3 He Injection Coils Christopher Crawford Genya Tsentalovich

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3 He Injection Coils Christopher Crawford, Genya Tsentalovich, Wangzhi Zheng, Septimiu Balascuta, Steve Williamson

3 He Injection Coils Christopher Crawford, Genya Tsentalovich, Wangzhi Zheng, Septimiu Balascuta, Steve Williamson n. EDM Collaboration Meeting 2011 -06 -07

Injection beamline magnetic elements TR 3 a Helmholtz coils (outer TR 3 b coils

Injection beamline magnetic elements TR 3 a Helmholtz coils (outer TR 3 b coils not in model) 77 K sheild 4 K shield TR 2 b coil at 300 K TR 2 a coil at 300 K TR 1 b coil at 77 K trouble regions TR 1 a coil at 4 K

Previous spin precession simulations doubling the injection field improves to 95% polarization Wangzhi Zheng

Previous spin precession simulations doubling the injection field improves to 95% polarization Wangzhi Zheng

Old approach ABS quadrupole PROBLEMS 1. The magnetic field from ABS quadrupole on μmetal

Old approach ABS quadrupole PROBLEMS 1. The magnetic field from ABS quadrupole on μmetal shield is about 2 G. 2. The solenoidal field near the ABS exit is too small to preserve polarization. 3. The field is less than Earth field outside the μmetal shield (active shielding doesn’t shield the external fields). 4. The direction of polarization is wrong before the entrance into cosθ coil.

Magnetic field direction H 45 ° H The up- and downstream coils shift the

Magnetic field direction H 45 ° H The up- and downstream coils shift the direction of the field making it more longitudinal (30° instead of 45°).

Tapered field Bx, no rotation (T 1 a/b region)

Tapered field Bx, no rotation (T 1 a/b region)

Placement of coils – gap between coils T 1 a/b coil @ 4 K

Placement of coils – gap between coils T 1 a/b coil @ 4 K T 2 a/b coil @ vacuum preferably outside vacuum (smaller diameter stub)

Continuity of field with gap in coil surface § Gap must be at constant

Continuity of field with gap in coil surface § Gap must be at constant potential (no wires) § Taper field down to zero in a “buffer region” § Potential 10 -8 G § Field <1 m. G 1 G

B-field along ABS axis Field rotates after taper Wangzhi Zheng

B-field along ABS axis Field rotates after taper Wangzhi Zheng

Ideal field: Taper and Rotate from 5 G to 50 m. G § Old

Ideal field: Taper and Rotate from 5 G to 50 m. G § Old version: calculate taper on single line using analyticity § Rotation: generalize approximation to include transverse component

B-field in TR 1 region – optimized taper 1 G Bz(z) n=1 n=-10 n=-1

B-field in TR 1 region – optimized taper 1 G Bz(z) n=1 n=-10 n=-1 50 m. G Edge of cos theta coil Bx(z) z End of TR 1 region

B-field in TR 1 region – optimized rotation 1 G Bz(z) m=5 50 m.

B-field in TR 1 region – optimized rotation 1 G Bz(z) m=5 50 m. G Edge of cos theta coil m=2 m=1 Bx(z) z End of TR 1 region

Adiabaticity parameter – optimized taper n=-10 n=1

Adiabaticity parameter – optimized taper n=-10 n=1

Adiabaticity parameter – optimized rotation § Adiabaticity parameter: 1/10 everywhere m=1 m=2 m=5

Adiabaticity parameter – optimized rotation § Adiabaticity parameter: 1/10 everywhere m=1 m=2 m=5

Tapered rotated field in T 1 a/b region Calculation vs. Simulation 50 m G

Tapered rotated field in T 1 a/b region Calculation vs. Simulation 50 m G U=0 fl u x tapered flux

Tapered field in T 2 a/b region

Tapered field in T 2 a/b region

Tapered field in T 2 a/b region – buffer region

Tapered field in T 2 a/b region – buffer region

Realization in 3 D geometry

Realization in 3 D geometry

Taper-rotated / linear rotated combination § Planar geometry in T 1 a/b region §

Taper-rotated / linear rotated combination § Planar geometry in T 1 a/b region § Cylindrical geometry in T 2 a/b region § Tuned to zero net flux out of gap

Inner coils

Inner coils

Inner coils – gap region

Inner coils – gap region

T 1 a/b coils

T 1 a/b coils

T 2 a/b coils

T 2 a/b coils

Tapered Cylindrical Double Cos Θ Coil 71 ‘m. G 50 25 total taper §

Tapered Cylindrical Double Cos Θ Coil 71 ‘m. G 50 25 total taper § § (center) § guide taper (edge) § B 0 taper 0 0 25 75 100 cm Field tapers from 5 G to 40 m. G in 2 m Segmented 6 x current between coil Merges into field of B 0 coil Inner/outer coils combined into single winding 50 Guide field windings shown with 25 turns

Construction of Surface Current Coils § Designed using the scalar potential method § FEA

Construction of Surface Current Coils § Designed using the scalar potential method § FEA simulation of windings § Staubli RX 130 robot to construct coil • • A series of rigid links connected by revolute joints (six altogether). The action of each joint can be described by a single scalar (the joint variable), the angle between the links. Last link is the end effector. Joint variables are: J 0, J 1, J 2, J 3, J 4, J 5

Link Frames § We can imagine attaching a cartesian reference frame to each link.

Link Frames § We can imagine attaching a cartesian reference frame to each link. § We might call the frame attached to the first link the inertial frame or the lab frame (the first link is fixed wrt the lab). § The frame attached to the last link is the end-effector frame.

Coordinate Transforms § Given the coordinates of a point in one frame, what are

Coordinate Transforms § Given the coordinates of a point in one frame, what are its coordinates in another frame? § The relationship between the end-effector frame and the inertial frame is of particular interest. (The location of the drill is fixed w/r the end-effector frame. The location of the electroplated form is fixed w/r the inertial frame). § Generally, six independent parameters are needed to relate one frame to another (3 to say where the second origin is, 3 to orient the second set of axes). § For the link frames, the position of each origin is flexible, so the relation can be specified with 4 parameters, one of which is the joint variable. These are the DH parameters.

DH Parameters / Homogeneous Transform Matrix § To repeat: the relationship between link frames

DH Parameters / Homogeneous Transform Matrix § To repeat: the relationship between link frames can be characterized by 4 parameters, one of which is the joint variable. The other 3 are fixed, and relate to the size and placement of the links. § Using the fixed DH parameters and the joint variable, we can compute a transformation matrix needed to translate one link's coordinates into the adjacent link's coordinates. § T(J) is a 4 x 4 matrix of the following form: § i' j' k' T ( 0 0 0 1 ) § We can compose transformations to relate any two frames.

Problem: Forward / Inverse Kinematics § With these concepts in place, we can address

Problem: Forward / Inverse Kinematics § With these concepts in place, we can address the following problem: § Given an actuation, determine the position and orientation (i. e. , the pose) of some body fixed in the endeffector frame with respect to the inertial frame. § {J 0, J 1, J 2, J 3, J 4, J 5} -> {x, y, z, alpha, beta, gamma} § Solution: Build the transformation matrix for the given actuation and apply it to every point in the body. Alpha, beta and gamma can be compute directly from i', j’, k'. § Conversely: § Given a pose, find an actuation that will produce it.

Problem: Calibration § Finally, given many (Actuation, Pose) pairs, find a set of DH

Problem: Calibration § Finally, given many (Actuation, Pose) pairs, find a set of DH parameters for best fit. § For each actuation, take actual measurements of the end-effector's pose. § Pick a few points fixed with respect to the end -effector frame. § This is easy to see if we select P 0=(0, 0, 0) P 1=(1, 0, 0) P 2=(0, 1, 0) P 3=(0, 0, 1) § Randomly actuate the robot. § Measure the position of each point w/r the inertial frame using a FARO arm. § Recover the translation vector from FARO(0) § Recover rotation matrix (Euler angles) from FARO(P 1)-FARO(P 0), FARO(P 2)-FARO(P 0), …

Positioning [Tooling] § While the location of the drill is fixed in the end-effector

Positioning [Tooling] § While the location of the drill is fixed in the end-effector frame, we don't know its exact position. § If we know the precise position of some location on a flat surface, then we can know the precise distance of the drill tip from that point using the laser distance meter. 60000 RPM 10 um accuracy

Geometry Capture/Wire Placement § Once the robot is calibrated (that is to say, we

Geometry Capture/Wire Placement § Once the robot is calibrated (that is to say, we know the pose of its end effector for any actuation), we can capture the geometry of the electroplated form using the laser displacement meter. § Coil Design: [Magnetic Scalar Potential Technique] 1. A digital representation of the form geometry. 2. A description of the field we desire within the form. § Feed output of COMSOL back to robot to drill windings on the form

Conclusion § New techniques • • Rotating fields Gap between current surface § Converging

Conclusion § New techniques • • Rotating fields Gap between current surface § Converging on designs for guide fields • • • Neutron guide 3 He injection tube 3 He transfer region § Developing the capability to construct coils • • • Robotic arm with laser displacement sensor high speed spindle