A Bitter-type electromagnet for complex atomic trapping and manipulation
J. L. Siegel, D. S. Barker, J. Fedchak, J. Scherschligt, S. Eckel
AA Bitter-type electromagnet for complex atomic trapping and manipulation
J. L. Siegel, a) D. S. Barker, J. A. Fedchak, J. Scherschligt, and S. Eckel b) Sensor Science Division, National Institute of Standards and Technology, Gaithersburg, MD 20899,USA (Dated: 26 August 2020)
We create a pair of symmetric Bitter-type electromagnet assemblies capable of producing multiplefield configurations including uniform magnetic fields, spherical quadruple traps, or Ioffe-Pritchardmagnetic bottles. Unlike other designs, our coil allows both radial and azimuthal cooling water flowsby incorporating an innovative 3D-printed water distribution manifold. Combined with a double-coilgeometry, such orthogonal flows permit stacking of non-concentric Bitter coils. We achieve a lowthermal resistance of 4 . ◦ C kW − and high water flow rate of 10 . − at a pressure of190(10) kPa.Generating, controlling, and shaping magnetic fields is es-sential for many laser-cooling experiments and applications.Techniques for manipulating atoms and molecules that re-quire magnetic fields include Zeeman slowing ; magnetictrapping ; magnetic transport ; and Feshbach or opticalresonance control . These manipulation methods are inte-gral to quantum devices such as optical lattice clocks , pri-mary vacuum sensors , atom interferometers , and preci-sion measurements .Water-cooled electromagnets made from wound coppertubing are a simple way to create the necessary magnetic fieldswith sufficient dynamic control. In these coils, the hydraulicresistance increases linearly with the winding length. To in-crease current density in the coil, flow channels are generallymade as small as possible, further increasing hydraulic resis-tance. Large hydraulic resistance results in low cooling fluidflows, limiting total cooling performance. In addition, a tem-perature gradient develops over the length of the coil, slightlyperturbing the magnetic field. Increasing cooling performanceand reducing temperature gradients is important for Feshbachresonance control and atomic clocks , respectively.There has been substantial effort to advance electromag-net current handling for atomic physics experiments beyondwound copper wire or tubing. These efforts fall undertwo broad umbrellas: immersing the coil in cooling waterwhile maximizing its surface area or using many paral-lel flow channels . A Helmholtz coil design, basedon Bitter-type electromagnets , has achieved the lowest ther-mal resistance . More recent modifications allow for multi-ple concentric Bitter coils . Despite Bitter coil’s superiorthermal performance, their geometric constraint, concentric-ity, renders them unsuitable for magnetic transport or Ioffe-Pritchard (IP) trap applications.We extend application of Bitter electromagnets to stacked,non-concentric coil geometries allowing for excellent ther-mal performance and complex spatial magnetic fields. Non-concentric Bitter coils necessitate cooling water to flow bothazimuthally and radially, complicating the distribution andcollection of cooling water. A 3D-printed water distributionmanifold permits cooling water to flow in multiple directions,making non-concentric Bitter coils possible. a) Present address: Department of Physics, University of Colorado, Boulder,CO 80309, USA b) Electronic mail: [email protected]
Our coil assembly can generate multiple field configura-tions, including uniform fields along the symmetry axis ˆ z ,spherical quadrupoles (quadrupole fields with azimuthal sym-metry), and even more complicated configurations for mag-netic trapping of neutral atoms. Of particular interest is the IPtrap, which creates a non-zero local magnetic field minimumthat traps atoms and is given by B = B + B (cid:48) x − y + B (cid:48)(cid:48) − xz − yzz − ( x + y ) . (1)To create this field configuration, our assembly features threeindependent coils. A pair of “curvature” coils creates B (cid:48)(cid:48) , withan offset that contributes to B . A pair of Helmholtz coils,called anti-bias coils, opposes the contribution of B from thecurvature coils. A pair of quadrupole coils, called clover coils,create B (cid:48) . This topology was first used for production of largesodium Bose-Einstein condensates , and allows for good op-tical access in the transverse plane. Moreover, using just theanti-bias coil we can create a uniform magnetic field for Fes-hbach resonance studies, or by switching the polarity of oneof the anti-bias coils, we can create a spherical quadrupole formagnetic trapping or a magneto-optical trap (MOT).Figure 1 shows one of our two identical Bitter coil assem-blies. As with other designs , our Bitter coil is composedof stacked alternating conducting OFHC copper and insulat-ing teflon crescents mounted to a water-distribution manifold.The inset in Fig. 1 shows the current and water flows in theBitter coil. Current flows around each conducting piece untilit reaches the notch in each crescent. A small copper short-ing piece lying in the notch of every insulating crescent al-lows current to flow vertically to the next layer. All pieceshave holes that align to form vertical cooling water columnsthat serve to supply water to and collect water from the en-tire stack. Supply and collection columns alternate spatially.Cutouts in the insulating layers allow water to flow hori-zontally between neighboring supply and collection columns.The horizontal flow contacts a large surface area of the ver-tically neighboring conducting pieces, cooling the magnet.Small silicone gaskets, not shown, seal the horizontal and ver-tical flow channels . In order to seal the Bitter coil, stainlesssteel screws with rubber sealing washers compress the top ofthe Bitter coil to the bottom of the manifold.The curvature and anti-bias coils in Fig. 1 have the sametopology. Current is injected through a partially threaded rodattached nearest the notch in the outer, top brass piece. Thecurrent carrying rods are made from chromium-copper (alloy a r X i v : . [ phy s i c s . i n s - d e t ] A ug FIG. 1. Rendering of one of the two Bitter coil assemblies. The 3D-printed water distribution manifold is white; a section has been cut awayto show the geometries of the supply and collection reservoirs. The four leafs of the clover coil sit directly on the distribution manifold; one ishidden to allow viewing of the manifold interior. The anti-bias coils and the curvature coils are stacked on the clover coil, with an insulatingG10 spacer in between. (Inset) An exploded view of the clover coil and the anti-bias coil near the G10 spacer (green), the curvature coil hasbeen omitted for clarity. Insulating Teflon spacers (white) create water flow channels between copper (brown) and brass (yellow) conductivecoil layers. Pink arrows mark the flow of electric current, and blue arrows mark the flow of cooling water.
C182) because of its high strength (similar to brass) and highconductivity (80 % that of copper). With respect to the ori-entation in Fig. 1, current flows counterclockwise around thecrescent and down the outer stack, before reaching the bottomcopper piece, best seen in the inset of Fig. 1. The bottom cop-per piece connects the inner and outer concentric rings suchthat current returns to the top of the coil with the same helic-ity. Current then returns up the stack and is extracted from theinner brass piece through another chromium-copper rod. Thisdouble-coil geometry allows for larger fields for a given cur-rent flow and for current to be inserted and extracted at thesame layer of the stack. Inserting and extracting current at thesame layer facilitates multiple coil stacking.The four parts to the clover coils, referred to individually asleafs, each function as a independent coil stack. Current is in-serted into the bottom of the first leaf (the rightmost in Fig. 1)via a small conducting foot (not shown) and flows counter-clockwise up the leaf. Current flows clockwise down the frontleaf (not shown). This pattern repeats for the left and backleafs. To simplify current transfer between leafs, the top andbottom brass pieces are shared. In order to transfer currentin this way, geometry constrains the number of layers to be N / + qN where N is the total number of vertical cooling chan-nels per leaf and q is any positive integer. In our design, wechoose q =
1. Note that in each leaf, cooling water flows bothazimuthally and radially.Because subtractive manufacturing cannot reasonably pro-duce both azimuthal and radial flows of cooling water for ourstacked Bitter coil geometry, we use a 3D-printed water dis-tribution manifold. As shown in Fig. 1, the manifold con-tains two reservoirs that supply and collect cooling water. Inthe manifold, the supply and collection columns have a crosssection that is quatrefoil-shaped to withstand the compressiveforce from the sealing screws. To connect the channel to the appropriate reservoir, the lobes of the quatrefoil are extendedto form X-shaped tubes. Below the X-shaped connections,the channels extend with circular cross section to the bottomof the manifold, allowing insertion of the sealing screws. Themanifold is made with Accura 48-HTR (a polycarbonate-likematerial) using stereolithography .With the two assemblies symmetrically mounted with aminimum spacing of 3 .
81 cm, we measured the magnetic fieldgenerated by each of the three coils using a three-axis Hallprobe (Lakeshore Model 360 ). The curvature coil generates B (cid:48)(cid:48) = − . / (cm A) and B = − . / A (seeEq. 1). The clover coil generates B (cid:48) = . / (cm A).Finally, the anti-bias coil, when run in Helmholtz configura-tion, generates B = . / A, and, when run in anti-Helmholtz configuration, creates B (cid:48) = − . / (cm A).These values are in good agreement with predictions of thefield strength.We measured the inductance and resistance of each coil bydriving a 100 Hz triangle current wave. Figure 2 shows aplot of applied current and measured voltage response for theclover coil. We fit the voltage response to a sum of a trianglewave and its derivative, a square wave. The amplitude of theformer yields the resistance through V = I / R and the latteryields the inductance through V = L ( dI / dt ). The fitted in-ductance and resistance of the { curvature, anti-bias, clover } coil is { } and { Ω ,13.0(9) m Ω , 32(2) m Ω } , respectively. These values indicatesthat the characteristic current switching time is approximately L / R ≈ { .
05 ms , . , } .We measure the water flow rate as a function of differen-tial pressure, shown in Fig. 3. We achieve a maximum flowof 10.0(3) L min − through the coils at a differential pres-sure of 190(10) kPa. The thermal resistance of the anti-biasand clover coils at 10 L min − flow are 4 . ◦ C kW − and −10.0 −7.5 −5.0 −2.5 0.0 2.5 5.0 7.5 10.0 Time (ms) −75−50−250255075 V o l t a g e ( m V ) −1.5−1.0−0.50.00.51.01.5 C u rr e n t ( A ) FIG. 2. Measurement of the clover coil’s inductance L and resis-tance R . The voltage response (blue) due to the current drive (red) isfit (dashed black line) to extract L and R (see text). P (kPa) Q ( L / m i n ) FIG. 3. Flow rate Q vs. differential pressure P . A power law fit(dashed curve) has an exponent lower than unity, indicating turbulentflow. . ◦ C kW − , respectively. The geometric constraints ofour apparatus prevent us from installing a thermocouple onthe curvature coil, but we have verified that its thermal resis-tance is between that of the clover and anti-bias coils usinga thermal imaging camera. We fit the measured flow rate vs.pressure to a power law, constrained to be zero flow at no dif-ferential pressure, and find an exponent less than unity. Thedeviation from linear behavior indicates the presence of tur-bulent flow in the system, most likely near the plumbing con-nectors of the reservoirs. We expect laminar flow inside thevertical columns and horizontal channels.We have demonstrated a pair of Bitter electromagnet as-semblies with multiple, independent, non-concentric coils that can produce spherical quadruple and Ioffe-Pritchard trapfields. This configuration requires both azimuthal and ra-dial cooling water flows, handled here by a 3D-printed man-ifold. We obtain a low thermal resistance flow rate of10.0(3) L min − at 190(10) kPa yielding a low thermal resis-tance. The manifold and coil design are available online .Our design can be adapted to other non-concentric coil ge-ometries that require fast switching and low thermal resis-tance, such as magnetic transport systems , transverse-fieldZeeman slowers , and uniform Feshbach field generationalong three orthogonal axes .We thank E. Norrgard and G. Reid for their careful read-ing of the manuscript. The data that support the findings ofthis study are available from the corresponding author uponreasonable request. G. Reinaudi, C. B. Osborn, K. Bega, and T. Zelevinsky, J. Opt. Soc. Am.B , 729 (2012). E. W. Streed, A. P. Chikkatur, T. L. Gustavson, M. Boyd, Y. Torii,D. Schneble, G. K. Campbell, D. E. Pritchard, and W. Ketterle, Rev. Sci.Instrum. , 023106 (2006). M. Greiner, I. Bloch, T. W. H¨ansch, and T. Esslinger, Phys. Rev. A ,031401(R) (2001). J. Johansen,
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