1. Simulation Study of Solenoidal-Lithium Lens Channel
K. Lee, D. Cline, A. Garren
March 02, 2011
MAP Winter Meeting at JLab
Feb 28-Mar 4, 2011

2. Previous Studies with Lithium lens
Curved Li lens (~2004-current) by Y. Fukui
Cooling Ring studies (~ ) using Li lens by A. Garren and Y. Fukui
Initial engineering considerations for a liq. Li lens (2008) with some inputs from J.P. Morgan and T. Leveling at Fermilab and BINP papers
Achieved some cooling with long periodic 3 cm length Li lens channel (2009)
MAP Winter Meeting at JLab
Feb 28-Mar 4, 2011

3. MAP Winter Meeting at JLab
Final Cooling Stages
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4. MAP Winter Meeting at JLab
Li Lens Properties
Strongly focusing
Low Z material for ionization cooling
B field ~ 10 T at surface
low  region
MAP Winter Meeting at JLab
Feb 28-Mar 4, 2011

5. Fermilab Solid Li Lens (Recent Design)
D 2.0 cm x L 15 cm
Induction Coils
J. Morgan
Lens Upgrade Note
MAP Winter Meeting at JLab
Feb 28-Mar 4, 2011

6. Cooling in an ideal Li Lens
azimuth. B
I 500 kAmps
Beam focusing parameter in the azimuthal B field
(cm, MeV/c, T)
Equilibrium beam parameters
(cm, MeV/c, T)
(cm, T)
MAP Winter Meeting at JLab
Feb 28-Mar 4, 2011
V. Balbekov, Aug. 2006

7. MAP Winter Meeting at JLab
Channel with One 10 cm x 135 cm Lens
Comparison between 10 T and 20 T exit solenoid
MAP Winter Meeting at JLab
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8. Series of 9 cm Li lens Channel of 300 cells
G=6.2 T/cm
RF=54 MV/m
MAP Winter Meeting at JLab
Feb 28-Mar 4, 2011
K. Lee, D. Cline, A. Garren

9. Series of 9 cm Li lens Channel of 300 cells
MAP Winter Meeting at JLab
Feb 28-Mar 4, 2011
K. Lee, D. Cline, A. Garren

10. MAP Winter Meeting at JLab
Only the lenses are simulated.
Ideal matrix is used instead of matching sections.
Schematic and idea of the channel (V.Balbekov, MCD Workshop, Dec. 2009)
Main parts of the channel:
Blue – solenoid coils
Red -- Li lenses
Green – 200 MHz cavities
Transition from high to low field region is adiabatic itself.
Li lens should provide the adiavatic transition from (+) field to (-) one
Li rod should have a special form to provide the adiabaticity (example)
With solenoid field B and lens gradient G, beta – function is:
Adiabaticity condition (Palmer)
Gray – fringe regions where a special study is needed ?
MAP Winter Meeting at JLab
Feb 28-Mar 4, 2011
V.Balbekov Mar 18, 2010

11. MAP Winter Meeting at JLab
Only the lenses are simulated.
Ideal matrix is used instead of matching sections.
Solenoid field
Blue: high-field solenoid coils, right-hand part
Pink: a half of Li lens (schematically). Volume of diameter 30 cm is provided for it
Axial field in the solenoid axes.
Maximal value 50 T
Transport 4 Tesla solenoid has inner radius 60 cm.
02c_rod.pdf
Other coils were considered as well (shape, size, etc.).
In all the cases, transition from high to low field is adiabatic (at proper current density),
and required beta-function is provided by optimization of the Li lens.
Conclusion: design of this assembly is an engineering problem, primarily.
MAP Winter Meeting at JLab
Feb 28-Mar 4, 2011
V.Balbekov Mar 18, 2010

12. 2-D Axial Field Map by COMSOL
50 cm 30 cm 20 cm
J = 3.18 108 A/m2
60 cm
15 cm
2 m
MAP Winter Meeting at JLab
Feb 28-Mar 4, 2011

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Li Lens Profile
100% 90% 50% 14%
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14. Solenoidal Li Lens Channel with ICOOL
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15. Solenoidal Li Lens Channel with ICOOL
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16. MAP Winter Meeting at JLab
Summary
Achieved some cooling with Balbekov’s suggestion
Complete the simulation in the next 9 months
Add more realistic features
Adjust the solenoid coils
Adjust the Li lens length
Windows
MAP Winter Meeting at JLab
Feb 28-Mar 4, 2011

17. Liquid Li Lens Outstanding Issues
Mechanical fracture from current pulsing at > 500 kAmps per pulse
Heat removal; achieved by rapid flow
Magnetic skin depth at faster than a few Hz rate
MAP Winter Meeting at JLab
Feb 28-Mar 4, 2011

18. Liquid Li Lens Development at BINP
The Li lens work by Dr. Silvestrov et. al at BINP was for use at the Tevatron anti-proton source (accord w/ Fermilab for run II) and at CERN.
The lens survived < 100k pulses at 7.5 T (design was 10M and 13 T).
Shock waves in the Li and cracking of the Ti septum.
MAP Winter Meeting at JLab
Feb 28-Mar 4, 2011

19. Observed Fermilab Li Lens Lifetime
B grad (T/m)
Avg. Life Time
(Pulses)
1,000
<500,000 (1.9 wk)
900
1,000,000 (3.8 wk)
800
3,000,000 (5.7 wk)
740
9,000,000 (17 wk)
700
>10,000,000 (19 wk)
J. Morgan
Lens Upgrade Note
MAP Winter Meeting at JLab
Feb 28-Mar 4, 2011

20. Initial Mechanical Design
D 2.54cm  L 30cm
Outer tube for heated oil above 200 C
Double layered tubes for liquid Li and heated oil
MAP Winter Meeting at JLab
Feb 28-Mar 4, 2011