Injection beamline magnetic elements

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Harry Jefferson
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1 3 He Injection Coils Christopher Crawford, Genya Tsentalovich, Wangzhi Zheng, Septimiu Balascuta, Steve Williamson nedm Collaboration Meeting

2 Injection beamline magnetic elements TR3a Helmholtz coils (outer TR3b coils not in model) 77K sheild 4K shield TR2b coil at 300K TR2a coil at 300K TR1b coil at 77K trouble regions TR1a coil at 4K

3 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 µ- metal shield is about 2G. 2. The solenoidal field near the ABS exit is too small to preserve polarization. 3.

4 Old approach ABS quadrupole PROBLEMS 1. The magnetic field from ABS quadrupole on µ- metal shield is about 2G. 2. The solenoidal field near the ABS exit is too small to preserve polarization. 3. The field is less than Earth field outside the µ- metal shield (active shielding doesnt shield the external fields). 4. The direction of polarization is wrong before the entrance into cosθ coil.

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

6 Tapered field Bx, no rotation (T1a/b region)

7 Placement of coils gap between coils T1a/b 4K T2a/b vacuum preferably outside vacuum (smaller diameter stub)

8 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 Field <1 mg 10-8 G 1 G

9 B-field along ABS axis Field Strength (G) 2 1 Negative Bx By Bz Distance (cm) Field rotates after taper Wangzhi Zheng

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

11 B-field in TR1 region optimized taper 1 G B z (z) n=1 n=-10 n=10 n=-1 50 mg B x (z) z Edge of cos theta coil End of TR1 region

12 B-field in TR1 region optimized rotation 1 G B z (z) m=5 50 mg m=2 m=1 B x (z) z Edge of cos theta coil End of TR1 region

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

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

15 Tapered rotated field in T1a/b region Calculation vs. Simulation tapered flux U=0 tapered flux

16 Tapered field in T2a/b region

17 Tapered field in T2a/b region buffer region

18 Realization in 3D geometry

19 Taper-rotated / linear rotated combination Planar geometry in T1a/b region Cylindrical geometry in T2a/b region Tuned to zero net flux out of gap

20 Inner coils

21 Inner coils gap region

22 T1a/b coils

23 T2a/b coils

Tapered Cylindrical Double Cos Θ Coil 71 mg 50 25 0 total taper B0 taper

in 2m Segmented 6x current between coil Merges into field of B0 coil

24 Tapered Cylindrical Double Cos Θ Coil 71 mg total taper B0 taper (center) guide taper (edge) cm Field tapers from 5 G to 40 mg in 2m Segmented 6x current between coil Merges into field of B0 coil Inner/outer coils combined into single winding Guide field windings shown with 25 turns

Construction of Surface Current Coils Designed using the scalar potential method FEA simulation of windings Staubli RX130 robot to construct coil A series of rigid links connected by revolute joints

25 Construction of Surface Current Coils Designed using the scalar potential method FEA simulation of windings Staubli RX130 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: J0,J1,J2,J3,J4,J5

26 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.

27 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.

28 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 4x4 matrix of the following form: i' j' k' T ( ) We can compose transformations to relate any two frames.

29 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. {J0, J1, J2, J3, J4, J5} -> {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 parameters for best fit. For each actuation, take actual measurements of the end-effector's pose.

30 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 P0=(0,0,0) P1=(1,0,0) P2=(0,1,0) P3=(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(P1)-FARO(P0), FARO(P2)-FARO(P0),

Positioning [Tooling] While the location of the drill

flat surface, then we can know the precise distance

31 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 RPM 10 um accuracy

32 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

33 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

EEE 187: Robotics Summary 2

1 EEE 187: Robotics Summary 2 09/05/2017 Robotic system components A robotic system has three major components: Actuators: the muscles of the robot Sensors: provide information about the environment and