S. Kahn 5 June 2003NuFact03 Tetra Cooling RingPage 1 Tetra Cooling Ring Steve Kahn For V. Balbekov, R. Fernow, S. Kahn, R. Raja, Z. Usubov

S. Kahn 5 June 2003NuFact03 Tetra Cooling RingPage 2 Tetra Ring Parameters ParameterValue Circumference m Kinetic Energy at Bends0.250 GeV Dipole Bending Field1.453 T Normalized Gradient Index0.5 Maximum Long Solenoid Field5.155 T RF Frequency MHz Accelerating Gradient15 MeV/m LH 2 Absorber Length1.2 m LiH Wedge Absorber14 cm

S. Kahn 5 June 2003NuFact03 Tetra Cooling RingPage 3 Tetra Ring Simulations Original concept for this ring comes from V. Balbekov. –Originally simulated in Valeri’s program. –Documented: V. Balbekov et al., Muon Ring Cooler for the Mucool Experiment, Proc PAC 2001 Conf., p Updated in MUCnote 249 (2002). GEANT simulation of Tetra Ring. –Worked on by Z. Usubov, R. Raja, and myself. ICOOL simulation of the Balbekov Ring. –MUCnote 258.

S. Kahn 5 June 2003NuFact03 Tetra Cooling RingPage 4 Hardedge Model Wedge Dipole: –Combined function Index =1/2  =52 cm defines reference radius –Step function s dependence. No dependence inside Zero outside Solenoids –Effect of fringe field is approximated by transverse impulse proportional to radial position.

S. Kahn 5 June 2003NuFact03 Tetra Cooling RingPage 5 Long Solenoid Arrangement: Boundary Condition Coils Actual Hardedge Coils Boundary Condition Coils Short Solenoid Arrangement: Actual Hardedge Coils Boundary Condition Coils Coil configuration to represent mirror plate boundary condition in ICOOL

S. Kahn 5 June 2003NuFact03 Tetra Cooling RingPage 6 ICOOL Hardedge Emittances

S. Kahn 5 June 2003NuFact03 Tetra Cooling RingPage 7 Tracking in GEANT This figure shows a sample of 500 events tracked in GEANT. The beam is smallest in the LH 2 absorber where the field is largest. The beam is the largest in the field flip short solenoid. –Muons are most likely to be lost in the vicinity of the bend magnets.

S. Kahn 5 June 2003NuFact03 Tetra Cooling RingPage 8 Emittances from GEANT Transmission 4D Emittance 6D Emittance

S. Kahn 5 June 2003NuFact03 Tetra Cooling RingPage 9 Toward a Realistic Muon Cooling Ring The hardedge field description of this cooling ring violates Maxwell’s equations. –It is likely that smoothing out a step function to a tanh or Enge function would solve this, but this has to be demonstrated. There is no free space in the lattice. –This space would be necessary for flux returns for the solenoids and field clamps for the dipole magnet. Flux returns and field clamps are necessary to separate the function of the different lattice elements. Difficult engineering issues like how to inject (eject) beam into (out of) this ring. –These kind of issues will be ignored at this point.

S. Kahn 5 June 2003NuFact03 Tetra Cooling RingPage 10 Saturation in Dipole Magnet Figure shows the permeability for the vertical midplane of the magnet.  <10 on inner edge of the aperture.

S. Kahn 5 June 2003NuFact03 Tetra Cooling RingPage 11 B y Off Vertical Symmetry Plane Angle Positionindex Index Calculated on Difference Planes:

S. Kahn 5 June 2003NuFact03 Tetra Cooling RingPage 12 Dipole Field along Reference Path Figure 4: Field components for a path displaced 10 cm vertically from the reference path Figure 3: B y along central reference path.

S. Kahn 5 June 2003NuFact03 Tetra Cooling RingPage 13 Field and Geometry of the Long Solenoid

S. Kahn 5 June 2003NuFact03 Tetra Cooling RingPage 14 Field and Geometry of the Short Solenoid Figure at left shows B s for cases: Mirror plate boundary condition Partial mirror plate with 18 cm aperture No mirror plate. Full 29 cm aperture

S. Kahn 5 June 2003NuFact03 Tetra Cooling RingPage 15 Comparison of Realistic to Hardedge Field

S. Kahn 5 June 2003NuFact03 Tetra Cooling RingPage 16 Inserting a Gap into the Lattice Part of the difficulty with the Tetra ring is that there is no extra space in the lattice for flux return, field clamps, etc. We have studied what is necessary to add a gap between the end of the solenoids and the dipole magnet: Dipole Magnet Long Solenoid Field Flip Solenoid Extra Focusing Coils

S. Kahn 5 June 2003NuFact03 Tetra Cooling RingPage 17 Inserting a Gap The extra focusing coils are placed symmetrically at the ends of the solenoids into the lattice to compensate and to match into the bending dipoles. The requirements on the focusing coils are –They retain the focusing of the solenoid, ie is unchanged. –The value of B s at the absorber remain unchanged. These requirements uniquely specifies the focusing and other solenoid currents. The RF frequency must be changed to account for the additional length. –The harmonic number is not changed. The wedge angle in the field flip solenoid should be adjusted for the focusing coil and other solenoid current changes.

S. Kahn 5 June 2003NuFact03 Tetra Cooling RingPage 18 Field Flip Solenoid Field with Extra Focusing Coil Original Coil ConfigurationAdjusted with extra focusing coil Difference of 5º phase between these two configurations. This is not corrected for.

S. Kahn 5 June 2003NuFact03 Tetra Cooling RingPage 19 Effect of Placing a Gap Between the Dipole Magnet and the Solenoids Curves show transmission,  tr,  L vs. extra focusing coil current. Cases shown are for 5cm, 10 cm, and 15 cm gaps. P L is held constant and no decays in this comparison.

S. Kahn 5 June 2003NuFact03 Tetra Cooling RingPage 20 Effect of Placing a Gap Using the Whole Momentum Range Gaussian distribution for P L with  P =18 MeV/c. Plots show T,  tr,  L vs. focusing coil current. Transmission drops with increasing gap

S. Kahn 5 June 2003NuFact03 Tetra Cooling RingPage 21 A More Realistic Description of the Solenoids in ICOOL As a step toward a more Maxwellian description to the solenoid fields was tried: –Mirror plate boundary conditions are removed in solenoid regions. –Fringe fields from solenoid sheets are superimposed on the dipole region. The solenoid fringe field along the reference path is the axial field. This, of course, is not correct. –The solenoid end kicks used to describe the fringe fields are removed. The wedge bend magnet is still the hardedge model. The following transparency shows the emittance calculated in ICOOL for this scenario.

S. Kahn 5 June 2003NuFact03 Tetra Cooling RingPage 22 ICOOL Emittances with Real Solenoids