1. Effects of External Fields on RF Cavity Operation
Diktys Stratakis
Advanced Accelerator Group
Brookhaven National Laboratory
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.)
Muon Collider Design Workshop – Jefferson Lab
December 09, 2008

2. Outline Motivation Introduction/ Previous Work Model Description
Results
Summary

3. Motivation
805 MHz
Maximum gradients were found to depend strongly on the magnetic field
Consequently the efficiency of the RF cavity is reduced
Moretti et al. PRST - AB (2005)

4. 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)

5. 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)? 5

6. Model Description
Model each individual emitter (asperity) as a prolate spheroid. Then, the field enhancement at the tip is:
Eyring et al. PR (1928)
Define the geometry of the asperity such that to produce a local field enhancement consistent with that on Norem’s experiment (i.e )
Use a surface field such that to produce the observed high local gradient on Norem’s experiment
(i.e )

7. Electron Emission Model
Assume that the electron emission is described by Fowler-Nordheim model (quantum tunneling through a barrier).
Current Density:
In RF:
Average Current density for an RF period:
Average Current:
where
R.H. Fowler and L.W. Nordheim, Proc. Roy. Soc. (1928)
J. W. Wang, PhD Dis. (1989)

8. Conditions at the Beam Source
Asperity
Current
Enhancement
rad. curvature = 0.03 μm

9. Simulation Details
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 B
Asperity
Initial Distribution (t=0)
Initial Energy = 1eV

10. Current and RF Phase
Particles emitted between deg. will reach the other side of the wall
Current will vary with phase
Oscillation will finally wash-out

11. Energy and Power at Impact Point
Final kinetic energies up to 1 MeV
Particles emitted between deg. are those with the highest impact

12. Dependence of Beamlet Radial Size with Field
At z=8.1cm
How rms beamlet radius scales with current at impact point?

13. Dependence of Beamlet Size with Current
Beam Envelope Equation:
Assume:
Conditions:
"Matched Beam"
Flat emitter (No radial fields)
Then:

14. 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

15. 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

16. 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 μm.
We found that the beamlet radial size scales as 0.38 with the current, and is independent from the external field.