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Jan 2004

Head-Tail and Coupled-Bunch Electron Cloud Instability and Benchmarking Mauro Pivi NLC Division SLAC. Jan 2004. Motivations and goals.

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Jan 2004

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  1. Head-Tail and Coupled-Bunch Electron Cloud Instability and Benchmarking Mauro Pivi NLC Division SLAC Jan 2004

  2. Motivations and goals Observations of electron cloud in many machines starting ~30 years ago in small, medium-energy proton storage rings, described as: Vacuum pressure, bump instability, e-p instability, or beam-induced multipacting: • Recent observation of single- and multi-bunch instability in PSR (LANL), PS and SPS (CERN), KEKB and PEP-II. • Study the instability, benchmark simulation codes • Provide possible cures and estimate reduction effect. • Study single- and multi-bunch effect in main damping ring of the NLC linear collider, PEP-II and LHC. • Estimate electron cloud intensity threshold for the single- and multi-bunch instabilities • Provide possible cures.

  3. Main sources of primary electrons Picture: The NLC positron MDR stores 3 trains, separated by 65 nsec with each train consisting of 192 bunches. Each bunch generates a small number of electrons by residual gas ionization which does not dissipate completely during the train-gap and may grow up to an equilibrium saturation limit due to space charge, secondary yield etc. Simulations starting with initial e- density near the saturation limit Concern for Luminosity in future hadron and linear colliders: TRC R2-3

  4. Strong and regular head-tail • Wakefields generated by betatron oscillations of the head of the bunch can drive oscillations in the tail. With high beam current this can lead to instability. In a two macroparticle model: • In the absence of synchrotron oscillation Qs=0, the beam is always unstable, since the tail is continuously driven by the head, and the amplitude of oscillation will increase without limit. • If one include the chromaticity (ξ=ΔQ/Q/ Δp/p) the growth rate of the head and tail oscillation mode is given by  need to correct the natural (negative) chromaticity to zero.

  5. HEAD-TAIL and PEHTS codes description G. Rumolo at CERN and K. Ohmi at KEK, single bunch interacting with an electron cloud. The electron-cloud density is given, the number of electrons is constant, the electron-cloud is re-initialized at each bunch passage. PIC calculation, FFT open space. Used also code developed at SLAC, see talk from Y. Cai. Dynamical slices approach to simulate bunch particles.

  6. HEAD-TAIL and PEHTS codes description (see Y. Cai for SLAC code) • Cloud and bunch modeled as ensemble of macroparticles. Bunch is also divided in Nsl slices. • typ. 100.000 e- and 300.000 e+ • typ. Nsl =70 bunch slices • Kick approximation assuming electrons induce a small perturbation (difference with QUICKPIC) • cloud localized at n=0,1,…Nint positions along the ring. Used n=1. • Momentum compaction, chromaticity, (space-charge, beam-beam, amplitude detuning) applied on a turn-by-turn basis. Impedance represented by the broad-band resonator model as a wake function kick at each turn, not included in these sim. Interaction between bunch particles and cloud electrons Transverse phase space coordinates of the generic bunch macrop. are transformed over one turn:

  7. Single-bunch head-tail instability NLC Main Damping Ring Average_electron_cloud_density_along_the_ring_(1/m^3): 1.0e+11 Number_of_particles_per_bunch: 0.75e+10 Horizontal_beta_function_at_the_kick_sections_[m]: 10.0 Vertical_beta_function_at_the_kick_sections_[m]: 10.0 Bunch_length_(rms_value)_[m]: 0.0055 Horizontal, Verticla_beam_size_(rms_value)_[m]: 4.900E-05, 6.000E-06 Longitudinal_momentum_spread: 0.000975 Synchrotron_tune: 0.0118 Momentum_compaction_factor: 1.388e-3 Number_of_kick_sections: 1 Number_of_laps: 2024 Multiplication_factor_for_pipe_axes x, y 10, 10 Horizontal, Vertical _tune: 21.150, 10.347 Horizontal, Vertical chromaticity: 0, 0 Flag_for_synchrotron_motion: 4 Switch_for_wake_fields: 0 Switch_for_pipe_geometry_(0->round_1->flat): 0 Res_frequency_of_broad_band_resonator_[GHz]:* 1.3 Transverse_quality_factor:* 1. Transverse_shunt_impedance_[MOhm/m]:* 10. Res_frequency_of_longitudinal_resonator_[MHz]:* 200 Longitudinal_quality_factor:* 140. Longitudinal_shunt_impedance_[MOhm]:* 0.0 Flag_for_the_tune_spread_(0->no_1->space_charge_2->random):* 0 Flag_for_the_e-field_calc_method_(0->no_1->soft_Gauss_2->PIC): 2 Magnetic_field_(0->no_1->dipole_2->solenoid_3->combined): 0 x-kick_amplitude_at_t=0_[m]: 0. y-kick_amplitude_at_t=0_[m]: 0. Flag_for_the_proton_space_charge: 0 Solenoid_field_[T]: 0.00 Switch_for_amplitude_detuning:* 0 Coherent_centroid_motion_(0->off_1->on): 1 El_distrib_(1->Rect_2->Ellip_3->[1_strp]_4->[2_strp]_5->Parab): 2 Linear_coupling_switch(1->on_0->off):* 0 Linear_coupling_coefficient_[1/m]:* 0.0015 Average_dispersion_function_in_the_ring_[m]:* 0. Position_of_the_stripes_[units_of_sigmax]: 3.0 Width_of_the_stripes_[units_of_sigmax]: 0.5 Kick_in_the_longitudinal_direction_[m]: 0. Number_of_turns_between_two_bunch_shape_acquisitions: 10 Cavity_voltage_[V]: 2.0e6 Cavity_harmonic_number: 714 Sextupolar_kick_switch(1->on_0->off):* 0 Sextupole_strength_[1/m^2]: -0.254564 Dispersion_at_the_sextupoles_[m]: 2.24 Switch_for_losses_(0->no_losses_1->losses): 1.0 Second_order_horizontal_chromaticity_(Qx''):* 0. Second_order_vertical_chromaticity_(Qy''):* 0. Switch_for_boundary_conditions(0->open_space_1->rect_box): 0 Switch_for random phase advance (0->no_1->yes): 0 Electrons are pulled into the bunch and oscillate in the beam well potential. Thus, electron oscillation frequency is important. If number of oscillation nosc~ 0 no instability expected. For nosc~1 instability tends to reach equilibrium. • synchrotron oscillations damping mechanism for fast head-tail instability

  8. Single-bunch instability … MDR • NLC MDR: time evolution of the horizontal and verticalbeam size at different electron-cloud density. Synchrotron tune of 0.0118. (Note: recent simulations with a round initial electron-cloud distribution and sinusoidal RF bucket).

  9. Single-bunch … MDR <yz> correlations: signature of head-tail • for cloud densities ~ 1e12 e/m3fast head-tail, growth time ~ 100ms* • *synchrotron tune = 0.0118

  10. Growth of beam size (courtesy K. Ohmi) • Projected size along z

  11. Single-bunch … MDR Configuration 2.8 ns bunch pacing, running SLAC single-bunch code

  12. Secondary electron yield - SEY Primary electron energy (eV) Electron-cloud generation in NLC/TESLA DR Secondary electron yield SEY (d) model dmax Single-bunch instability threshold for the NLC MDR • Threshold for the development of the electron-cloud head-tail instability in the NLC field free region is at ~1E+06 e/cm3occuring for a peak SEY dmax~1.5÷1.6.

  13. Long range wake multi-bunch simulations. • Computed vertical long range wake after displacing 22nd bunch cloud density 2E+13e/m**3: estimated vertical growth rate0 = 7.976 E+03 [1/s] growth time = 125 ms vertical coherent tune shift = 0.002540. At cloud density 2E+12e/m**3 growth time ~900 ms

  14. Conclusions so far • Single-bunch head-tail instability simulations in NLC MDR: • Coupled-bunch instability in NLC MDR: • Emittance growth threshold for a cloud density ~8e11 e/m3 which constrains SEY ≤ 1.5 • Need an estimate of threshold in dipoles, quadrupoles, wigglers • Computed vertical wake field with a growth time of ~100 microsec for a neutralization electron density.

  15. Simulations benchmarking: input parameters for simulations SEY ?! generation of the cloud Electron-cloud density ?! single/multi bunch instability

  16. Observation of instabilities CERN SPS H V bunch centroid motion

  17. Observation of instabilities CERN SPS • CERN SPS observed since ‘99 for the LHC-type beams. e-cloud mainly in dipoles, above a threshold intensity • Horizontal inst.  Multi-bunch instability • Rise time is few turns and is weakly dependent on the bunch population. Depends on stripes formation. Can be cured by transverse feedback. • Vertical inst.  head-tail  e- cloud + broad band impedance • Several sidebands are visible close to the main tune and with a separation close to synchrotron frequency Qs~0.004, signature of head-tail nature of instability. • Only cure found so far is running at high positive chromaticity ξ y > 0.1 • Simulations: assuming a cloud density 1e+12 e/m3 • Growth rate of the instability and • beneficial effect of chromaticity the as experimentally observed are reproduced by simulations including electron cloud space charge and broad-band impedance. (see also PRST 5 121005)

  18. Observation of instabilities KEKB • KEK, ecloud observed since ’99 early operation period are summarized • the blow-up was a single beam and a multi-bunch effect • has a threshold intensity which was determined roughly by (bunchcurrent)/(bunch spacing) • almost independent of betatron tunes, did not depend on the positions of the vertical masks, which are among the main impedance sources, did not depend on the vacuum pressure, especially for hydrogen, in the arc; and • The coherent dipole oscillation of positron along the bunch caused by the wake force due to electrons appear as either regular or strong head-tail instability. • no dipole oscillation has been observed when the vertical chromaticity is enough high • no blow-up was observed in the horizontal plane. • Simulations: above a threshold density of 5e+11 e/m3 • instability develops vertically rather than horizontallly • Positive chromaticity suppress instability

  19. Observation of instabilities CERN PS • CERN PS, e-cloud observed since 2000 with the LHC-type beams (!): • Single-bunch sets in above a threshold intensity of 4-5e10 p/b particularly evident in the horizontal plane. • Rise time is about 3-4 ms and causes emittance growth a factor 10-20 in the H plane and 2 in the V plane. • no significant change of the instability behavior was observed, when the horizontal chromaticity was varied by several tenths of units. • Simulations: assuming a SEY=1.9 and consequent cloud density 3e+12 e/m3, results in combined function magnets: • instability threshold lies around Np=3e10 p/b with few ms rise time • a faster growth in the vertical emittance, up to a factor 20 with a rise time of a few milliseconds. • estimate strong horizontal wake field, that cannot fully explain the observation of stronger horizontal instability • Positive chromaticity of 0.5 can completely suppress the simulated instability. It is worthwhile stressing that the PS observations are not in agreement with the predictions of numerical simulations. More work is underway and more measurements have been planned at the PS. (see also PRST 6 010101)

  20. Simulations of instabilities CERN PS • computed strong horizontal wake field • faster growth in the vertical emittance, up to a factor 20 with a rise time of a few milliseconds.

  21. continuous electron cloud • Open question: discrepancy between codes may depend on the number of kicks applied discrete IPs

  22. Summary • Head-tail and coupled-bunch in NLC MDR: • Estimated thresholds and growth times - positive chromaticity and larger synchr. tune are beneficial • Need to estimate threshold in multipole elements of the arc and wigglers • Self-consistent code: include generation of secondary electrons • Benchmarking of single-bunch kick-approach codes with observations give good confidence in the order of the assumed cloud density. Some discrepancies with observations (PS) to be understood. • Codes comparison open question: discrete kick approach may overestimate head-tail effect. Code comparison for linear colliders.

  23. Builds on the experience of many colleagues and friends; I am particularly grateful to: • J. S. Berg, Y. Cai, A. Chao, F-J Decker, M. Furman, O. Gröbner, K. Harkay, S. Heifets, N. Hilleret, R. Kirby, J.M. Laurent, G. Lambertson, A. Novokhatski, F. Le Pimpec, R. Macek, K. Ohmi, J. Rogers, R. Rosenberg, G. Rumolo, G. Stupakov, J. Seeman, T. Raubenheimer, G. Vorlaufer, F. Zimmermann, A. Wolski

  24. Benchmark specific with rings PS, SPS and KEKB ECLOUD02 Observations KEK Fukuma http://conf-ecloud02.web.cern.ch/conf-ecloud02/papers/allpdf/fukuma_rev.pdf PAC2003 Observations SPS Arduini et al. http://doc.cern.ch/archive/electronic/cern/preprints/lhc/lhc-project-report-637.pdf PRST-AB General Simulations and results for SPS & LHCfor http://prst-ab.aps.org/abstract/PRSTAB/v5/i12/e121002 PRST-AB: Simulations and Comparison for PS http://prst-ab.aps.org/abstract/PRSTAB/v6/i1/e010101 PARTICLE-IN-CELL SIMULATION OF BEAM ELECTRON CLOUD INTERACTIONS.By K. Ohmi (KEK, Tsukuba),. KEK-PREPRINT-2001-49, PAC-2001-TPPH096, Jul 2001. 6pp. Prepared for IEEE Particle Accelerator Conference (PAC 2001), Chicago, Illinois, 18-22 Jun 2001.code comparison:TRANSVERSE 'MONOPOLE' INSTABILITY DRIVEN BY AN ELECTRON CLOUD?By E. Benedetto, D. Schulte, F. Zimmermann (CERN), K. Ohmi, Y. Papaphilippou (KEK, Tsukuba & ESRF, Grenoble), G. Rumolo (Darmstadt, GSI),. CERN-AB-2003-036-ABP, May 2003. 3pp. ELECTRON CLOUD STUDIES FOR KEKB.By G. Rumolo, F. Zimmermann (CERN), H. Fukuma, K. Ohmi (KEK, Tsukuba),. CERN-SL-2001-040-AP, PAC-2001-TPPH093, Jul 2001. 3pp. Prepared for IEEE Particle Accelerator Conference (PAC 2001), Chicago, Illinois, 18-22 Jun 2001.

  25. Checking the linearity of the long range wake: • Displaced bunches 90 then 91 then 90+91. PEP-II simulations

  26. “POSINST” simulation codes features • Started ‘96 by Miguel Furman at LBNL, implemented together with M. P. since 2000, • single or multi-bunch passages, short or long bunches, and effective bunch profile • the electron cloud is dynamically generated from: • residual gas ionization • secondary electron yield (SEY), detailed model included • other possible sources: photoelectron emission LHC, proton losses in PSR and SNS • field-free region, dipole sections, solenoid field, quadrupole, sextupole, wiggler, etc. • bunch divided longitudinally into Nk kicks (typ. 251 for NLC) • 3D electron kinematics • purely transverse electron space-charge effects • purely transverse beam-electron forces • round or elliptical vacuum chamber geometry, with a possible antechamber • perfect-conductor BCs (surface charges included)

  27. M. Pivi electron cloud studies – Mar 2003 NLC Main Damping Ring (MDR) and PEPII parameters parameter symbol NLC MDR TESLA PEPII beam energy E, GeV 1.98 5 3.1 number of particles per bunchNp0.75 X 1010 2.0 X 1010 1.0 X 1011 circumference C, m 299.8 7500 2199 dipole field at 1.98 GeV (NLC) B, T 1.2 - - bunch length rms sz ,mm 3.6 6 13 bunch size transverse sx , symm 49, 6 230, 230 700, 230 bunch spacing T, ns 1.4 20 8.4 / 6.3 / 4.2 average beta functions bx,y , m 3.97, 6.89 - - vacuum chamber str. sec. round rw, mm20 50 40 beam tube materialmatsurf. Aluminum, TiN Aluminum stainless steel, TiN length of drift sectionls, m 0.975 3.5 7.15 length of BB dipole section ld, m 0.96 - - simulation code as for NLC simulations: we assume that the ring consist of 36 identical, evenly-spaced BB dipole bending magnets of length 0.96m, 68 field free D3 drift sections of length 0.975m and 45 D2F inj. sections in between every pair of dipole. circumference= 299.7m

  28. Electron Distribution in multipole elements Mauro Pivi NLC Division SLAC Jan 2004

  29. Summary • Head-tail and coupled-bunch in NLC MDR: • Estimated thresholds and growth times - positive chromaticity and larger synchr. tune are beneficial • Need to estimate threshold in multipole elements of the arc and wigglers • Self-consistent code: include generation of secondary electrons • Benchmarking of single-bunch kick-approach codes with observations give good confidence in the order of the assumed cloud density. Some discrepancies with observations (PS) to be understood. • Codes comparison arises open questions: kicks approach may overestimate head-tail. Code comparison for linear colliders ?!

  30. Time-averaged electron cloud distribution e-/cm3 e-/cm3 field free region dipole section (Left) histogram of the electron distribution, averaged over the all bunch passages, in an NLC field free region, in units of 106e-/cm3 ; (Right) in a dipole section in units of 109e-/cm3 .

  31. Strip detector

  32. NLC MDR wiggler field model where I(nkr) is the modified Bessel function of the first kind, and the summation is extended to the first 10 modes Sample field model for the NLC MDR wiggler. The wiggler vacuum chamber design includes an 8 mm radius with an antechamber on both sides. The solid line shows the field data, the dotted (purple=By, red=Bz) line show the fit included in the posinst code (M. Woodley and A. Wolski from LCC-0113, CBP Tech Note-276).

  33. Thresholds for the electron cloud in NLC MDR wiggler and dipole regions Snapshot of the transverse electron distribution in a wiggler section with an antechamber design on both sides, Bymax = 2.1 T Dependence of the electron density (at saturation) with the peak SEY in wiggler and dipole sections of the NLC main damping rings. Threshold for the development of the electron-cloud in the wiggler and dipole region is dmax ~ 1.3 and 1.4 respectively.

  34. Electron distribution in the TESLA wiggler Snapshot of the transverse x-y phase space electron distribution in the TESLA wiggler • Equilibrium density in the TESLA wiggler. Threshold occurs at peak SEY~1.2÷1.3

  35. Model 3D quadrupole field with fringe fields D1 QF D2 x=0 0.5m 0.25m 0.5m Schematic of section simulated x=2cm Longitudinal variation of quadrupole field By (T) at different horizontal positions Bz=0.1 Bz=0 y (m) Contourplot of Bz at quad edge (grey  0, black white  ± 0.5) Longitudinal variation of quadrupole field Bz (at fixed x,y) x (m)

  36. NLC main damping ring quadrupole long decay time: electron trapping mechanism snapshot of electron distribution in the NLC quadrupole 3D model during the bunch passage (Left) Threshold for the development of the electron-cloud (left) in the 35 T/m quadrupole is at dmax ~ 1.25. (Center) Decay of the electron-cloud, in a long gap, in a quadrupole (3D model with fringe fields) compared with field free and dipole regions.

  37. quadrupole

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