Study of Helical Cooling Channel

1
Study of Helical Cooling Channel
Muons, Inc.

• Katsuya Yonehara
• APC, Fermilab

2
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

3
New Fernow-Neuffer plot
Goal phase space
? 0.325 GHz ? 1.0 0.8 m
? 0.65 GHz ? 0.5 0.3 m
100 _at_ z 0 m
Study2a
97 _at_ z 40 m
91 _at_ z 49 m
REMEX
89 _at_ z 129 m
? 1.3 GHz ? 0.3 m
84 _at_ z 129 m
84 _at_ z 303 m
PIC

• GH2 pressure 160 atm
• 60 µm Be RF window
• E 27 MV/m
• Detailed parameter will be given in later slide
  (slide 15)

4
Helical Cooling Channel (HCC)
5
Stability condition in transverse phase space
Stability condition is, therefore
with
Stability condition can be represented by g
(field index) and q ( kc/k-1)
and
6
Test cooling decrement
Fdrag drag force
? ?? 0.047 /meter
7
Benefit of cryogenic operation

• Low resistivity RF cavity
• High RF Q value
• Thin skin depth
• Low gas pressure
• Thin pressure window

8
Design RF window in HCC

• HCC is entirely filled with GH2
• Here 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 wont be
  issued
• Ex) 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

9
What is the minimum RF window thickness?
Skin depth
Aluminum window (? 2.8210-8 O/m _at_ room temp, ?
325 MHz)
m
Beryllium window (? 18.510-8 O/m _at_ room temp,
? 325 MHz)
m
The modeled RF window in simulation is five times
thicker than d (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

10
RF window effect

• Compare transmission efficiency in HCC with
  three different
• window materials (no material, Aluminum,
  Beryllium)
• Window thickness is 0.1 mm

eNo window 100 eBe window 89 eAl window
67
11
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 mmF with GH2 pressure 50
atm ( 200 atm at 300)
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 mmF
Present design Required window thickness 5 mm
(Inconel 718)
Estimated ?p 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
Correction non-linear dE/ds effect
dE/ds GeV/m
Make some correction in dispersion function
160 atm GH2
where D can be determined from dp/ds
µ Momentum GeV/c
Dispersion 0.13 m (Close to isochronous
condition)
Dispersion 0.35 m (path length is overestimated)
Dispersion 0.28 m (dE/ds correction)
Long path at hi p
Short path at lo p
13
RF bucket dependence
v 400 MHz, ?1.0, ?1.0 m GH2 pressure 200
atm (at room temp)
Old design
New design
E 31.4 MV/m, ?160, Lrf 100 mm
E 16.0 MV/m, ?140, Lrf 50 mm
?E GeV
?E GeV
14
Past studies by Balbekov

• 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

15
Emittance evolution in HCC
Let us revisit new Fernow Neuffer plot on slide 3
eLongitudinal mm
? 0.325 to 0.65 GHz
Beam phase space is self-adjusted
? 0.65 to 1.3 GHz
eTransverse mm rad
16
Parameter list
Z ?r ?p/p b b bz ? ? ? Nµ eT eL e6D
unit m cm T T/m T GHz m mm rad mm mm3
Channel length Full Width Full width _at_ ref _at_ ref _at_ 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
17
Beam parameter
Beta tune Q 0.918 Beta tune Q- 0.730 Beta
function 0.27 m at ? 1.0 m
0.09 m at ? 0.3 m Momentum slip factor
? 0.661 Dispersion D 0.28 m Cooling decrement
?/3 0.0184 /m
18
Transmission efficiency and beam size
1
2
3
4
5
6
7
8
? 0.325 to 0.65 GHz
? 0.65 to 1.3 GHz
1
? 0.325 to 0.65 GHz
2
3
? 0.65 to 1.3 GHz
5
6
4
8
7
?p/p and beam size are taken full width of
distribution
19
Emittance evolution
1
? 0.325 to 0.65 GHz
2
? 0.65 to 1.3 GHz
3
5
4
6
8
7
Merit factor e6D,init/e6D,final Transmission e
20
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

21
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 issue
• If E 16 MV/m, then
• Merit factor 2 103 (tested with short channel)

22
Summary

• First full HCC simulation has been done
• Merit factor gt 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!)