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Study of ep instability for a coasting proton beam

Study of ep instability for a coasting proton beam. K. Ohmi, T. Toyama, G. Rumolo ECLOUD04, 19-23 April, 2004, Napa. Introduction. Coasting beam traps electrons. Does instability always occur for coasting beam?

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Study of ep instability for a coasting proton beam

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  1. Study of ep instability for a coasting proton beam K. Ohmi, T. Toyama, G. Rumolo ECLOUD04, 19-23 April, 2004, Napa

  2. Introduction • Coasting beam traps electrons. • Does instability always occur for coasting beam? • Does electron production rate play some roles in the instability?

  3. Linear theory : Wake field • Proton beam interacts with electron cloud which is gathered at beam position. • We consider motion of beam and cloud centroids. • Coasting beam and cloud model. • Q factor becomes finite due to non-linearity and beta modulation.

  4. Effective impedance of electron cloud

  5. Instability threshold Keil-Zotter theory wesz/c>>1 Coasting beam model

  6. Threshold of neutralization factor for coasting beam JPARC-MR PSR ISIS AGS FNAL-MI KEK-PS L(m) 1567.5 90 163 202 3319 339 g 50.9 1.85 1.07 1.2 128 12.8 Np(x1013) 33 3 3 1.8 3 0.3 lp (x1011/m) 2.1 3.3 1.8 0.89 0.09 0.089 sr(cm) 0.35 1 3.8 1 0.17 0.5 • -0.0013 -0.187 -0.83 -0.65 0.002 0.022 Dp/p(%) 0.25 0.4 0.5 0.5 0.03 0.3 weL/c 7739 195 69 226 6970 246 fth 0.0015 0.025 0.45 0.15 0.00055 0.05

  7. Build-up time due to ionization for the instability • Ionization (2x10-7 Pa) Y1,i=8x10-9e-/(m.p) t= fth/cY1,i =0.4 fth • JPARC-MR 0.6ms • PSR 10 ms instability is observed • ISIS 180 ms no instability • AGS booster 60 ms instability • AGS 10 ms no instability • FNAL-MI 0.2 ms • KEK-PS 20 ms no instability

  8. Nonlinear and many body problem • Not only proton beam but also electrons become unstable in the instability regime. • Electrons are more unstable than beam. Electron diffusion Saturation of beam amplitude (emittance) if

  9. Image the physical system • Linear theory Beam is represented by a string. Electrons are represented by a string or a macro-particle. Linear force acts between them. Exceeding a threshold, beam and macro-electron become unstable. The amplitude of electron is much larger than beam yb=weT ye>>ye. Trick of linear theory. • Nonlinear and many body system Beam is represented by a string. Electrons are represented by many macro-particles. Nonlinear force acts between them. Exceeding a threshold, beam and macro-electron become unstable. Landau damping of electrons is much faster than beam, we>>D wb, wehDp/p. Electrons diffuse on the phase space immediately, and the power causes instability is lost.

  10. Instability parameters for JPARC-MR • we=1.39x109 s-1 n = we/w0 = 1150. • Landau damping rate • Threshold le~ 4.5x108 m-1 • ne = 2.5x106 m-1T0-1(P= 2x10-7 Pa,Ye=8x10-9 /m.p) • number of ionization electron created in a revolution time. • le/ne = 180 turn build-up time until the threshold

  11. Electron diffusion • Electron oscillates 105 period until starting the instability. • Do electrons oscillate stably during so much long term? • The proton beam fluctuates or becomes unstable, electrons may disappear, with the result that the instability may saturate.

  12. Electron motion in the beam potential beam position modulation of 1mm Fixed coasting beam Red: fixed beam. Green: 10 turn. Blue: 100 turn

  13. Simulation • Interaction between the coasting beam and electrons created by ionization or proton loss. • Electrons are added in every revolution by ne. • Secondary emission for absorbed electrons is taken into account. • Beam is represented by a series of macro-particles (1000) distributed along the longitudinal direction uniformly. • Landau damping is considered as x=(1-D)x, where D=1.1x10-2/rev

  14. Ye and growth The simulation was performed for the following 5 cases, Ye = 10-7 m-1 2 x 10-6 Pa thr. 20 turn = 10-6 m-1 2 x 10-5 Pa thr. 2 turn = 10-5 m-1 2 x 10-4 Pa thr. 0.2 turn (PSR loss, H- injection) = 10-4 m-1 2 x 10-3 Pa thr. 0.02 turn = 10-3 m-1 2 x 10-2 Pa thr. 0.002 turn P=2 x 10-7 Pa was too low pressure to show interesting results.

  15. Ye = 10-7 /m.p 2 x 10-6 Pa ne = 2.5x107 /mT0 This value is for 1/10 turn. ** Horizontal axis is 10x Turn

  16. Ye = 10-6 /m.p 2 x 10-5 Pa ne = 2.5x108 /mT0 ** Horizontal axis is 10x Turn This value is for 1/10 turn.

  17. Ye = 10-5 /m.p 2 x 10-4 Pa ne = 2.5x109 /mT0 (PSR loss, H- injection level) ** Horizontal axis is 10x Turn The amplitude grows 1/10 sx. This value is for 1/10 turn.

  18. Ye = 10-4 /m.p 2 x 10-3 Pa ne = 2.5x1010 /mT0 ** Horizontal axis is 10x Turn The amplitude grows ~sx. This value is for 1/10 turn.

  19. Ye = 10-4 /m.p 2 x 10-2 Pa ne = 2.5x1011 /mT0 PSR loss x100 multipactoring level ** Horizontal axis is 10x Turn This value is for 1/10 turn.

  20. Ionization and instability • Strong instability is caused by high pressure P>103 -104Pa. • Ionization was too week as source of coasting beam instability for a normal vacuum P>106-107Ps . • If the electrons are supplied by H- injection foil or proton loss, instability can grow. • Electrons produced by injection Foil. Ye,F = 2 / rep/L. For rep=500, and L=300m (JPARC-RCS), Ye,F = 1.x 10-5 /m.p. • Electrons produced at the chamber wall, which are not trapped for static potential, may be important.

  21. High efficiency electron source at the chamber wall • Electrons are absorbed after one interaction with the beam, if no beam perturbation. • Perturbation due to beam motion may make trap the electrons. • Threshold le~ 4.5x108 m-1 • Electron yield Ye,L = 4x10-6 /m.p (PSR value) • ne= Ye,L Np=1.33x109 /mT0 • The number of electron created in one revolution time already exceed 10 times of the threshold.

  22. Ye = 10-6 /m.p ne = 2.5x108 /mT0 Red : created at the center Blue : created at the wall Electron line density Beam amplitudes Cloud size ***Turn number is 1/10 for the actual machine. Electrons are not trapped, therefore the line density is very small.

  23. Ye = 10-5 /m.p ne = 2.5x109 /mT0 (PSR level) Red : created at the center Blue : created at the wall Electrons are somewhat trapped, therefore the line density increase. Beam amplitude is 2% of the size, that is about half for electrons created at the center,

  24. Ye = 10-4 /m.p ne = 2.5x1010 /mT0 Red : created at the center Blue : created at the wall Electrons are trapped. The line density increase clearly. Beam amplitude is comparable with the size.

  25. Conclusion • We study a coasting beam ep instability caused by Ionization electron. • Electrons are trapped basically, but they are diffused when beam becomes unstable. • The diffusion weakens the beam instability, therefore stability is determined by the comparison with Landau damping. • Secondary electron is created by the diffused electron. • The energy of the absorbed electron was small for a weak instability of beam (Dx<sx). • Even consider the secondary effect, ionization electron can not cause ep instability. • High intensity source like Proton loss, which contributes a fast build-up, can cause the instability.

  26. Conclusion II • We also study a coasting beam ep instability caused by electron created at the wall. • Electrons are not trapped basically, but they are trapped during a short period or are accelerated when beam becomes unstable. • Secondary electron is created by the accelerated electrons. • Electrons with the high yield of PSR level due to proton loss may cause the instability. • Landau damping is treated as amplitude decrement in this model. • It is better to be treated as phase mixing=>G.Rumolo.

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