fcc electron cloud study plan k. ohmi (kek) mar.5. 2015 fcc electron cloud study meeting cern
TRANSCRIPT
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.