Study of Helical Cooling Channel
Katsuya YoneharaAPC, Fermilab
12/02/09 1
Muons, Inc.
Agenda for HCC session
• HCC simulation effort, K. Yonehara– Test HCC theory– Optimize HCC parameter by using
numerical simulation • HCC magnet design effort, V. Kashikhin– Magnet design status– Demonstration test– etc
• HCC RF study, M. Neubauer– Design dielectric loaded RF cavity– etc
12/02/09 2MC Design workshop @BNL
K. Yonehara
New Fernow-Neuffer plot
ν = 0.325 GHzλ = 1.0 – 0.8 m
ν = 0.65 GHzλ = 0.5 – 0.3 m
ν = 1.3 GHzλ = 0.3 m
100 % @ z = 0 m
97 % @ z = 40 m91 % @ z = 49 m
89 % @ z = 129 m
84 % @ z = 129 m
84 % @ z = 303 m
• GH2 pressure = 160 atm• 60 μm Be RF window• E ~ 27 MV/m• Detailed parameter will be given in later slide (slide 15)
PIC
REMEX
12/02/09 3
Goal phase space
Study2a
Helical Cooling Channel (HCC)
12/02/09 4
Stability condition in transverse phase space
12/02/09 MC Design workshop @BNL, K. Yonehara 5
Stability condition is, thereforewith
andStability condition can be represented by g (field index) and q (= kc/k-1)
Test cooling decrement
12/02/09 MC Design workshop @BNL, K. Yonehara 6
Λ± = Λγ = 0.047 /meter
Fdrag : drag force
Benefit of cryogenic operation
• Low resistivity RF cavity–High RF Q value– Thin skin depth
• Low gas pressure– Thin pressure window
12/02/09 7MC Design workshop @BNL, K.
Yonehara
Design RF window in HCCHCC is entirely filled with GH2Here is some advantage:• Any hydrogen safety window may not
be required in beam path– Only RF window is needed to generate
ideal E field• GH2 works on RF window as a coolant– RF power deposition into RF window won’t
be issuedEx) Thickness of RF window in 200 MHz vacuum
cavity is designed 380 μm made of Beryllium to avoid frequency shift caused by RF power deposition in RF window
12/02/09 8MC Design workshop @BNL, K.
Yonehara
What is the minimum RF window thickness?
Skin depth
Aluminum window (ρ = 2.82×10-8 Ω/m @ room temp, ν = 325 MHz)
Beryllium window (ρ = 18.5×10-8 Ω/m @ room temp, ν = 325 MHz)
m
m
The modeled RF window in simulation is five times thicker than δ (ex. 60 μm Be window)• This assumption will be premature • For instance, the Lorentz force on the window is not involved• More mechanical analysis will be needed
12/02/09 9MC Design workshop @BNL, K.
Yonehara
RF window effect• Compare transmission efficiency in HCC with three different window materials (no material, Aluminum, Beryllium)• Window thickness is 0.1 mm
εNo window = 100 %εBe window = 89 %εAl window = 67 %
12/02/09 10MC Design workshop @BNL, K.
Yonehara
Consider pressure end plate• End plate is not involved in simulation, yet• More mechanical analysis is needed to determine thickness of entrance/exit pressure windows
Here is some estimation based on past mechanical analysis
Past result: Required window thickness = 1” (Inconel 718) with 500 mmΦ
with GH2 pressure = 50 atm (= 200 atm at 300)
Present design: Required window thickness = 5 mm (Inconel 718)
Now, GH2 pressure is 40 atm, assume window has a curve shape that makes 3 times stronger than flat plate, and window size is 320 mmΦ
Estimated Δp in entrance window ∼ 10 MeV/c
Thickness of exit window will be much thinner than 5 mm since beam size is approximately 16 times smaller than initial beam size
12/02/09 11MC Design workshop @BNL, K.
Yonehara
Correction non-linear dE/ds effect
12/02/09MC Design workshop @BNL, K.
Yonehara12
Make some correction in dispersion function
where D’ can be determined from dp/ds
dE/ds [GeV/m]
μ Momentum [GeV/c]
160 atm GH2
Dispersion = 0.28 m(dE/ds correction)
Short pathat lo p
Long pathat hi p
Dispersion = 0.13 m(Close to isochronous condition)
Dispersion = 0.35 m(path length is overestimated)
RF bucket dependence
E = 31.4 MV/m, ψ=160˚, Lrf = 100 mmE = 16.0 MV/m, ψ=140˚, Lrf = 50 mm
v = 400 MHz, κ=1.0, λ=1.0 mGH2 pressure = 200 atm (at room temp)
Old design New design
ΔE
[G
eV
]
ΔE
[G
eV
]
12/02/09 13MC Design workshop @BNL, K.
Yonehara
Past studies by Balbekov
12/02/09MC Design workshop @BNL, K.
Yonehara14
• HCC has been simulated with totally independent simulation code by Balbekov• The simulation results are reproduced in two different simulation codes• He also pointed out that there is strong frequency dependence on the longitudinal acceptance• The admittance of HCC is given in PRSTAB paper
Emittance evolution in HCCε Lo
ngitu
dina
l [m
m]
εTransverse [mm rad]
ν = 0.325 to 0.65 GHz
ν = 0.65 to 1.3 GHz
12/02/09 15MC Design workshop @BNL, K. Yonehara
Beam phase space is self-adjusted
Let us revisit new Fernow Neuffer plot on slide 3
Parameter listZ ±Δr ±Δp/p b b’ bz ν κ λ Nμ εT εL ε6D
unit m cm % T T/m T GHz m mm rad mm mm3
Channel length
Full Width
Full width
@ ref
@ ref @ ref RF
1 0 15 22 1.3 -0.5 -4.2 0.325 1.0 1.0 388 20.4 42.8 12900
2 40 8 10 1.3 -0.5 -4.2 0.325 1.0 1.0 375 5.97 19.7 415.9
3 49 7 10 1.4 -0.6 -4.8 0.325 1.0 0.9 354 4.01 15.0 10.8
4 129 3 2.5 1.7 -0.8 -5.2 0.325 1.0 0.8 327 1.02 4.8 2.0
5 219 1.7 1.8 2.6 -2.0 -8.5 0.65 1.0 0.5 327 0.58 2.1 3.2
6 243 1.6 1.3 3.2 -3.1 -9.8 0.65 1.0 0.4 327 0.42 1.3 0.14
7 273 1.3 1.3 4.3 -5.6 -14.1 0.65 1.0 0.3 327 0.32 1.0 0.08
8 303 1.2 1.1 4.3 -5.6 -14.1 1.3 1.0 0.3 327 0.34 1.1 0.07
12/02/09 16MC Design workshop @BNL, K. Yonehara
Beam parameter
12/02/09 MC Design workshop @BNL, K. Yonehara 17
Beta tune Q+ = 0.918Beta tune Q- = 0.730Beta function = 0.27 m at λ= 1.0 m 0.09 m at λ = 0.3 mMomentum slip factor η = 0.661Dispersion D = 0.28 mCooling decrement Λ/3 = 0.0184 /m
Transmission efficiency and beam size
1 2 3 45 6 7 8
Δp/p and beam size are taken full width of distribution
ν = 0.325 to 0.65 GHzν = 0.65 to 1.3 GHz
12
3
4 5 6
78
ν = 0.325 to 0.65 GHz
ν = 0.65 to 1.3 GHz
12/02/09 18MC Design workshop @BNL, K. Yonehara
Emittance evolution
Merit factor = ε6D,init/ε6D,final × Transmission ε
12/02/09 19MC Design workshop @BNL, K. Yonehara
1
2
3
4 5 6
7
8
ν = 0.325 to 0.65 GHz
ν = 0.65 to 1.3 GHz
Remaining challenge issue• Mechanical design of HCC– Need HCC RF cavity and HCC magnet studies
• Some study has been done (see Mike & Vladimir)• Is it possible to generate E = 27 MV/m?
– Need cryogenic study– Need mechanical analysis
• Pressure vessel, Support, etc– Investigate hydrogen safety
• High pressurizing GH2 filled RF cavity test• Design 6D demo experiment– Including with the study of phase space
matching
12/02/09 20MC Design workshop @BNL, K.
Yonehara
Any more simulation effort?
I can reproduce these simulation results in real HCC if we can generate…
• E = 27 MV/m• Maximum B = 14 Tesla• Solve matching issueIf E = 16 MV/m, then• Merit factor ~2 103 (tested with short
channel)
12/02/09 21MC Design workshop @BNL, K.
Yonehara
Summary
• First full HCC simulation has been done• Merit factor > 105 in z = 300 meters• See individual beam element study, HCC
RF and magnet in following speakers• All simulations have been done in g4bl-
v1.16(Thanks Tom!)
12/02/09 22MC Design workshop @BNL, K.
Yonehara