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

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

MAP Winter Meeting at JLab Final Cooling Stages MAP Winter Meeting at JLab Feb 28-Mar 4, 2011

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

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

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

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 Feb 28-Mar 4, 2011

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

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

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

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

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

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

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

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

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

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

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

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

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