1. Effects of External Magnetic Fields on the operation of an RF Cavity D. Stratakis, J. C. Gallardo, and R. B. Palmer Brookhaven National Laboratory 1 RF Workshop III, FNAL, July 7-8 2009

2. Outline Motivation Introduction and previous work Breakdown model description Particle tracking results within the pillbox cavity under external magnetic fields Discussion of the effects of different cavity materials Summary 2

3. Motivation/ Introduction Maximum gradients were found to depend strongly on the external magnetic field Consequently the efficiency of the RF cavity is reduced Available data suggest that such problems are associated with the unwanted emission from locally enhanced regions. 805 MHzMoretti et al. PRST - AB (2005) 3 B

4. Model Description Step 1: Emitted electrons from an asperity are getting focused by the magnetic field and reach the far cavity side or window. Step 2: Those high power electrons strike the cavity surface and penetrate within the metal up to a distance d. Step 3: Surface temperature rises. The rise induces thermal fatigue leading to surface damage and most likely to breakdown 4 4 B=1 T StartEnd R MetalVacuum d δ

5. Pulsed Heating Experiments at SLAC Mushroom-type cavity used with no surface electric fields at the bottom flange Sample bottom surface is pulsed heated from magnetic fields (eddy currents) due the high powered rf pulse. Different sample materials were tested. For Cu considerable degree of damage at 50 degrees Pritzkau, PRST AB (2003) L. Laurent HG Meeting(2009) S. Tantawi HG Meeting (2009) 5

6. 6 Thermal Fatigue The metal surface heats up during each pulse and cools down between pulses The temperature rise is enough so that expansion and contraction of the surface causes internal stresses which create deformation As the number of pulses increases, finally microcracks appear. Damage occurs; likely breakdown starts.

7. 7 Objectives of this Study As in the SLAC case it is likely that the pillbox cavity surface may experience thermal fatigue by the repeated bombardment of dark current electrons as they are focused by the B-fields ΔΤ~ Deposited Energy, beamlet geometry/ size, material properties, # pulses To estimate ΔΤ we simulate the transport of emitted electrons from field enhanced regions (asperities). In the simulation we include: –RF and externally applied magnetic fields –The field enhancement from those asperities –The self-field forces due space-charge 7

8. Simulation Details Model each individual emitter (asperity) as a prolate spheroid. Then, field enhancement at the tip: Electron emission is described by Fowler-Nordheim model 8 J. W. Wang, PhD Dis. (1989) R.H. Fowler and L.W. Nordheim, Proc. Roy. Soc. (1928) 8

9. B electrons 2R Particle Tracking inside Cavity 9 z=0.02 cmz=0.0 cmz=8.1 cm 400 μm 400 nm R STARTEND Asperity was placed on axis Particles launched normal to surface at 1 eV energies Cavity identical to the 805 MHz pillbox (PB) Es, B similar to the PB

10. Scale of Final Beamlet Size with B For any gradient, final beamlet radius scales as: 10 R METAL

11. Beam Transport in a Uniform Focusing Channel Beam Envelope Equation: Assume: – Conditions: – "Matched Beam" Then: 11 Flat emitter (No radial fields) 805 MHz RF

12. Scale of Final Beamlet Size with Current and B for Asperities In real experiments we have asperities with radial fields that reduce the space-charge effect. So: This result is independent from the magnetic field strength 12 For Asperities

13. 13 Off-Axis Beamlet Sweep Sweeping was ignored in my previous talks. Variation of the RF Phase: –Spot on-Axis: –Spot off Axis: Sweeping on the x-y plane As Bob showed in previous talks the sweeping is B-field dependent. R σ

14. 14 CASINO Simulation of Electron Penetration CuBe 1 MeV CASINO, Scanning 29, p. 92 (2007) Simulation assumed zero magnetic fields on metal

15. Energy Deposition on Wall 15 Beryllium, BeAluminum, AlCopper, Cu Note that electrons penetrate deep in Beryllium Thus, less surface temperature rise would be expected.

16. Average Energy Deposition at Surface 16 Note that electrons penetrate deep in Beryllium Thus, less surface temperature rise would be expected.

17. Summary Electrons were tracked inside an 805 MHz RF cavity with external magnetic fields Necessary parameters to predict the outcomes of future experiments such as spot geometry, beamlet size, energy deposition were determined. Also scaling laws with external magnetic fields were offered. Current data can provide an estimate of ΔT (Palmer). Precise calculation of the temperature rise requires a detailed simulation of the surface physics (ANSYS?, PENELOPE?, other?). Beryllium appears to be a better material candidate 17