1. Injection Energy Review D. Schulte

2. Introduction Will review the injection energy So could answer the following questions: Which injection energy can be accommodated in the baseline? To identify the minimum energy that is acceptable with reasonable risk Requires to identify margins and budgets for effects that have not been considered in detail Which changes are required to adapt to a given injection energy? Allows to understand the design and cost impact of different energies if we stay at the same risk level We can at some level answer with a relative comparison

3. Assumptions Made for Baseline The main drivers for the injection energy are Impedance the main impedance is coming from the beamscreen other collective effects are not dominating Dynamic aperture we need at least the same beam stay clear as in LHC in beam sizes the same ratio of top to injection energy as in LHC may ensure the magnet field quality a tentative choice to deal with the uncertainty of the magnet errors (Amount of beam that can be transferred in one pulse)

4. Lattice Baseline The goal has been to minimise the magnet aperture This requires to minimise the beamscreen aperture Tentative assumptions Cell design similar to LHC The shortest cell that reaches the same dipole filling factor as LHC This minimises the average beta-function, which minimises the impedance effects  Cell length about 2 times LHC cell length

5. Tentative Conclusions for Baseline The injection energy should be at least 3.3 TeV Tentative assumption is based on magnetic field error consideration At this energy the impedance is the dominating factor for the beam screen aperture, the beam stay clear is larger than in LHC This is opposite to the LHC, where mainly the beam stay clear has been an issue and the impedance less critical The impedance requires a≈13mm This translates into 1.8 times more space in the arcs For the same emittance it would be 1.4 times

6. Impedance Effect Scalings Coupled-bunch impedance effect per turn scales as D. Schulte: Beam pipe kickoff meeting Local resistive wall impedance Ratio of FHC to LHC coupled-bunch effect scale Example at 50K and 25ns spacing at injection Or: Why was a potential problem to be expected? Assuming the same fractional tune in FCC and LHC

7. Impedances, Instability and Feedback First, preliminary conclusions from impedance studies: Beamscreen resistive wall at injection Multi-bunch instability rise time is O(25 turns) Copper layer on beamscreen must be 300  m thick TMCI threshold is 5x10 11 protons Pumping holes TMCI threshold is reduced to 2x10 11 protons  Worth to reduce amount of holes (as considered by vacuum team) Synchrotron radiation slit Little impact on the impedance Beamscreen and collimation at collision energy TMCI threshold is 1.5x10 11  Close to the limit  Feedback is of great importance  Much better performance than in LHC required  Novel solutions? HTS? O. Boine-Frankenheim U. Niedermayer, B. Salvant, N. Mounet X. Buffat, E. Metral There seems to be little margin Can gain margin by increasing the injection energy initially used as fallback safety margin (assuming LHC as injector) now have to spell it out Have to be very careful in choosing the stability criteria e.g. assumptions about chromaticity determining how much margin is required and in which form Remember two decisions were made in the process: Fractional tune below 0.5 Give up parameter set for 50ns bunch spacing => Check if we still agree with them

8. Impact on Injection Currently assuming that total energy per injected train has to remain below 5MJ  Higher energy means less charge per train  Requires shorter gaps between trains  Requires faster kickers  or more charge per bunch, which we would like to avoid Check if this is a serious concern or if we can accept shorter rise times for the moment Also check impact of injection energy on turn-around time

9. Next Steps Have to determine the minimum injection energy field errors dynamic aperture Have to more precisely determine the impedance limit include all relevant terms sometimes with guesses agree on model of beam stability chromaticity etc. include proper feedback models as transfer functions include sufficient margin Since this seems to give the limit we have to really explore the limits Verify that the other assumptions are OK i.e. that only dynamic aperture and impedance are important limits Then have to understand the impact of the other potential injection energies identify a small set of potential values matching to the injector options

10. Example for Illustration Multi-bunch instability example Assuming: a=13mm beamscreen radius is just right for 3.3TeV Δ BS =12mm are need between beamscreen and magnet the cost scales as Cost goes up 5% at 2TeV and down by 4% at 5TeV

11. Beamscreen Design Centre of the beamscreen is not he centre of the magnet – Need to explore the options to deal with this The pumping holes are an important part of the impedance – Need to agree on the amount of holes needed

12. Conclusion Much more work to be done to give as precise answers as possible: Does our rational hold true? Did we miss something? Which injection energy can be accommodated in the baseline? Get full evaluation process in control Which energy ranges could be provided by each injector? Pick a limited number of values to limit the study Which changes are required to adapt to a given injection energy? To evaluate the cost impact