1. Electron Motion in a RF Cavity with external Magnetic Fields Diktys Stratakis Brookhaven National Laboratory RF Workshop – FermiLab October 15, 2008

2. Introduction Asperities can arise from material imperfections on the cavity surface. At the tip of an asperity the field is enhanced. Emission of electrons is possible. Emitted electrons are accelerated by the RF field and can impact a wall far from the emission point. Strong external magnetic fields can act to focus the electrons to a particular point increasing the probability to damage there (surface heating, secondary emission). How space-Charge affects this process is still an open question

3. 3 Objectives of this Study Model the propagation of field emitted electrons from asperities through an RF cavity. In the simulation we include: –RF and externally applied static magnetic fields –The field enhancement from those asperities –The self-field forces due space-charge Demonstrate a design of a magnetically shielded cavity

4. 4 Simulation Tools at BNL CAVEL (R. C. Fernow - BNL) –3D Code –Particle tracking within cavity fields and external fields PARMELA (LANL) –Can also do particle tracking within cavity fields and external fields –Includes space-charge effects We successfully benchmarked those two codes (no space-charge)

5. Electron Tracking under External Fields (1) Electron is emitted from the location of maximum field enhancement (the cavity iris) and tracked at various RF phases. No space-charge included In the presence of magnetic fields they get focused to a particular point with large energies. B=0 TB=1 T B=1 T, tilted

6. Electron Tracking under External Fields (2) Note the second peak in energy (green color) Returning electrons can also damage the material

7. The Solution (?): Insulated 805 MHz Cavity B. Palmer

8. Insulated 805 MHz Cavity Electrons are emitted normal to the surface at various phases Initial electron energy is 1 eV Maximum axial Field is 17 MV/m All particles return to surface with low energies

9. Test of Cavity Tolerances d A cavity displacement greater than 2 mm reduces the efficiency of insulation Cavity becomes “more sensitive” to uncertainties at higher magnetic fields

10. Asperities in RF Cavities Assume: and Then, consistent with experimental observations. Model asperity as a prolate spheroid. Then, the field enhancement at the tip is: Dark current (Fowler-Nordheim model):

11. Field Enhancement around Asperity z (μm) R (μm) : Enhanced field from asperity : Local field (no asperity)

12. Simulation Details Asperity is placed on the axis of a 805 MHz cavity A 1mA, 1ev electron beam is uniformly distributed 1 μm around the asperity tip. A grid that is a superposition of the RF fields and the asperity enhanced fields is used as the field map. Gradient on axis is equal to 1 MV/m. We have a uniform 1T external magnetic field. 805 MHz

13. Very Preliminary Results Electrons reach the other side of the cavity They reach energies up to 1 MeV for both cases Indeed space-charge is defocusing electrons, generating so larger spots With Space-Charge No Space-Charge

14. Outlook Further study is required. Issues to be addressed are: –Electron initial distribution –Beam Current –Asperity geometry –Multiple Asperities –External field orientation

15. Summary Field Emitted electrons were tracked with PARMELA under the influence of RF, static magnetic fields and self- fields (space-charge). Tested the efficiency of a 805 MHz magnetically insulated cavity. We collaborate with: –Tech X –Imperial College, Lancaster University: (A. Kurup, K. Long, R. Seviour, A. Pozimski, A. Zarrebini)