1. Drilling a Double Cosine-Theta Coil Hunter Blanton, Spencer L. Kirn, Christopher Crawford University of Kentucky Abstract: A double cosine theta coil is a magnetic coil with a uniform magnetic field on the inside and no field on the outside. We wanted to be able to create this coil using circuit boards drilled onto copper plated G-10. The magnet has two different coils, one on the outside and one on the inside. A Stabuli RC-130 robotic arm programmed in Matlab was used to drill the circuit board. Motivation As an alternative to searching for new physics at higher energies (such as at the LHC), there is a new class of precision low energy experiments that are sensitive to small loop corrections due to high energy intermediate states. For example, the neutron EDM violates time and parity symmetry, key symmetries involved in the baryon asymmetry of the universe. To measure an nEDM as small as 10 -28 e cm, one needs magnetic field uniform at the level of: Design Considerations To design the coil, we started with 2D placement of wires along the cylinder. The physical wires along either cylinder are distributed uniformly in the x-direction to ensure a homogenous magnetic field. The inner wires formed two sets of circuits: one circuit looping along the outer cylinder and a second circuit running across the middle of the coil. The traces along the endcaps followed the equipotential counters described to the left. Sample end caps are shown below, with holes drilled on the inner and outer circles to attach wires. Double Cosine Theta Coil The double cosine theta coil is a special coil with two cylindrical layers to produce a uniform magnetic field on the inside of the coil, with no fringe field on the outside. In our design, we use printed circuit boards for the endcaps, connected by copper wires along the cylinders in between. The printed circuits are a better approximation of surface currents and can be milled with very high precision, compared to grooves for wires, as shown in the picture. We use this method to construct coils optimized with COMSOL, a finite element simulation code. Rerouting Traces from One Loop to the Next In order to form a single complete circuit, current must be “rerouted” to the next current segment somewhere along the current loop. Each reroute must be balanced by a reroute in the opposite direction, so that it does not affect the final magnetic field. Example endcaps are shown above. The left endcap shows surface cuts with no rerouting. The right endcap shows a the current of our current rerouting scheme. The rerouting of the inner current being shifted to the right is countered by rerouting of the outer current being shifted to the left. We designed the route to be symmetric, so that none of the traces cross over each other. Milling the endcaps The endcaps require placement precision of 35 um. Drilling is performed with a Staubli RX130 robotic arm fitted with a laser displacement sensor (LDS) and a high-speed spindle. To achieve the required precision, we performed several calibrations: Magnetic Scalar Potential We design our coils by solving a boundary value problem for the magnetic scalar potential, a method developed in our group. The coil is wound along equipotential contours to produce the exact calculated field. Due to the simple geometry and z-symmetry of a cylindrical coil, the magnetic potential field can be solved analytically in 2D as a function of the inner (a) and outer (A) radius: This allows us to generate an equipotential path from any starting or ending point between the inner and outer cylinders. We parameterized the equipotentials in terms of the radial distance s to get (x,y) coordinates along each contour path, where the current should flow: Future Work A side effect of our current design is the easy modification it allows for. Once the coil has been built, it will be possible to add digital potentiometers to have fine tune control of the current flow. One-resistor-per-loop circuits could be controlled pragmatically to quickly test the effects of altered current even after circuit creation. A) Conversion from the 14-bit LDS reading (0 – 16368) to physical dimensions: While the intrinsic resolution of the LDS is 3 um, the LDS was only linear to 1 mm. We used two cross- calibrated linear stages with a generalized linear fit to calibrate the LDS within 10 um. B) Mounting position of the LDS sensor on the robotic arm: to find the origin the LDS in terms of the robot reference frame, we measured the distance from the laser to a tooling ball from several different angles of the robot. These were fit for the position of the tooling ball, and the position and angle of the laser. C) Position of the mill end with respect to the LDS sensor: We milled a cross pattern with the drill and then scanned the depth profile with the LDS mounted in the same tool flange. The position of the cut was determined from the dips in the laser scan. From this we calculated the offset between the laser origin and drill tip. Our robot control software also includes a 3-d model of the arm to implement collision detection It integrates signals of the LDS and other sensors with readout and control of the robot to safely automate drill movements within the robot cell workspace.