David Neuffer Cary Yoshikawa March 2009 International Design Study Front End Capture/Phase Rotation & Cooling Studies David Neuffer Cary Yoshikawa March 2009

Outline Study 2A – ISS baseline discussion Target-capture Buncher, Rotator. Cooler Shorter bunch train example(s) nB= 10 Better for Collider; as good for ν-Factory (but larger V’) ICOOL/G4Beamline simulations Rf cavities in solenoids? high gradient cavities may not work in ~2T fields Risk management strategy Use lower fields (B, V’) Use Alternating solenoid lattice higher energy capture ? use “magnetic insulation” ASOL lattice use gas-filled rf cavities electron drift in gas ???

Official IDS layout

Solenoid lens capture Target is immersed in high field solenoid Particles are trapped in Larmor orbits B= 20T -> ~2T Spiral with radius r = p/(0.3 Bsol) =Bρ/B Particles with p < 0.3 BsolRsol/2 are trapped p,max < 0.225 GeV/c for B=20T, Rsol = 0.075m Focuses both + and - particles

High-frequency Buncher and φ-E Rotator Form bunches first Φ-E rotate bunches

Study2B June 2004 scenario (ISS) Drift –110.7m Bunch -51m 12 rf freq., 110MV 330 MHz  230MHz -E Rotate – 54m – (416MV total) 15 rf freq. 230 202 MHz P1=280 , P2=154 NV = 18.032 Match and cool (80m) 0.75 m cells, 0.02m LiH Captures both μ+ and μ- ~0.2 μ/(24 GeV p)

IDS Study 2B baseline Base lattice has B=1.75T throughout buncher and rotator rf cavities are pillbox grouped in same-frequency clusters 7 to 10 MV/m Buncher; 12.5 Rotator with 200μ to 395μ Be “windows”, 750μ windows in “Rotator” Cooling Lattice is alternating-solenoid with 0.75 half-period 0.5m pillbox rf cavity 1cm LiH absorbers 15.25MV/m cavities

Study 2A Beam within acceptance 0.8GeV/c Momentum spread reduced from 0.075 to 0.8 GeV/c to 0.18 to 0.25 MeV/c Bunch length 60+ bunches (90m long) Accepted emittance is εL,rms= 0. 026m (AL<0.15m) εt,rms= 0.0035m (Ax+ Ay < 0.03m) 0.2 μ/24GeV p

IDS - Shorter Bunch train Reduce drift, buncher, rotator to get shorter bunch train: 217m ⇒ 125m 57m drift, 31m buncher, 36m rotator Rf voltages up to 15MV/m (×2/3) Obtains ~0.26 μ/p24 in ref. acceptance Similar or better than Study 2B baseline Better for Muon Collider 80+ m bunchtrain reduced to < 50m Δn: 18 -> 10 500MeV/c -30 40m

Further iteration/optimization Match to 201.25 MHz cooling channel Reoptimize phase, frequency f = 201.25 MHz, φ = 30º, Obtain shorter bunch train Choose ~best 12 bunches ~ 21 bunch train for Collider at NB= 18 case ~12 bunches (~18m) ~0.2 μ/pref in best 12 bunches Densest bunches are ~twice as dense as NB = 18 case

Shorter Buncher-Rotator settings Buncher and Rotator have rf within ~2T fields rf cavity/drift spacing same throughout (0.5m, 0.25) rf gradient goes from 0 to 15 MV/m in buncher cavities Cooling same as baseline ASOL lattice 1 cm LiH slabs (3.6MeV/cell) ~15MV/m cavities also considered H2 cooling Simulated in G4Beamline optimized to reduce # of frequencies ASOL lattice

MC Front End Layout in G4beamline rotator capture drift buncher “Cool and Match” 3 m (4x75 cm cells) “Cool” 90 m of 75 cm cells Rotator 36 m long 75 cm cell 1 cm LiH 23 cm vacuum 50 cm 201.25 MHz RF cavity

Reduce number of independent frequencies Initial example had different rf frequency for each cavity Buncher- 42 cavities -31.5m 360to 240 MHz Rotator- 48 cavities -36m 240 to 202 MHz Reduce # by 1/3 14 in buncher; 16 in rotator Nearly as good capture (<5%less) Similar to study 2B baseline Reduce by 1/6 7 in buncher, 8 in rotator Significantly worse (~20%)

Rf in magnetic fields? Baseline has up to 12 MV/m in B=1.75 Experiments have shown reduced gradient with magnetic field not precise duplicate of front end May not permit operation at our parameters … V’max  (frf)1/2 ??? Future experiments will explore these limits will not have 200 MHz in constant magnetic field ~ Open cell cavities in solenoids? did not show V’ /B limitation

Risk mitigation strategies For IDS, we need an rf cavity + lattice that can work Potential strategies: Use lower fields (V’, B) Use non-B = constant lattices alternating solenoid Magnetically insulated cavities Is it really better ??? Alternating solenoid is similar to magnetically insulated lattice Use gas-filled rf cavities V’ independent of B electron effects?

Changing Buncher strengths To test whether a lower gradient rf would be OK for the buncher section baseline has gradient increasing along buncher from 0 to 15 MV/m V’(z) = 6(z/L) + 9 (z/L)^2 We tested varying the maximum buncher gradient from 0 to 15 MV/m Icool simulations 6MV/m limit as good as baseline 3MV/m ~8% worse 9 to 15 MV ramp is better than baseline (~5%) Table:  Capture with varying Buncher rf strengths Vmax’ (MV/m) μ/ 8 GeV p at z=128m /p at z=210m Total rf voltage 0.032 0.058 0 MV 3 (z/L) 0.041 0.075 31.5 MV 6 (z/L) 0.042 0.081 63 MV 9 (z/L) 0.047 0.084 94.5 MV 12 (z/L) 0.046 0.087 126 MV 15 (z/L) 157.5 MV 6 (z/L) + 9 (z/L)2 - baseline parameters 0.039 0.082

Use ASOL lattice rather than 2T Study 2A ASOL Bmax= 2.8T, β*=0.7m, Pmin= 81MeV/c 2T for initial drift Low energy beam is lost (P < 100MeV/c) Bunch train is truncated OK for collider Also tried weaker focusing ASOL Bmax= 1.83T, β*=1.1m, Pmax = 54 MeV/c 1.33 T for initial drift Match scaled from 2A match ASOL lattice + -

ASOL results Simulation results 1.8T ASOL Baseline (2T -> ASOL) had 0.18 μ/24 GeV p (0.059 μ/8 GeV p) Cools to 0.0075m 1.8T ASOL 0.198 μ/24 GeV p (0.064 μ/8 GeV p) ~10% better than stronger focussing Cools to 0.0085m Baseline (2T -> ASOL) had ~0.25 μ/24 GeV p ~0.08 μ/8 GeV p

Variant-capture at 0.28 GeV/c 2T → 2.8T ASOL s=59m s=66m 0.0 1.0GeV/c 1.0GeV/c s=200m s=126m 0.0 -30m +40m -30m +40m

Capture at 280 MeV/c Captures more muons than 220 MeV/c For 2.T -> 2.8T lattice But in larger phase space area Less cooling for given dE/ds Δs Better for collider Shorter, more dense bunch train If followed by longitudinal cooling 220 MeV/c 280 MeV/c

Better (?) Variant Use B=const for drift + buncher Low-gradient rf ( <6 MV/m) Use ASOL for rotator + Cooler (could be H2 cavities) 12 to 15 MV/m rf 0.75 half-cells Simulation: appears to have better acceptance than using ASOL for buncher to end. Lose some low energy mu’s bunch train shortened ~0.25 μ/24p after 60m H2 cooling ~0.19 μ/24p after 60m LiH cooling Best variant to date … ?

Gas-filled rf cavities prevent rf breakdown Experiments show V’>50MV/m no magnetic field dependence With higher gradient can cool and rf rotate in same system Can move all cooling into rotator section (V’ = 20 to 24 MV/m) gas-filled transport can replace LiH as absorber material improved capture / cooling V’ = 15 MV/m But beam-gas charge production may drain energy from cavity

Gas-filled rf cavities in COOLer Replace cooling system Choose H2 gas density of 0.0103 gm/cm3 (P = ~125 Atm) Compare with LiH (~Study 2A) Simulated in G4beamline Acceptance in ν-Factory improved ~30% more μ/p transverse rms emittance reduced from ~0.008 to ~0.006m similar to ICOOL studies Longitudinal mismatch is noted could match be improved?

Gas-filled rf cavities – limitations? ?????? ? Tollestrup has suggested that electrons produced within the gas may drain energy from the cavities. Production of electrons is large: ~energy loss / 35eV ~1000 e- /cm at ~100 Atm Assume electrons remain free in the H2 gas, developing into a swarm with mean energy ε̅, and a mean velocity (∥ E) given by μ E/P: ~1 eV: v̅ ~ 106 cm/s Formulas based on results in kV/cm, P < 1atm, dc E not P> 100 atm, E>10MV/m, f>100MHz

Energy Loss in Gas-filled cavities Calculate energy loss per e- over one rf cycle multiply by Nμ x Ne/μ Compare with energy stored in rf cavity Example: P=120 atm, E=10MV/m, Nμ=1012 E/P= 1.2 v/cm/mmHg ΔW= ~0.06 J/cm Pill-box cavity: W = ~1.236 J/cm “Q” = 130 but Nμ could be larger Enough to matter ? If all electrons remain free oscillators maintaining drift v free lifetime could be ns to μs recombination e + H+ -> H diffusion associative attachment: e- + H2 -> H + H- Add SF6 : e-+ SF6 -> SF6- ??

Planned experiment Fermilab MTA area 400MeV proton beam from Linac produces secondaries and charged beam passing through test cavity Measure effects of concurrent beam on cavity energy loss, breakdown 6e12 protons ~1.2e13 muons (?) test cavity will be within solenoid test magnetic field effects

Risk Management Assessment

Summary High frequency phase-energy rotation + cooling can be adapted and used for the IDS Rf in magnetic field problem must be addressed Need rf configuration that can work with high confidence V’ (B(s)) at ~200MHz ?? V’ vs I with gas-filled rf ?? Need to establish scenario that is reliable Drift and bunch at constant B (V’ < V’max (B)) Switch to different lattice or gas-filled rf when higher gradient is needed. rf experiments will give some guidance

Another viewpoint