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Simulation Study of Solenoidal-Lithium Lens Channel

Simulation Study of Solenoidal-Lithium Lens Channel. K. Lee, D. Cline, A. Garren March 02, 2011. Previous Studies with Lithium lens. Curved Li lens (~2004-current) by Y. Fukui Cooling Ring studies (~2002-2004) using Li lens by A. Garren and Y. Fukui

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Simulation Study of Solenoidal-Lithium Lens Channel

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  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 (~2002-2004) 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. Final Cooling Stages MAP Winter Meeting at JLab Feb 28-Mar 4, 2011

  4. B field ~ 10 T at surface low  region • Li Lens Properties • Strongly focusing • Low Z material for ionization cooling 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. I 500 kAmps Cooling in an ideal Li Lens azimuth. B 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. Channel with One 10 cm x 135 cm Lens Comparison between 10 T and 20 T exit solenoid MAP Winter Meeting at JLab Feb 28-Mar 4, 2011

  8. 3 cm 3 cm 3 cm 3 cm 3 cm 3 cm 3 cm 3 cm 3 cm 3 cm 3 cm 3 cm 3 cm 3 cm 3 cm 3 cm G=6.2 T/cm Series of 9 cm Li lens Channel of 300 cells 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. 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. 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

  13. Li Lens Profile 100% 90% 50% 14% MAP Winter Meeting at JLab Feb 28-Mar 4, 2011

  14. Solenoidal Li Lens Channel with ICOOL MAP Winter Meeting at JLab Feb 28-Mar 4, 2011

  15. Solenoidal Li Lens Channel with ICOOL MAP Winter Meeting at JLab Feb 28-Mar 4, 2011

  16. 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 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

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