Post on 14-Jan-2016
description
Effects of External Fields on RF Cavity Operation
Diktys StratakisAdvanced Accelerator Group
Brookhaven National Laboratory
Muon Collider Design Workshop – Jefferson LabDecember 09, 2008 1
Thanks to: J. S. Berg, R. C. Fernow, J. C. Gallardo, H. Kirk, R. B. Palmer (PO-BNL), X. Chang (AD-BNL), S. Kahn (Muons Inc.)
Outline
• Motivation• Introduction/ Previous Work• Model Description • Results• Summary
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Motivation
• Maximum gradients were found to depend strongly on the magnetic field
• Consequently the efficiency of the RF cavity is reduced
805 MHz
Moretti et al. PRST - AB (2005) 3
Introduction and Previous Work (1)
• Dark currents electrons were observed in a multi-cell 805 MHz cavity
• They arise most likely from field enhanced regions on the cavity iris.
• Measured local field gradients where up to 10 GV/m. Such enhancement is mainly due: (i) the cavity geometry (iris), and (ii) material imperfections
• Those electron emitters are estimated to be around 1000, each with an average surface field enhancement βe=184.
Norem et al. PRST - AB (2003) 4
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Objectives of this Study
• Model the propagation of emitted electrons from field enhanced regions (asperities) through an RF cavity. In the simulation we include:– RF and externally applied magnetic fields– The field enhancement from those asperities– The self-field forces due space-charge
• Estimate the surface temperature rise after impact with the wall.
• Can we explain the dependence of the maximum gradient on the strength of the magnetic field (measured in Moretti's and Norem's experiment)?
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Model Description
• Use a surface field such that to produce the observed high local gradient on Norem’s experiment
(i.e. )
• Define the geometry of the asperity such that to produce a local field enhancement consistent with that on Norem’s experiment (i.e )
c
b
• Model each individual emitter (asperity) as a prolate spheroid. Then, the field enhancement at the tip is:
16μm, 0.7μm, 184ec b β
ln(2 ) 1TIP surf e surf
crE E β Ebr
2br
c
Eyring et al. PR (1928)
TIP (184) 50MV/m 10GV/mE 6
Electron Emission Model
• Current Density:
9 1.5
0.5
6.53 102 26 4.521.54 10 10 e surf
φ
β Ee surf φβ EJ e
φ
2
2 ( ) 1dR
ds πR z dzdz
• Average Current density for an RF period:
I Jds
9 1.5
0.50,
6.53 102.5 2.50,12 4.52
1.750
1( ) 6.0 10 10 e surf
φTβ Ee surf φβ E
J J t dt eT φ
J. W. Wang, PhD Dis. (1989)R.H. Fowler and L.W. Nordheim, Proc. Roy. Soc. (1928)
0, sin( )surf surfE E ωt• In RF:
• Assume that the electron emission is described by Fowler-Nordheim model (quantum tunneling through a barrier).
• Average Current: where
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Asperity
Current
Enhancement
Conditions at the Beam Source
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rad. curvature = 0.03 μm
Simulation Details
9
0 19 /E MV m
Asperity
B
• SUPERFISH/MATLAB is used to create a grid that is a superposition of the RF fields and the asperity enhanced fields and PARMELA is used for electron tracking
Initial Distribution (t=0)
Initial Energy = 1eV
Current and RF Phase
• Oscillation will finally wash-out
• Particles emitted between 20-110 deg. will reach the other side of the wall
• Current will vary with phase
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Energy and Power at Impact Point
• Final kinetic energies up to 1 MeV• Particles emitted between 90-95 deg. are those with the
highest impact
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Dependence of Beamlet Radial Size with Field
• How rms beamlet radius scales with current at impact point?
At z=8.1cm
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Dependence of Beamlet Size with Current • Beam Envelope Equation:
2 2 2
2 2 3 3
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2 2θpγ R γ R qB ε K
Rβ γ β γ mcβγ mcβγ R R R
: Canonical angular momentum
: Beam emittance
: Generalized perveance
: RMS beamlet radius
θp
ε
K
R
• Assume:– Conditions:– "Matched Beam" – Flat emitter (No radial fields)
0, 0θp ε 0, 0R R
• Then:0.5
0
2 ( )
2
βγR I
qIB
mc
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Dependence of Beamlet Size with Current in Asperities
• The asperity radial fields will reduce the effect of space-charge
• Therefore, less beam defocusing is expected
jIR
B
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Dependence of Beamlet Size with Current and Field
• Higher fields reduce the final beamlet size but increase the energy density
• How much damage it creates to the cavity wall has to be estimated
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jIR
B
Summary
• Electrons were tracked inside an 805 MHz RF cavity with external magnetic fields
• Electrons, get focused by the external magnetic field and hit the cavity wall with large energies (1MeV).
• Space-charge is deflecting the electrons leading to larger beams.
• Depending on the field the final beamlet rms size is found to be 200-700 μm.
• We found that the beamlet radial size scales as 0.38 with the current, and is independent from the external field.
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