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Electron cloud effect for Linear Collider damping rings

This research study examines the electron cloud effect in linear collider damping rings and its impact on stability and beam size. The study analyzes parameters such as electron density, synchrotron radiation, and instability caused by the electron cloud.

shirleywebb
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Electron cloud effect for Linear Collider damping rings

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  1. Electron cloud effect for Linear Collider damping rings K.Ohmi, KEK ECLOUD04, 19-23 April, 2004, Napa

  2. Parameters

  3. Electron cloud build-up (EC2002) • Ante-chamber R=1cm, half width of slot 0.5 cm. • In KEKB test ante-chamber, electron current 1/5 of cylindrical chamber was observed. • Average Photoelectron yield Y1g=0.015 e-/(m.e+) for Yg=0.65 g/(m.e+). (KEKB 0.015 e-/(m.e+) for Yg=0.15 g/(m.e+)) • Peak secondary yield is assumed d2=1.0 e/e

  4. Multipacting from seed electrons • Recently, M. Pivi et al. have studied multipacting condition from starting seed electrons. • We first try to reproduce the results.

  5. SEY and multipactoring

  6. Requirement for SEY • GLC bend, dmax <1.2-1.3. • GLC drift, dmax <1.4-1.5 • TESLA drift, dmax <1.9 Consistent with Pivi’s results dmax should be suppress to be around 1.2.

  7. Synchrotron radiation • Yg=0.65(I) or 0.86(II) g/(m.e+), (KEKB : Yg=0.15 g/(m.e+)) • Most of photons must be protected in slot of the antechamber. • Angular divergence of synchrotron radiation K.J.Kim, S. Kamada • uc=1.75 keV at E=1.98 GeV, B=0.67T • sy=1 mrad for u=10 eV.

  8. Electron density (EC2002) Summary at 2002 • We need further reduction of the electron cloud of 1/5~1/10. The electron yield per positron and meter is required Y1+2<0.002 e-/(m.e+) for suppress both of the coupled and single bunch instability. 20% of SRcontributes. dmax <1. Synchrotron radiation should be protected much more.

  9. Assume that 99.5% of SR is protected by antechamber slot. • Y1g=3.3x10-4 e-/(m.e+) As shown latter, this cloud density level is limit considering instability threshold. Take care of electron flow from antechamber slot (Liu,BEPC)

  10. Instability caused by electron cloud • Coupled bunch instability • Single bunch instability

  11. Coupled Bunch Instability caused by electron cloud • Wake force is calculated by a numerical method as follows, • Equilibrium electron cloud. • A (i-th) bunch Dyi with a displacement passes through the cloud. • Calculate kick Dpy,j of j-th bunch. • Growth of the coupled bunch instability is estimated by

  12. Medium range Wake force and growth of CBI (Fill 1.4ns) ECLOUD 2002 • Wake force Mode stability Growth time 20 turns 26ms

  13. Medium range Wake force and growth of CBI • Wake force Mode stability 99% protected (I,II) Growth ~300ms 99.5% protected (II) Growth ~ 600ms

  14. Single bunch instability caused by electron cloud • The single bunch instability is analyzed by wake field method and tracking simulation. Wake field • Linearized model. • Numerical calculation including nonlinearity. (Similar way to the calculation of the multi-bunch wake field)

  15. Short range wake field induced by electron cloud • Short range wake for coasting beam Analytical solution with a simplified linear theory cR/Q=1.4x107 m-2 (0.94x107 m-2) we = (5.5x1011 s-1 )

  16. Threshold of fast head-tail instability • Bounce frequency of electrons in the positron beam potential wesz/c=9.5 (V)>>1 2.6 (H)>1 • Coasting beam model • Stability criteria

  17. Threshold cloud density of some positron rings Q=Min(wesz/c, 5)

  18. PIC simulation (PEHTS) • Transverse mesh. 2D electric field calculation for electrons and positron bunch. Based on a beam-beam simulation code for the strong-strong model (BBSSP). • A bunch was sliced into 30~50 in the longitudinal direction. • A bunch interacts with electron cloud with a projected density rexL for each traveling of L. We choose L=C : circumference in this presentation, and the case of more interaction points in a ring L=C/n is equivalent to lower cloud density re/n.

  19. Positrons in a bunch and electrons in the cloud are mapped on a 2D mesh. Electric potential is calculated by solving the Poisson equation. • Particle In Cell method y Cloud x Bunch y x z

  20. Characteristics of the head-tail instability • Dipole coherent motion along z. • The instability is characterized by thewake strength per a synchrotron phase advance. • The instability does not depend on the transverse tune except for a special value, for example synchro-beta resonance. • Beam size and coherent amplitude are comparable before experience of strong Landau damping. • We can distinguish whether the instability obtained by the simulation is head-tail type by investigating the above characteristics.

  21. Beam and cloud structures along z • ns=0 ns=0.002 Tail Head

  22. Growth of beam size • Projected size along z

  23. Scaling of ns and cloud density • In the theory of the strong head-tail instability, the instability should be scaled by the ratio of the wake strength (cloud density) and the synchrotron tune.

  24. From the results of the PIC simulation (for GLC I) • Threshold of the strong head-tail instability due to the electron cloud is around re/ns =1012/0.01 m-3. • Growth for re=1012 m-3 is deviated from others, namely the scaling is broken. • Kick due to cloud with the projected density rex C is too strong. The instability occur due to localization of the cloud, and may be not realistic. • For the case that the electron cloud distributes whole of ring, the coherent head-tail instability is dominant.

  25. Summary I • We assume primary electron yield Y1g= 6.6x10-4 and 3.3x10-4 e-/(m.e+) for GLC damping ring. This value is 1% and 0.5% of the direct photoelectron yield. • Electron cloud average densities are 0.8x1012 m-3 and 0.4x1012 m-3 for 1% and 0.5% SR ratio, respectively. • The growth of the coupled bunch instability is 300ms and 600ms for 1% and 0.5% SR ratio, respectively. • The growth can be recovered by bunch by bunch feedback.

  26. Summary II • The threshold cloud density of the fast head-tail instability is re=2.6x1012 m-3 for parameter I (ns=0.01) and re=6.2x1012 m-3 for parameter II (ns=0.0118) in the linear wake approximation. • The wake approximation neglects some effects: nonlinearity, pinching of electrons… • A PIC simulation has performed to study the effects in detail. • The threshold of the fast head-tail instability was re/ns =1012/0.01 m-3 for parameter I. It will be higher for parameter II. • It is a factor 2-3 lower than that of the wake approximation. This discrepancy is due to an ambiguity or accuracy (pinching, choice of Q, coasting beam approximation) of the wake approximation. • Anyway, the threshold is higher than the density of the present estimation based on our model (assumption).

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