1. Longitudinal aspects on injection and acceleration for HP-PS Antoine LACHAIZE On behalf of the HP-PS design team

2. Longitudinal painting First considerations on RF system Summary and Next Steps Contents

3. Longitudinal painting SPL bunches 352 MHz HP-PS 40 MHz buckets HP-PS chopping scheme The LP-SPL base line parameters are: ParameterValuesUnits Kinetic Energy4[GeV] Beam pulse length0.9[ms] Average pulse current20[mA] Peak pulse current32[mA] Protons per pulse1.13 x 10 14 - The present design of the LP-SPL can “only” deliver 1.13x10 14 ppp including 0.5 chopping factor. We need up to 2.5x10 14 ppp. 2 ms pulse Empty buckets Full buckets

4. Longitudinal painting Optimization of painting process depends on which value of longitudinal emittance we want after injection in the HP-PS. Longitudinal emittance delivered by SPL is 0.6 eV.s but, in order to be injected safely in the SPS beam must satisfy a stability criteria in terms of longitudinal emittance : Ԑ l = 0.35 eV.s for N = 1.5x10 11 ppp So, for our 2.5x10 14 proton pulse (50 GeV) this leads to : Ԑ l = 1.2 eV.s The corresponding voltage is 6 MV ! For 75 GeV the required intensity is 1.67x10 14 leading to : Ԑ l = 1 eV. The corresponding voltage is 4 MV

5. Longitudinal painting Beam from LP-SPL is injected with an energy offset of 8 MeV (50 GeV). After 500 turns the required intensity is achieved and the beam emittance is 1.21 eV.s -0.500.51 -0.500.51

6. RF system : first considerations 50 / 70 GeV 4 GeV Injection Extraction 50 ms 500ms 400ms 50 ms 500ms 400ms 1 second HP-PS Basic Magnetic Cycle

7. RF system : first considerations The Voltage/phase curves have been calculated during cycle assuming a constant ratio of 1.5 between longitudinal beam emittance and bucket acceptance for various types of magnetic field laws. 50 GeV Injection field : 0.17 T Extraction field : 2.1 T

8. RF system : first considerations Voltage program Phase program 50 GeV Maximum voltage : 8.5 MV Maximum phase : 48 deg.

9. RF system : first considerations The Voltage/phase curves have been calculated during cycle assuming a constant ratio of 1.5 between longitudinal beam emittance and bucket acceptance for various types of magnetic field laws. 75 GeV Injection field : 0.17 T Extraction field : 3.13 T

10. RF system : first considerations Voltage program Phase program 75 GeV Maximum voltage : 5.8 MV Maximum phase : 55 deg.

11. RF system : first considerations 1 SS dedicated to RF in HP-PS : available length for RF around 45m. Needed length for RF now : around 30m assuming 300kv per 1m long cavities.

12. Summary Longitudinal painting Painting using injection with energy offset into single harmonic bucket has been simulated, given required longitudinal emittance after injection. RF system RF voltage and phase programs have been analytically calculated assuming constant ratio between beam emittance and bucket area. This gives a maximum voltage of 8.5 MV in cavities leading to ~ 30m of cavities in the dedicated SS, assuming present performances of PS 40 MHz cavities (300kV / 1m long).

13. Next steps RF is challenging : high voltage, high intensity : State of art of technology to be check. Full RF cycle simulations including collective effects.