • Maximum acceptable impedances for p-ring required to run design beam current are obtained.

21. From the microwave instability threshold formula p-ring can tolerate the longitudinal impedance up to 14 Ω. • From the transverse mode coupling instability follows the limit on the transverse impedance

22. Assumed impedances are well within the above limits. As expected proton beam in p-ring is not likely to suffer from single-bunch instabilities. • Coupled-bunch instabilities were observed in several proton rings at about 1013 protons. Instabilities are also expected in MEIC p-ring. The total number of protons in MEIC p-ring is 2.1 1013 • Calculations of ZAP with CEBAF cavity data show unstable longitudinal modes (from Shahid Ahmed) • We will need feedback systems to control as in e-ring.

23. Intrabeam scattering and Touschek scattering • Scaling e-ring results from growth time for emittance in p-ring is estimated to be about the same as for the electron beam. • Scaling from e-ring results based on Touschek half-lifetime for 60 GeV proton beam is estimated to be about two order of magnitude larger than that of 5 GeV electron beam in e-ring. Momentum aperture assumed is 0.2 % provided from the RF system.

24. Beam-gas scattering • Beam-gas scattering with residual gas nuclei which is critical to the lifetime of electron beam as we saw in the first half is not critical anymore . Both the bremsstrahlung and elastic scattering on nuclei provide completely negligible contribution to the beam loss rate. • Angular scattering of the proton beam by multiple Coulomb scattering in the gas can cause an emittance degradation. This effect may be estimated from

25. For 60 GeV beam at 5 nTorr (room temperature) the growth time is estimated to be about 30 minutes. • Electron trapping may be a problem due to very short bunch spacing. It may be necessary to provide a gap in the bunch train. Such a gap in p-ring may lead to a slight reduction in luminosity due to a likely beam-gap collision. • Background rates of secondary particles reaching the detectors due to beam-gas scattering will be taken into account later in selecting the operating vacuum pressure in p-ring.

26. Electron clouds • Very short bunch spacing in MEIC makes forming electron clouds through the multipacting mechanism rather complicated. One may use the following relation to estimate the resonance which gives hy = 1.5 mm. This indicates multipacting is unlikely. • Electron clouds once formed can produce both single- and coupled-bunch instabilities for the proton beam (and the positron beam in e-ring). Single bunch transverse mode coupling instability is possible when the density of electron clouds is greater than the threshold density • For both p-ring and e-ring the electron cloud threshold density is estimated to be about 5 x 1012 /m3. Numerical study is necessary to determine whether such a cloud density can be reached in MEIC rings.

27. E-Cloud Simulation Original code development : CERN Simulations includes electric field of the beam, arbitrary magnetic fields, electron space charge field and image charges of both beam and electrons. Simulations performed by Shahid Ahmed, CASA Parameters: (Rep rate 1x) Nbunch = 360 Np/ bunch = 4 x 1011 Bunch spacing = 7.48 m Bunch length = 30 cm Energy = 50 GeV Circumference = 1446.4 m Bending Field = 1.7 T

28. The growth rate of coupled-bunch instability caused by electron clouds may be estimated from • A rough estimate gives the growth time of this instability in p-ring at about a few millisecond. • Numerical study is necessary to find out whether MEIC rings will suffer from these instabilities. If necessary, MEIC will consider various measures (solenoid coils, coating the vacuum chamber with TiN, etc) which have been taken at B-factories to avoid electron cloud problems.

29. Summary • As long as the design of vacuum chamber follows the examples of ring colliders, especially B-factories, we will be safe from the single-bunch instabilities. No bunch lengthening and widening due to the longitudinal microwave instability is expected and no current limitation from the transverse mode coupling instability. • The performance in MEIC collider rings is most likely to be limited by coupled-bunch instabilities. Feedback system able to deal with the growth has to be designed. • All ion species will be trapped at the e-ring. Total beam current limitation and beam lifetime will depend upon the ability of the vacuum system to maintain an acceptable pressure, about 5 nTorr in the presence of 3 A of circulating beam.

30. The following problem areas require special attention for the MEIC design team: • HOM damping of CEBAF cavity • Feedback system • Vacuum system • Dynamic aperture