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

2. 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
???

3. Official IDS layout

4. 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 < GeV/c for B=20T, Rsol = 0.075m
Focuses both + and - particles

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

6. 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 =
Match and cool (80m)
0.75 m cells, 0.02m LiH
Captures both μ+ and μ-
~0.2 μ/(24 GeV p)

7. 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

8. 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= m (AL<0.15m)
εt,rms= m (Ax+ Ay < 0.03m)
0.2 μ/24GeV p

9. 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

10. Further iteration/optimization
Match to MHz cooling channel
Reoptimize phase, frequency
f = 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

11. 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

12. 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 MHz RF cavity

13. 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%)

14. 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

15. 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?

16. 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

17. 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 + -

18. 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 m
1.8T ASOL
0.198 μ/24 GeV p (0.064 μ/8 GeV p)
~10% better than stronger focussing
Cools to m
Baseline (2T -> ASOL) had
~0.25 μ/24 GeV p
~0.08 μ/8 GeV p

19. 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

20. 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

21. 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 … ?

22. 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

23. Gas-filled rf cavities in COOLer
Replace cooling system
Choose H2 gas density of 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?

24. 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

25. 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- ??

26. 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

27. Risk Management Assessment

28. 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

29. Another viewpoint