# Presentation: 298844

## Electron Cloud - Status and Plans

- Miguel A. Furman
- LBNL
- _[mafurman@lbl.gov](mailto:mafurman@lbl.gov)_
*Collaboration Mtg.*
*FNAL, April 18-20, 2007*

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

_**US LHC Accelerator Research Program**_

## Summary

- Assessment of ecloud for upgraded LHC and injectors
- With build-up code POSINST (no effects on the beam)
- Effects on the beam
- With code WARP/POSINST
- Quasi-static mode “QSM”
- Lorentz-boosted frame method
- Progress towards full self-consistency
- RHIC measurements
- Status and future goals

## Assessment of ecloud buildup for LHC upgradeand injectors

- Assessment of ecloud buildup for LHC upgradeand injectors

-  Initial results for injectors presented at LUMI06
-  Substantial improvements since then:
-  Numerical convergence required in some cases up to 500 kicks/bunch (integration time step t=3x10–11 s)
-  ecloud much more benign than initial estimate
- Limited investigation:
-  Bunch spacings: tb=12.5, 25, 50, 75 ns
-  Dipoles only
-  Eb, Nb, z fixed according to FZ’s files “psplusetcparameters” and “lhcupgradeparameters
- Example:
- PS2 (Eb=50 GeV) vs PS+ (Eb=75 GeV)

| tb [ns] | 25 | 50 | 75 |
| --- | --- | --- | --- |
| Nb [1011] | 4 | 5.4 | 6.6 |

- Nb depends on tb:

## Assessment of ecloud buildup for LHC upgrade and injectors: conclusions

- Heat load depends inversely with tb both for LHC and injectors:
- tb=75 ns is best, closely followed by 50 ns
- tb=50 ns much better than 25 ns
- tb=12.5 ns is terrible
- Cu (or Cu-coated) chamber much better than St.St.
- But this conclusion _*is premised on a particular set of measurements of the SE energy spectrum for St.St.*_
- Need to re-measure energy spectrum in order to verify this conclusion
- Not much difference in heat load between gaussian vs. flat longitudinal bunch profile for the LHC, at least for tb=50 ns
- Not much difference between PS2 and PS+, nor between SPS50 and SPS+a50, except at high max for tb=25 ns
- See my LUMI06 proceedings paper (_*not*_ my PPT file)
- A full, definitive report is forthcoming
- _Caveats_:
- So far, heat load in the dipole bends only
- z, Nb, ... not independently exercised

## Ecloud effects on the LHC beam:code WARP, QSM approx.

- Recent example of emittance growth
- Assume e=1014 m–3
- 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 6000 stations
- Actual LHC chamber shape
- Constant focusing approx.
- Conclusion: need to resolve  to reach convergence, as expected (ie., no. of EC stations > tune)
- More studies to come
- Actual optics, vary e, vary Nb, etc
- Look at instability, not simply emitt. gr., multibunch, more self-consistency
- Benchmark against CERN results!

**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

## 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
- Simulations carried out thus far have been problematic
- Partly due to code problems (now believed fixed)
- Partly due to complexity of two coexisting beams in common-pipe region
- Detectors now interfaced to the RHIC control system (Eric Blum, BNL)
- Improved power supply for the magnets
- No useful results at present
- I look forward to results in the near future

## 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)

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

- Courtesy J.-L. Vay

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

##  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

## Related developments (outside LARP scope, but synergistic)

- ecloud at the FNAL MI upgrade (HINS effort)
- Direct e– measurements with RFA at the MI (R. Zwaska)
- Interesting effects at transition (shortest z)
- Also ecloud evidence at the TEVATRON (X. Zhang)
- In parallel, simulations at LBNL of:
- ecloud build-up at MI: code POSINST
- Extensive (but still ongoing) studies
- Qualitative agreement w/ measurements
- Quantitative: there’s a fly in the ointment (to be understood)
- Effects on the beam (emittance growth, single-bunch and multibunch inst.): code WARP
- Microwave transmission technique (F. Caspers & T. Kroyer): code VORPAL
- Hopefully new experiments at PEP-II will help to calibrate

## More related stuff

- ECLOUD07 (Korea, last week)
- Significant new effort reported from KEKB: dedicated SEY equipment
- SEY of metals condition down to max≈1 (Cu, StSt, TiN, TiZrV)
- When bombarded with 5 keV e– beam (dose: 0.01–1 C/cm2)
- “Graphitization” of the surface (XPS analysis)
- Also tested 500 eV e– beam bombardment; will redo at 100 eV
- Also measured ecloud conditioning by ecloud in the e+ beam
- Results slightly less favorable
- Synchrotron radiation spoils graphitization (consistent with PEP-II tests)
- Some of these new results seem at odds with previous from CERN & SLAC
- Why do existing machines still have an ecloud problem?
- (they would not if max≈1)

## Status summary and future goals

- Nominal LHC heat-load estimate and POSINST-ECLOUD benchmarking: (*) done
- Upgraded LHC heat load: (*) done
- Upgraded injector upgrade heat load: (*) done, but beam parameters not independently exercised (only certain SEY-related parameters varied)
- Effects from ecloud on beam: (*) recent initial results, after substantial code development
- 3D beam-ecloud self-consistent simulations: continuing
- AMR, QSM, adaptive time stepping, parallelization: implemented in code
- Development of Lorentz boosted frame method: proof of principle exists; needs more developments for realistic applications
- Effects of ionized gas on heat load and beam: not started
- Analyze SPS data, esp. measured heat load and e– spectrum: (*) first set of results; need to benchmark against expts.
- Help define optimal LHC conditioning scenario: (*) not started; delayed in favor of 2, 3 and 4. This is our intended next task this year in the area of ecloud buildup.
- Apply Iriso-Peggs maps to LHC: (–) ongoing at low level; should it be deleted from LARP list?
- Quick understanding of global ecloud parameter space, phase transitions
- Simulate e-cloud for RHIC detectors and benchmark against measurements: (**) continuing
- Simulate ecloud for LHC IR4 “pilot diagnostic bench:” not started

- (–) 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