#### Transcript Conceptual Design of the Neutron Guide Holding Field

```3He
Injection Coils
Christopher Crawford,
Genya Tsentalovich,
Wangzhi Zheng,
Septimiu Balascuta,
Steve Williamson
nEDM Collaboration Meeting
2011-06-07
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
Previous spin precession simulations
doubling the injection
field improves to 95%
polarization
Wangzhi Zheng
Old approach
ABS
PROBLEMS
1. The magnetic field from
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
°
45
°
H
The up- and downstream
coils shift the direction of
the field making it more
longitudinal
Tapered field Bx, no rotation (T1a/b region)
Placement of coils – gap between coils
T1a/b coil @ 4K
T2a/b coil @ vacuum
preferably outside vacuum
(smaller diameter stub)
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 mG
1G
B-field along ABS axis
Field Strength (G)
Bx
By
Bz
2
Negative
1
0
-1
0
60
120
Distance (cm)
Field rotates after taper
Wangzhi Zheng
180
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
B-field in TR1 region – optimized taper
1G
Bz(z)
n=1
n=-10 n=10
n=-1
50 mG
Edge of cos theta coil
Bx(z)
z
End of TR1 region
B-field in TR1 region – optimized rotation
1G
Bz(z)
m=5
50 mG
Edge of cos theta coil
m=2
m=1
Bx(z)
z
End of TR1 region
n=-1
n=-10
n=10
n=1
m=1
m=2
m=5
Tapered rotated field in T1a/b region
Calculation
vs.
Simulation
tapered flux
U=0
tapered flux
Tapered field in T2a/b region
Tapered field in T2a/b region – buffer region
Realization in 3D geometry
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
Inner coils
Inner coils – gap region
T1a/b coils
T2a/b coils
Tapered Cylindrical Double Cos Θ Coil
71
‘mG
50
(center)
total taper
guide taper (edge)
25
B0 taper
0
0
25

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
50
75
100 cm
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 (six altogether).
The action of each joint can
be described by a single
scalar (the joint variable),
Last link is the end effector.
Joint variables are:
J0,J1,J2,J3,J4,J5
 We can imagine attaching
a cartesian reference
 We might call the frame
the inertial frame or the
lab frame (the first link is
fixed wrt the lab).
 The frame attached to the
frame.
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 can be
characterized by 4 parameters, one of which is the joint
variable. The other 3 are fixed, and relate to the size and
 Using the fixed DH parameters and the joint variable, we
can compute a transformation matrix needed to translate
coordinates.
 T(J) is a 4x4 matrix of the following form:

i' j' k' T
(0001)
 We can compose transformations to relate any two
frames.
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.

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 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 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 on designs for guide fields
•
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Neutron guide
3He injection tube
3He transfer region
 Developing the capability to construct coils
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Robotic arm with
laser displacement sensor
high speed spindle
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