1. Muon Cooling Channel Superconducting Magnet Systems Muon Collider Task Force Meeting on July 31, 2006 V.S. Kashikhin

2. Muon Cooling Channel Design
K. Yonehara - Muon Beam Cooling Simulations
V.V. Kashikhin - Helix Dipole + Solenoid
V.S. Kashikhin - Helix Solenoid
I. Novitski - Mechanical Design
M. Kuchler - Cryostat conceptual design
A. Zlobin - Quench protection
N. Andreev - Design and manufacturing issues

3. Magnet System Parameters
Magnet system length, m
4 - 6
Bore diameter, m
1.0
Radius of muon reference orbit, m
0.255
Solenoidal field, T (z in meters)
Bz = *z
Helical dipole field, T
Bd = – 0.123*z
Helical quadrupole gradient, T/m
G = – *z
Helical pitch
Pitch angle, radians
0.781
Helical periods for dipole and quadrupole, m
Maximum solenoidal field at z = Tesla
Minimum solenoidal field at z = 4 m Tesla
Two magnet system versions under consideration:
Large Bore Solenoid + Helical Dipole + Helical Quadrupole
Helix Solenoid + Correction Coils
July 31, 2006

4. Superconducting Solenoid
LHC Cables parameters:
Inner cable 14 kA at 7 T & 4.2 K
Outer cable 8.5 kA at 7 T & 4.2 K
LHC short samples:
Jc = 2750 A/mm2 at 5 T & 4.2 K
LHC cables leftover:
Inner cable m
Outer cable m
Solenoid has 8-12 sections wound separately on identical bobbins
All sections connected in series
Ferromagnetic end plates improve ends field quality
Holes in end plates provide path for muon beam inlet and outlet
Needed coil mechanical stability provided by SS or Al bandage
Total solenoid ampere-turns
12 MA
Current
10 kA
Number of turns
1200
First section Lorentz force Fr, N
14 MN
Support SS ring thickness at 200 Mpa, mm 22
Superconducting cable length
3960 m
July 31, 2006

5. Solenoid Magnetic Field
Flux lines of solenoidal field
Specified linear solenoidal field decay along Z axis
provided by proper chosen number of turns for each section:
W1= W5 = 136
W2 = W6 = 126
W3 = W7 = 114
W4 = W8 = 114
July 31, 2006
Solenoid flux density distribution, Bmax = 5 Tesla

6. Helical Dipole, Quadrupole, Sextupole
Shell type Helix Coils have length 1,2,3 and 4 meters and wound one after other.
They will be epoxy impregnated together.
Support cylinder will provide mechanical stability.
Because of relatively low field decay 1 m long sections will be enough for proper field approximation.
Parameter
Dipole
Quadrupole
Maximum field strength
0.95 T
0.6 T/m
Minimum field strength
0.454 T
0.4 T/m
Coil Ampere-turns/pole
862 kA
78.5 kA
Coil Lorentz force Fx
208 kN/m
2.4 kN/m
Coil Lorentz force Fy
-289 kN/m
-6.2 kN/m
Energy of magnetic field
752 kJ/m
133 kJ/m
Coil inner radius
0.55 m
0.57 m
Superconductor max field
1.81 T
0.33 T
Helical period
2.0 m
Separate short sections length
1.0 m
July 31, 2006

7. Helical Dipole + Solenoid
Red – Sectional Large Bore Solenoid
Blue –Helical Dipole, several shell type dipoles with different length for field decay
July 31, 2006

8. Helical Dipole+Solenoid
Solenoid maximum field 7.2 Tesla
Inner bore diameter 1 meter
Number of solenoid sections - 12
Number of dipole sections - 4
July 31, 2006

9. Helical Dipole + Solenoid
Only first sections in high field area
Half solenoid has less than 4 Tesla field
July 31, 2006

10. Helical Dipole + Solenoid
Good agreement with analytical field used by K.Yonehara for beam cooling simulation
July 31, 2006

11. Helical Solenoid Helical Solenoid: Small bore diameter 0.5 m
Helix period 1.6 m
Number of coils 73
Coil width 50 mm
Outer helix diameter 1 m
Max coil current 201 kA
July 31, 2006

12. Helical Solenoid Fields
Field at radius 0.49 m Field at center orbit radius m
Max field 4.3 T
July 31, 2006

13. Helical Solenoid Fields
Field at m radius with helix period 1.6 m
July 31, 2006

14. Helical Solenoid Quadrupole Field
Period 1.6 m, G=-0.83 T/m, dG/dz=-0.11 (T/m)/m
Helix Solenoid Gradient
Period 1.4 m, G=-1.0 T/m
K. Yonehara, AD Meeting July 27, 2006
Kappa = 0.8, Helix period = 2 m, G = T/m
Kappa = 1.0, Helix period = 1.6 m, G=-0.83 T/m
Kappa = 1.15, Helix period = 1.4 m, G=-1.0 T/m
Specified dG/dz = -0.1 T/m
July 31, 2006

15. Summary Both superconducting magnet systems are feasible
Short sections approach is a reasonable way of system manufacturing
Beam inlet and outlet matching areas should be investigated
Values of operating currents and current leads number should be optimized
Superconducting test of separate sections is an economic way to control
whole system performance and reduces the risk
Labor of helical coils fabrication is relatively large. Configuration and number of coil sections should be optimized
Mechanical structure should be capable to withstand large Lorentz forces
Magnet cryogenic system should provide effective cooling at K
Active quench protection system should be used to protect magnet system
July 31, 2006