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Forces in the Capture Solenoid
Peter Loveridge
STFC Rutherford Appleton Laboratory, UK
16-09-2008
Peter Loveridge, 16-09-2008
Scope
• Have carried out a study of the magnetic forces acting on the capture solenoid coils. Will present a summary of results for:
– “Study-2” geometry
– “Helmholtz” geometry
• Thoughts on optimisation of field vs bore vs magnetic forces
• Next steps
Peter Loveridge, 16-09-2008
Study-2 Solenoid
• Baseline design from Study-2 (2001)– Superconducting outer solenoid
• Nb3Sn CICC @ 1.9 K, generates up to 14 T
– Normal conducting insert
• Water cooled copper coil, generates up to 6 T
• Generates high field (20 T) in a large bore (150 mm) in order to capture pions– Pion capture is related to the product of B x R
– In study-2, B is pushed to an absolute maximum in order to minimise the overall size (and cost) of the magnet
On-axis field profile
Fie
ld (
T)
Position (m)
Study-2 coil geometry
Peter Loveridge, 16-09-2008
Study-2 Solenoid Forces
• Cumulative axial compressive force in excess of 10,000 metric tonnes!– Axial Forces between the first 5 SC coils ~balance
– They share a single cryostat and react against one another
• Forces balanced inside the cryostat
• Radial forces are enormous– Equivalent to an internal pressure of ~1000 bar in first SC coil
– Large radial force = large tensile hoop stress in the coil
– Could be a particular problem for the (low strength) copper insert coils
Magnetic forces acting on the study-2 capture solenoid coils
Peter Loveridge, 16-09-2008
“Helmholtz” Split Solenoid
• A development of the study-2 design to include a gap at the target location– So-called “Helmholtz” design
– Gap permits lateral access for a target “wheel” or conveyor
• Field quality issue – field “trough” at the target interaction region– Initial studies suggest that this causes a loss in captured pions of the order ~10%
– Increasing the gap size further exaggerates the field trough
• i.e. we should reduce the gap to a minimum
• Currently 400 mm
– Note: trough in field profile generated almost entirely by contribution from insert coils
On-axis field profile
Fie
ld (
T)
Position (m)
Helmholtz coil geometry
Peter Loveridge, 16-09-2008
“Helmholtz” Split Solenoid Forces
• Cumulative axial compressive force in excess of 16,000 metric tonnes!– Axial Forces between the first 6 SC coils ~balance
– Can we house all these coils in a single cryostat?
• Would like to avoid transferring loads up to room temperature
– Balancing forces must be transferred across the Helmholtz gap
• The subject of current design studies
• Radial forces are enormous– Similar hoop-stress issues as seen in study-2 solenoid design
Magnetic forces acting on the Helmholtz capture solenoid coils
Peter Loveridge, 16-09-2008
Thoughts on optimisation of field vs bore vs force
• How is the axial (attractive) force between coils related to– Peak on-axis field?
– Coil bore radius?
• Consider the much simplified case of a symmetrical “Helmholtz” pair of coils, having characteristic capture solenoid dimensions
– Represents coils SC01 and SC02 in the Helmholtz capture magnet
L LG
R1
R2
J J
B0
CHARACTERISTIC VALUES
COIL LENGTH L 900 mm
GAP LENGTH G 400 mm
BORE RADIUS R1 636 mm
OUTER RADIUS R2 1278 mm
CURRENT DENSITY J 23.4 A/mm2
OUTPUT QUANTITIES
PEAK ON-AXIS FIELD B0
AXIAL FORCE ON COIL FZ
Characteristic Helmholtz cross-section
Peter Loveridge, 16-09-2008
Thoughts on optimisation of field vs bore vs force
1. Same bore, vary field:
• Fix bore radius = 636 mm
• Achieve desired on-axis field by adding or removing turns
2. Same field, vary bore:
• Desired on-axis field = 13 T
• Vary coil bore radius, adding or removing turns to achieve desired field
3. Bore x field = constant
• Try various combinations of bore and field
Same IR, Vary B
0
5000
10000
15000
20000
0 5 10 15
Peak On-Axis Field (T)
Ax
ial F
orc
e o
n C
oil
(to
nn
es
)
Same B, Vary IR
0
5000
10000
15000
20000
0.000 0.250 0.500 0.750
Inner Radius (m)
Axi
al F
orc
e o
n C
oil
(to
nn
es)
B x R = Constant
0
5000
10000
15000
20000
0 5 10 15
Peak On-Axis Field (T)
Ax
ial F
orc
e o
n C
oil
(to
nn
es
)
But… reducing field is bad for pion capture
But… reducing bore radius is bad for pion capture
In this case, optimising for low force is not necessarily bad!
Peter Loveridge, 16-09-2008
Summary
Comments:• The combination of very high field and large bore required by the capture solenoid
constitutes a formidable engineering challenge• The magnetic forces generated by the capture solenoid are huge and require careful
mechanical design• It is not easy to reduce the magnetic forces without a simultaneous reduction in pion
capture
Scope for Optimisation?• There appears to be some scope to reduce the magnetic forces through an
optimisation in the field vs bore parameter space• In the Helmholtz magnet - try to optimise the geometry / parameters in order to
reduce the “field trough”
Mechanical design:• Need an outline design to tell us if it is possible to support the huge compressive
axial forces across the Helmholtz gap
