Study of Helical Cooling Channel

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


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


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


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 %


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


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

]


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


Beam parameter


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


Emittance evolution

Merit factor = ε6D,init/ε6D,final × Transmission ε


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


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)


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!)


Yonehara

Study of Helical Cooling Channel

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