FCC electron cloud study plan

K. Ohmi (KEK)Mar.5. 2015

FCC electron cloud study meetingCERN

Simulation using cylindrical chamber in PEI code• Space charge off, stop when line density is

over 2x beam line density.• 25 ns 5ns d2,max=1.15-1.9,

Emax=300 eV

Eelctron cloud simulation using exact boundary

• Uniform mesh in the transverse plane.• Solve difference (discrete Poisson) equation

using Band Matrix Method.

Potential solver

Necessary revision on PEI code

• Electron production at the boundary• Beam force satisfying the boundary condition

Coupled bunch instability• Corrective motion between beam and electron

cloud.• based on buildup code, PEI.• Instability due to electron cloud in bending

magnet in DAFNE (rectangular chamber).

White : beam centerViolet: electron cloud

Single bunch instability• Strong head-tail instability caused by electron

cloud• Threshold of electron density

Electron frequency in the beam field

Tune shift of the beam

Electron motion (3.3TeV-50TeV)• b=200 m, g=3517, sz=8cm, ns=0.002– Np=1011(25ns), en=0.44x10-6 m.

• we/2p=3.56 GHz (3.3TeV) 13.9 GHz (50TeV)

• wesz/c=5.97 (3.3TeV) 23.3 (50TeV)

• re,th= 4.4x1010 (3.3) 5.7x1011 m-3 (50)

• Dn(re,th)=0.00039(3.3) 0.00033 (50)

– Np=2x1010 (5ns), en=2.2x10-6 m. • we/2p=3.58 GHz (3.3) 13.9 GHz (50TeV)

• wesz/c=6.00 (3.3) 23.3 (50TeV)

• re,th= 4.4x1010 (3.3) 5.7x1011 m-3 (50)

• Dn(re,th)=0.00039(3.3) 0.00033 (50)

Electron density during interaction with beam• Transverse electron profile along z. (drift space)• Electron initial energy v0=106 m/s (3eV) is assumed.

• Variation of electron density and size along the bunch interaction, z.

• Density increase to 25x of initial.

z=-3sz z=-2.4sz z=-0.4sz

• In strong Bending magnet

• Tune shift increases 5x at interaction with bunch center, z~0. (drift).

• Variation of electron density and size along the bunch interaction, z.

• Density increase to 5x of initial.

z=-2.4szz=-1.8sz z=+0.6sz

Emittance growth caused by electron cloud

• Electron cloud potential induces tune spread and resonances.

• The strength of the resonances are characterized by the width in amplitude space, DJ.

• Modulation of the resonances due to synchrotron motion etc. results in emittance growth.

Electron cloud induced tune spread and resonance term

• U(x,y): integrated effective potential due to electron cloud

• Resonance driving term is Fourier component of U.

H0: lattice transformation of s’ to s

Tune shift and slope due to Gaussian electron cloud

• Tune shift

• Tune slope

Tune slope and resonance width • Tune

Example: J-PARC space charge

• Tune shift is very small, Dn=0.0003, even at the threshold of coherent instability.

• The tune shift can be x5 higher due to pinching, Dn=0.0015. Not very large.

• How electron cloud with the tune shift causes emittance growth.

Future plan • Study Electron cloud Build up using accurate

boundary.• Evaluate growth rate and unstable mode of

the coupled bunch instability.• Evaluate Resonance width and simulation

using resonance model.