photoemission, secondary emission, magnetic

Transcription

1 Electron-Cloud Simulations: Build Up and Related Effects Frank Zimmermann, G. Rumolo,, SL/AP (1) Simulation model photoemission, secondary emission, magnetic fields, beam fields, image charges, space charge (2) Example Results threshold in dipole field vs. field-free region, SPS fixed-target beam, signal on LHC pick ups, multibunch instability, spatial structure, trapped electrons, e build up for electron beams

2 simulation programs for e cloud build up PEI, KEK, 1995 POSINST, LBNL, 1997 ECLOUD,, 1997 codes at IHEP (Z. Guo, J. Xing, et al.) and KEK (L. Wang)

3 Simulation recipe for e build up (code ECLOUD) represent by macroparticles (2000/bunch), slice bunches and interbunch gaps for each bunch slice, create photo-el. and accelerate existing in beam and beamimage fields if hit the wall secondary ; change macro charge at each gap slice the are propagated in the magnetic field; kicks from spacecharge and image charges

4 Geometry Transverse aperture in the LHC arcs. The solid line describes the actual cross section of the LHC beam screen. Sometimes we approximate it by the inscribed ellipse, e.g., for accurate modeling of image charges.

5 Photoemission Left: initial azimuthal distribution of photoelectrons for 10% and 100% photon reflectivity; right: initial photoelectron energy distribution at the moment of emission and after the first bunch passage.

6 Photoemission (a) 20% reflected photons Distribution (arb. units) φ θ Azimuthal angle φ (in units of π) (b) 100% reflected photons 2 cos distribution cosine distribution 3 cos distribution Distribution (arb units) Azimuthal angle φ (in units of π) left: definition of angles and ; right: initial azimuthal distribution of photoelectrons for (a) 20% and (b) 100% photon reflectivity, considering different distributions [I. Collins, private communication, 2000].

7 ! ", ) $ Magnetic Field Schematic view of electron motion in a strong vertical dipole field. In the simulation, often only a net vertical kick is applied, since for LHC at 7 TeV. Larmor radius 6 m for 200 ev. *%+ *%- #%$ &('

8 DC GFE BA GFE Beam Field K LM J F I H IH = > < ;:< : K LM J F I H IH G Electrons at large amplitudes do not move much during the bunch passage and simply receive a kick. Electrons near the bunch oscillate in the beam potential. The two situations are called kick region and autonomous region, respectively [S. Berg, 1997].

9 P O N Energy Gain of Stationary Electron (No Magnetic Field) LHC: σ =0.2 mm, σ l =7.7 cm, N= Rectangular Bunch Gaussian Bunch Energy for Single Kick Potential Energy (Rectangular) 4 Energy Gain (kev) Initial Radius (cm) Maximum energy gain vs. initial particle radius for nominal LHC parameters [S. Berg].

10 R\ Y [ZW WSYX WVU cc cc cc cc z z ƒ ~ cc } cc { z cc cc cc e cc cc y rqpn on SQ b\ b ^U Z VQ YY WaQ R\ SY ^Q `Q U S_ R\ V ^QX ]\ Secondary Emission TSQ RQ Š e c ˆ Š gc ˆ Š e cc ˆ Š cgc ˆ Š iic ˆ d ccc ccc d cmc d clc d ckc d cjc d cic d chc d cgc d cfc d ccd c d e cf e d cc e d c cl d c cj d c ch d c cf d Normalized secondary electron energy distribution for conditioned copper, revealing three components: true secondaries ( elastically scattered ( ), ) and rediffused (in between). [N. Hilleret, 2001] stuv w x

11 Œ Secondary emission yield for perpendicular incidence vs. primary electron energy with and w/o elastically scattered electrons. Parametrization based on measurements [Noel Ž ŒŽand Hilleret, 2001]. Two parameters:.

12 Ž [Furman, 1997]. Yield for Œ Secondary emission yield: True secondaries [Seiler et al.]: Ÿ œž š Ž Œ where angle w.r.t. surface normal, elast. scattered / rediffused part [Furman, 1997]:, Recent measurements [Ian Collins, 2000]:, and ev. When e hits wall, throw coin:

13 Ž [Furman, 1997]. Œ Alternative expression for true secondaries [M. Furman]: Ž Œ where (N. Hilleret), angle w.r.t. surface normal, Alternative expression for the yield of elast. scattered / rediffused part : obtained from measurements

14 recent measurements on Cu were fitted as for ev:,,,, ev for :,,,, ev

15 Initial energy spectrum of true secondaries as modelled in 1999/2000 compared with new parametrization by Noel Hilleret, October Now for.

16 Initial angular distribution of secondary electrons vs. the polar angle w.r.t. surface normal.

17 Image Fields with image charges without image charges Electric field pattern for a beam centered in an elliptical chamber with [left] and without [right] image charges.

18 Horizontal electric beam field vs. horizontal position at for an elliptical chamber with mm half apertures and a beam offset of 4.3 mm in both transverse planes.

19 Electron Space-Charge Fields Horizontal electric space-charge field of electron cloud vs. horizontal position after the passage of 8 bunches in the LHC. Parameters:,,, ev.

20 Longitudinal Electron Motion Contributions: emission angle, beam magnetic field, drift in dipole field, gradient drift, typical longitudinal velocities: m/s. Longitudinal coordinate versus time for two sample electron trajectories in a field free region (left) and in a 1-T dipole field (right). Sometimes neglected.

21 Example Simulation Results Dipoles vs. Field-Free Region Simulated electron-cloud build up in the SPS for a field-free region (left) and a strong dipole (right), comparing various bunch populations. In field-free regions threshold is higher, but build up above threshold stronger.

22 Build Up for SPS FT and Energy Spectrum Electron-cloud line density vs. time in a dipole field for the SPS fixed-target beam with 5-ns spacing (left) and the corresponding energy spectrum of electrons hitting the wall (right).

23 Different Dipole Models Electron-cloud line density vs. time in a 0.26-T dipole field for an e beam in the KEKB HER comparing two different models of electron motion.

24 Multibunch Wake Electron cloud couples motion of subsequent bunches. 1.2e e+09 x-density before bunch displacement x-density after bunch displacement 1e+09 1e+09 8e+08 8e+08 6e+08 6e+08 4e+08 4e+08 2e+08 2e Projected horizontal electron charge density in an LHC bending magnet before the 41st bunch in the train is horizontally displaced by 1 cm [left] and just prior to the arrival of the 42nd bunch [right]. The horizontal axis is in units of meters; the vertical coordinate is the charge (in units of ) per, bin and per grid point. Other parameters: 500 grid points,,.

25 Multibunch Instability Multibunch instability growth rate as a function of maximum secondary emission yield for the LHC. Other parameters:, and. Growth rate small for LHC at 7 TeV. ev, " ª

26 Effect on Beam Diagnostics? 2nd electrode 1st electrode photoelectrons from direct illumination 48 mm incoming beam 3rd electrode 4th electrode Schematic cross section of a BPM in the LHC arc [G. Rumolo, 2000]. Length of the device is 24 mm. Direct synchrotron radiation illuminates the first electrode.

27 Œ x Charge (in units of e-) x Charge (in units of e-) Time ( µs) Time ( µs) Net charge deposited or emitted at the four electrodes of an LHC arc BPM for [G. Rumolo, 2000]. Negative values indicate a net flow of electrons away from the plate. Ž (left) and 1.9 (right)

28 Current (ma) Instantaneous electron current at the first electrode vs. time (top) and its power density spectrum vs. frequency (bottom) for a maximum secondary emission Time ( µs) 800 [G. Ru- yield molo, 2000] Power spectrum (arb. units) Frequency (MHz) 0

29 Spatial Structure: Vertical Stripes Electron flux on chamber wall in A/m position in an SPS dipole. vs. the horizontal

30 Spatial Structure: and Ionization Electron flux on chamber wall in A/m vs. the horizontal position in an SPS dipole for various values of ; left: launching primary e at the wall; right: launching primary e inside beam (ionization). Ž Œ

31 Build Up: Launch Point of Primaries Ž Œ ; SPS electron line density vs. time for various values of left: launching primary e at the wall; right: launching primary e inside beam (ionization).

32 Electron Trapping in Quadrupoles 3.5e e+10 with space charge without space charge after last bunch 3e+10 3e e e+10 2e+10 2e e e+10 1e+10 1e+10 5e+09 5e e-07 2e-07 3e-07 4e-07 5e-07 6e-07 7e-07 8e e-07 2e-07 3e-07 4e-07 5e-07 6e-07 7e-07 8e-07 Electron line density vs. time; left: including electron space-charge and image fields; right: only magnetic forces after the last bunch

33 0.12 after 50 bunches Left: histogram of after 50 bunches; right: fraction of electrons for which (trapping condition), where «%«based on discussions with K. Ohmi and L. Wang

34 Electron Cloud for Electron Beams Electron-cloud line density vs. time in a 0.26-T dipole field for the KEKB HER comparing e beam and e beam

35 Conclusions simulation is sensitive to parametrizations for secondary emission and photoemission; image charges, electron space charge, and magnetic fields are also important simulated electron build up in good agreement with observations at SPS and KEKB discrepancy in position of the two vertical stripes electrons may be trapped inside quadrupoles e cloud can build up for electron beams as well

36 Thanks to: G. Arduini, V. Baglin, O. Bruning, R. Cappi, F. Caspers, A. Chao, I. Collins, K. Cornelis, H. Fukuma, M. Furman, M. Giovannozzi, O. Grobner, K. Harkay, S. Heifets, N. Hilleret, M. Jimenez, T. Katsouleas, E. Metral, K. Ohmi, K. Oide, E. Perevedentsev, M. Pivi, A. Rossi, F. Ruggiero, L. Wang, and many others