1. C.Limborg-Deprey Beam Dynamics with mode 0limborg@slac.stanford.edu November 3 rd 2004 Beam Dynamics in the presence of mode 0 C.Limborg-Deprey 0 and PI modes PARMELA simulations for  f = -3.5 MHz, -8 MHz, -15 MHz, Ambiguity in phase lifted up Optimization of klystron pulse

2. C.Limborg-Deprey Beam Dynamics with mode 0limborg@slac.stanford.edu November 3 rd 2004 0 and Pi Mode Accelerating mode 2.856 GHz

3. C.Limborg-Deprey Beam Dynamics with mode 0limborg@slac.stanford.edu November 3 rd 2004 PARMELA Simulations L.Young implemented two frequency RF structure for studies on third harmonic gun here two frequencies are 2856 MHz for PI mode and (2856 -  f) MHz for the 0 mode What is the V cathode ? Depends on klystron pulse What is relative phase between the two modes Danger == being wrong by 180  Comparison different  f cases Need to reoptimize baseline (== no mode0)

4. C.Limborg-Deprey Beam Dynamics with mode 0limborg@slac.stanford.edu November 3 rd 2004 Standard case : mode separation -3.5 MHz zoom

5. C.Limborg-Deprey Beam Dynamics with mode 0limborg@slac.stanford.edu November 3 rd 2004 Larger mode separation Mode separation of 15 MHz After reoptimization, the ”baseline”  is improved for larger mode separation dF-3.4 MHz-8 MHz-15 MHz  projected 0.9850.960.935

6. C.Limborg-Deprey Beam Dynamics with mode 0limborg@slac.stanford.edu November 3 rd 2004 Finding the correct phase mode 0 lags behind Pi mode by 90  in full cell, opposite in photocathode cell From Zenghai Li’s talk  +90 degrees in PARMELA Units

7. C.Limborg-Deprey Beam Dynamics with mode 0limborg@slac.stanford.edu November 3 rd 2004 dF-3.4 MHz-8 MHz-15 MHz 3  s, V cath. in 0 mode 11.77 MV/m4.96 MV/m2.67 MV/m 0.82  s, V cath. in 0mode 10 MV/m5.7 MV/m2.86 MV/m

8. C.Limborg-Deprey Beam Dynamics with mode 0limborg@slac.stanford.edu November 3 rd 2004

9. C.Limborg-Deprey Beam Dynamics with mode 0limborg@slac.stanford.edu November 3 rd 2004 Conclusion Problem not as scary as first thought However, needs careful attention klystron pulse needs shaping only one or two injection points (depending on mode separation) Improvement in emittance for larger  f “baseline”  better No physical explanation smaller variation of  larger  f is more difficult to tune Should we proceed with the design at  f =-8MHz? Have we forgotten anything ?