Multi-turn proton injection into MI/RR• Multi-turn proton injection must be a Liouvillian process such that

ring > DNturnslinac

• The term D is a dilution factor which is typically > 1.5, but can be greater.• The specified final emittance for either the MI or Recycler injection is

25mm-mr.• Implies maximum of ~16 turns (for D=1.5)

• The revolution period for MI/RR is ~11 s.• Implies linac pulse length of 176 s

• The design proton intensity for PD/Project X is ~1.5E14 protons/MI cycle . – In PD era this was accomplished in a single linac cycle. – The Project X concept utilized the RR to accumulate 3 linac cycles (due to a

lower linac current, i.e. 9 mA vs 27 mA).– Accumulation from proton linac only on a single linac cycle

• Assuming adiabatic RF capture (populate all linac bunches), the required average linac current is about 140 mA (neglecting ring abort gap) and greater for injecting into RF buckets.

– This is about factor 3 higher current than available from current (or planned) proton linacs capable of producing small emittance.

Beams-doc 3186

Compare Proton vs H- Injection   Proton H-minus

Process Liouvillian yes no

Number of injection turns 10-20 100's-1000's

Requires use of injection septum yes no

Merging dipole no yes

Phase space painting techniques yes yes

Lorentz stripping no mitigated

Black body radiation no mitigated

Gas stripping no mitigated

Stripping Mechanism (foil/laser) no yes

Injection absorber no yes

Transport line collimation small i.p. large i.p.

Linac current >100mA ~27 mA

Linac pulse length 100-200 s 1 -3 ms

Linac emittance [mm-mr] (95% normalized at 8 GeV) < 1 >1

Note: i.p. stands for impact parameter