Magnetic Scalar Potential Method Coil design of winding pattern Design and Fabrication of Precision Surface Current Coils for Neutron Experiments Ben Riley, Hunter Blanton, Ali Frotanpour, Christopher Crawford Department of Physics and Astronomy, University of Kentucky Motivation Drill-Etching The electric dipole moment (EDM) changes its sign as time is reversed. This is directly related to CP-violation. The CP-violation present in the standard model is insufficient to explain the abundance of matter and the lack of antimatter in the universe. The SNS nEDM collaboration aims to measure the electric dipole moment of the neutron to a precision of a few x 10-28 e cm by measuring the Larmor precession of the neutron in a magnetic field modulated by a reversing electric field. An essential requirement for this measurement is precision magnetic fields to guide the spins of polarized neutrons and 3He atoms into the precession cell. These coils must have uniform fields, zero fringes, and may not contain any magnetic materials. Using a fine tip pneumatic CNC router mounted on the end of the robot, paths were milled to produce the desired current traces. By laminating G10-FR4 board with a thin sheet of copper, a highly resilient circuit was created. This method is well suited for construction of geometries with zero Gaussian curvature, such as cylinders and plane faces, due to the lamination procedure. Additionally, this method produced circuits that are capable of withstanding the supercooled temperatures that are present in the nEDM experiment. Substrate and Copper Plating The 3-d coil surface substrate is fabricated using stereolithography (SLA) using a high-temperature ABS-like resin. This method is quick, less prone to human error, with feature detail of 0.1 mm. We ordered two printed pairs from stratasys.com and quickparts.com. and coated 0.125 mm of copper using electroless electroplating at epner.com 1 1 Magnetic Scalar Potential Method Surface Current Magnetic flow sheets (scalar equipotential) Magnetic flux lines Photolithography is widely used for device fabrication such as integrated circuits and thin film patterning. Ultra-violet (UV) laser light was used to sensitize a photoresist mask on each cylinder for etching. One of the benefits of this method is its non-destructive patterning: before etching, we can verify our traces. Another benefits the precession and fine detail (100 micron). Positive type photoresist is coated on the electroplate surface using a spray coating. A UV laser attached to the robot traces the desired lines, sensitizing the photoresist. It is removed with a developer solution Exposed copper is etched with ferric chloride . Photo-Etching We developed a method to design and construct precision surface current coils at the University of Kentucky based on a novel physical interpretation of the magnetic scalar potential. It is a source potential in the sense that the corresponding magnetic field is generated the source currents running along its equipotentials. If one wire is wrapped around around each equipotential contour of the magnetic scalar potential along the boundary of the coil, it will generate the gradient field inside the volume of the coil. This interpretation results from the boundary conditions of Ampere's law We use this principle to design coils as follows: We solve the scalar potential U using Neumann exterior boundary conditions, specifying the magnetic flux. We create a 3-d printed circuit with traces following the equipotential contours of U along the boundary. It is necessary to construct such a coil around the boundary of each region with a non-zero field. 3D Printing In addition to milling and photoresist techniques, an alternative is being tested. By 3D printing the geometry with trapezoidal grooves, copper wire is run along the surface of the substrate to produce the desired magnetic field. Pieces have been constructed to test the ability of the substrate to hold the wire, and we are working to print a cylinder with the desired paths. Coil design of winding pattern Robot Calibration This project is to demonstrate practical CNC construction techniques for surface current coils. The prototype is a tapered double cos-theta coil with a transverse field which decreases axially down the cylinder. The coil is constructed of two half-cylinder clam shells which clamp together around the 3He transport tube. The equipotential contours were obtained by numerically a Laplace boundary value problem in the finite element software package COMSOL. The boundary conditions were: a) dU/dn=0 on the outer surface; b) dU/dn=G z cos(θ) on the inner surface. Contours were numerically extracted from COMSOL in Matlab and passed along to the robot control software for etching of the circuit traces. The robot we are using has a 35µm repeatability, which is ideal for our work. Optimally, the precision of the arm would also be at the 35µm level. A complete calibration is necessary to achieve this. The six joints of the robot arm give six degrees of freedom to reach a given point(x,y,z) with a specified orientation (roll, pitch, yaw). The kinematics of each joint are determined by 4 parameters, describing the transformation from one joint to the next. Combined with the tool tip and the world system, and accounting for free parameters, a total of 29 parameters must be fit. The calibration model involves positioning the robot into various poses and measuring the distance between the tool tip and a metal sphere, using a precision laser displacement sensor. Then using a non-linear generalized least-squares fit, the parameters can be recovered by comparing measured and modeled distances. This work was supported by the DOE Office of Science under contract DE-SC0008107