# Presentation: 298845

## Electron Cloud - Status and Plans

- Miguel A. Furman
- LBNL
- _[mafurman@lbl.gov](mailto:mafurman@lbl.gov)_
*Collaboration Mtg.*
*SLAC, 17-19 Oct., 2007*

***bnl - fnal- lbnl - slac***

_**US LHC Accelerator Research Program**_

## Summary

- Effects of ecloud on the beam
- With code WARP/POSINST
- Quasi-static mode “QSM”, and with
- Lorentz-boosted frame method, fully self-consistent “FSC”
- Assessment of ecloud build-up for PS2
- With build-up code POSINST (no effects on the beam)
- RHIC measurements
- Related ecloud R&D (non LARP)
- Status

## Effects of ecloud:  growth in LHC beamcode WARP (J.-L. Vay)

- one-turn  growth simulation
- E=450 GeV, Nb=1.1x1011, single bunch,
- Code WARP, parallel, 3D calc.
- Quasi-static approx. mode (QSM)
- AMR, parallel 8 processors
- Beam transfer maps from EC station to next
- Up to 3000 stations
- Actual LHC chamber shape
- Constant focusing approx.
- Electrons allowed to move vertically only
- No synchr. oscillations
- Beam launched offset by 0.1y
- Conclusion: need to resolve  to reach convergence, as expected (ie., # of EC stations > tune)

- 1-turn fractional emittance growth vs. Nstn
- for 3 values of the ecloud density

**Notes:**
Np = 1.1e11 # nb protons in bunch
mo = 938280000.
gamma_b = 479.6  #gamma of beam
E  = gamma_b*mo     # beam energy (eV)
De = 1.e14   # e-cloud density (m^-3), highest limits at  
commissioning (from MA Furman, 03/30/07)
bx = 64.28 # betatron tune in X
by = 59.31  # betatron tune in Y
Rb = 0.884e-3 # beam transverse rms size (m; Gaussian)
sigx=sigy=Rb
Lb = 0.13   # beam rms length (m; Gaussian)
Rp=2.2e-2# Chamber radius
Rc = 26.659e3  # ring circumference (m)
betax = Rc/(2.*pi*bx)
betay = Rc/(2.*pi*by)

- # of meshes in z (longitudinal) = 128 (mesh goes from -4.*sigmaz to  
+4.*sigmaz)
- transversely, there is ~4 meshes/sigmax for finest resolution patch  
and 16 meshes/Rp for coarsest resolution grid
- # beam macroparticles: 300000
- # electrons: each injected slice had 256x256 macro-electrons,
- duration run 6000 stations: ~ 6.5 hours

## Effects of ecloud:  growth in LHC beam1-turn  growth vs. ne

- Emittance growth simul.
- Same conditions as previous slide
- except Nstn=3000=fixed
- Conclusion:
- /  ne  as ne-->0

- 1-turn fractional emittance growth vs. ecloud density
- (Nstn=3000)

## Ecloud effects on the LHC beam: growth vs. time

- Same conditions as previous slides
- Conclusions:
- Fully Self-Consistent (FSC) approx. in Lorentz-boosted frame agrees well with QSM
- You can get away with much fewer ecloud stations if you are willing to wait for a while
- Except at very high ne
- Emittance growth quite large; is this real?
- Aggravating factors:
- No synchr. osc., no E-spread
- Continuous focusing (?)
- Offset beam
- ???

## Ecloud build-up in PS2 at 50 GeVvs. chamber radius

- Looked only at a bending dipole
- Vary pipe radius keeping all else fixed
- Nb=4x1011 for tb=25 ns, Nb=5.4x1011 for tb=50 ns; other parameters as specified in LUMI06 by FZ
- Averages taken over 2 trains
- PS+ also looked at
- Conclusions:
- Low heat load wants small radius
- Low e– density wants large radius
- Beam-induced multipacting condition broadens and gets shifted to lower radius relative to the impulse approximation (Gröbner,                 )

- heat load

- density

## Ecloud build-up in PS2 at 50 GeV (contd.)vs. chamber radius

- e–  flux at the walls (*J*e)
- Conclusions:
- Ratio *J*e/*n*e in good agreement with analytic expectation as *r*-->0:
-                       (R. Zwaska)

## RHIC studies

- Two CERN e– detectors installed in RHIC common-pipe region >1 yr ago
- Inside a weak adjustable dipole magnet
- Electron detectors & installation was not a LARP-funded effort (M. Jiménez, CERN VAC)
- But LARP funds simulation & benchmarking activity
- Detectors now interfaced to the RHIC control system (Eric Blum, BNL)

- e– detector signal

- Au beam current

## Related developments (not LARP-funded, but synergistic)

- Microwave detection of ecloud
- Recent experiments at PEP-II successful !
- S. deSantis et. al., submitted for publication
- Simulations at LBNL (K. Sonnad; TechX code VORPAL)
- ecloud at the FNAL MI intensity upgrade
- Direct e– measurements with RFA at the MI (I. Kourbanis, R. Zwaska)
- Simulations at LBNL (M. Furman and K. Sonnad)
- ecloud build-up studies (extensive and ongoing)
- Effects on the beam (emittance growth, ...): newer effort

## SLAC-LBNL ecloud R&D at SPSNOTE: SLAC portion is funded by SLAC

**Electron Cloud Studies for the SPS**
- SINGLE-BUNCH INSTABILITY SIMULATION
-  Code benchmarking and long term simulation runs for the SPS and LHC.
-  _Collaborators_: K. Sonnad (LBNL), M. Pivi (SLAC), F. Zimmermann (CERN).
- _CERN Contact_: F. Zimmermann.
- SPS EXPERIMENTAL TESTS:
-  groove insertion in the SPS 4-magnet dedicated experiment (grooved; clearing electrode; coated;  plain SS)
-  At SLAC we are working on manufacturing a groove insertion to fit in one of the 4 dipoles new installation of the SPS. This is part of a larger project to investigate mitigation techniques for the electron cloud in the SPS.                                                               _Collaborators:_ M. Venturini, M. Furman, (LBNL), M. Pivi, M. Morrison, L. Wang, (SLAC) G. Arduini, E. Chapochnikova (CERN).
- _CERN Contact_: G. Arduini.

|  | FY08 | FY09 |
| --- | --- | --- |
| FTEs | 0.25 | 0.25 |
| M&S | 20.0 k$ | --- |
| Travel | 5.0   k$ | 5.0   k$ |

- R&D combined effort: SLAC FTEs, M&S and Travel (PRELIMINARY)

## SPS has an ecloud instability for LHC beams
Single bunch in V, coupled bunch in H; spectrum ~700 MHz
SLAC-LBNL proposed effort (J. Fox and J.Byrd)
Similar system used for PSR ecloud instability
CERN interested (O. Brüning’s talk, this morning)

- SPS has an ecloud instability for LHC beams
- Single bunch in V, coupled bunch in H; spectrum ~700 MHz
- SLAC-LBNL proposed effort (J. Fox and J.Byrd)
- Similar system used for PSR ecloud instability
- CERN interested (O. Brüning’s talk, this morning)

- PSR signal

- See _J. Fox_’s talk
- tomorrow

## Status summary and future goals

- Nominal LHC heat-load estimate and POSINST-ECLOUD benchmarking: (*) done
- Upgraded LHC heat load: (*) done
- Injector upgrade heat load: (*) continuing
- Effects from ecloud on beam: (*)
- AMR, QSM, adaptive time stepping, parallelization: implemented in code
- Applications to LHC in constant-focusing approximation and other simplifying assumptions
- 3D self-consistent simulations: challenging; continuing
- Lorentz-boosted frame method: shows good agreement with QSM in benchmarks
- Effects of ionized gas on heat load and beam: not started
- Analyze SPS data, esp. measured heat load and e– spectrum: (*) need to benchmark against expts.
- will simulate effects on the beam
- Help define optimal LHC conditioning scenario: (–) delayed or deleted
- Apply Iriso-Peggs maps to LHC: (–) delayed or deleted
- Simulate e-cloud for RHIC detectors and benchmark against measurements: (**) continuing
- Simulate ecloud for LHC IR4 “pilot diagnostic bench:” not started
- ecloud suppression at SPS:
- 700 MHz feedback system: _new intiative_ (SLAC-LBNL) (J. Fox, tomorrow afternoon)
- Specialized chambers (grooved, coated, cl. electrodes): _new initiative_; SLAC portion is SLAC-funded

- (–) no longer endorsed by CERN AP group

- (*) endorsed by CERN AP group
- (**) endorsed by CERN vacuum group

## Additional material

## Quasi-static mode (“QSM”)

- 2-D slab of electrons (macroparticles) is stepped backward (with small time steps) through the _frozen_ beam field
- 2-D electron fields are stacked in a 3-D array,
- push 3-D proton beam (with large time steps) using
- maps - “WARP-QSM” - as in HEADTAIL (CERN) _or_
- Leap-Frog - “WARP-QSL” - as in QUICKPIC (UCLA/USC).

- s0

- lattice

- 2-D slab of electrons

- 3-D beam

- s

## Benchmarking WARP-QSM vs. HEADTAIL

- Time (ms)

- Emittances X/Y
- (-mm-mrad)

- 2 stations/turn

- Time (ms)

- Emittances X/Y
- (-mm-mrad)

- 1 station/turn

- CERN code benchmarking website

## Towards “full self-consistency”: Lorentz-boosted frame method

- “Fully self-consistency” (FSC)
- Beam and ecloud affect each other
- Beam-gas ionization, secondary electrons, lost protons striking wall, etc
- This is a formidable problem
- We’ll approach it step by step
- In the end, probably use FSC only as spot-checks on simpler, faster calculations
- But all necessary “modules” already in code WARP
- Essential computational problem in ecloud: wide disparities of time scales needed to resolve e– motion, proton motion and lattice (eg., betatron wavelength)
- Found that self-consistent calculation has _similar cost_ than quasi-static mode if done in a _Lorentz-boosted frame (with ____>>1)_, thanks to relativistic contraction/dilation bridging space/time scales disparities (J. L. Vay, with partial LARP support)
- Computational complexity is not a Lorentz invariant (for certain problems)

## Speedup x1000

- Boosted frame calculation sample:proton bunch through a given e– cloud

- Hose instability of a proton bunch
- b=500 in Lab
-  L= 5 km, continuous focusing
- Mag. field: B=kr
-  No chamber
-  Nb=1012
-  e=1013 m–3

- electron
- streamlines

- beam

- proton bunch radius vs. z

**CPU time:**
** ****lab frame: ****>2 weeks**
** ****frame with ********2****=512: ****<30 min**

**Speedup x1000**

- J.-L. Vay, PRL **98**, 130405 (2007)

##  Added complications:

-  moving boundary conditions
-  non-rectilinear moving frame (in curved trajectories)
-  sort out simultaneity of events for useful Lab frame diagnostics
-  ...
-  Need to be understood and implemented
-  Real-life simulation case not yet available
-  But clear indications of breakthrough in self-consistent simulations

- Lorentz-boosted method: my concerns