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Effects of External Fields on RF Cavity Operation

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.).

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Effects of External Fields on RF Cavity Operation

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  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 • 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)

  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 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. ) Model each individual emitter (asperity) as a prolate spheroid. Then, the field enhancement at the tip is:

  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 Enhancement Current 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 20-110 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 90-95 deg. are those with the highest impact

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

  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 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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