Efficient Water-Cooled Bitter-Type Electromagnet for Zeeman Slowing in Cold-Atom Experiments

Abstract

We describe the design, construction, and characterization of a Bitter-type electromagnet that produces a spatially-dependent magnetic field used for Zeeman slowing in cold-atom experiments. The coil consists of stacked copper arcs separated by PTFE spacers of varying thicknesses, generating a near-optimal field profile using a single power supply. With an electrical resistance of $26.5(3)$~m$Ω$ and self-inductance of $19.1(1)$~$μ$H, our design achieves a fast electrical switching time of $τ\approx 180$~$μ$s in a compact, 30-cm-long package. Water circulating helically through holes in the copper and channels in the spacers ensures efficient thermal management, limiting the temperature rise to $\sim 5^\circ$~C over $36$~s of continuous operation at $200$~A.

Figures (8)

• Figure 1: Geometry of the coil parts. a) Each conducting layer is an annular piece of OFHC copper of constant thickness, with a single gap, 10 holes for axial cooling water flow, and small alignment notches. Between the layers, a PTFE spacer and copper spacer of equal thickness fit together. The PTFE spacer has 4 channels for azimuthal cooling water flow, and one clover-shaped hole to admit axial cooling water flow, while preventing the threaded rod from contacting the neighboring copper layers. For thin copper spacers, a rubber gasket fits inside the hole and seals the neighboring layers from cooling water leaks. For thicker layers, a thin channel is cut out around a 7 mm hole on both sides of the spacer, so two gaskets form a seal with the neighboring layers. b) The overall coil has 71 copper layers, separated by PTFE spacers, and is held together with axial tension provided by 10 threaded rods. The PEEK endcaps have connections for cooling water---10 at the oven end of the coil, and 2 at the MOT end.
• Figure 2: Schematic of coil layer construction. In one copper layer, the azimuthal electric current, indicated with a green arrow, flows counter-clockwise, and cooling water flows axially in the direction indicated by blue arrows. In the spacer between copper layers, a copper spacer carries electrical current axially, while channels in the PTFE insulator guide the water to flow azimuthally. The strength of the axial magnetic field in the coil center, shown in orange, is controlled by varying the layer and spacer thicknesses.
• Figure 3: Iterative field profile design. (a) a single layer produces a field profile similar to a loop of current, $B(z)\propto a^2/(z^2+a^2)^{3/2}$, where $a$ is the loop radius. The location of the layer is shown with a vertical blue line segment. (b) a collection of many identical layers and spacers produces a nearly constant field profile, similar to a solenoid. (c) increasing the spacing of some of the layers and spacers decreases the local field strength. (d) after several rounds of manually changing the layer spacings among the set of stock thicknesses, we designed a ZS coil to produce a nearly-ideal field profile (green curve) when combined with the field produced by a pair of MOT coils (red curve).
• Figure 4: Magnetic field profile of the Bitter ZS coil at $I = 200$ A. The measured field strength along the central axis of the coil is shown in blue dots and agrees well with the predicted field of the ZS based on our simulations (green curve). The minute deviations are likely due to compressive forces slightly decreasing the length of the PTFE spacers. The total magnetic field (yellow curve) includes contributions from the ZS coil, as well as other electromagnet coils on the experimental chamber. It matches the ideal ZS field profile (dotted line) well between $z\approx 40$ mm and $z=380$ mm, roughly 10 mm from the capture volume of the MOT.
• Figure 5: Electrical impedance $Z$ of the ZS coil as a function of AC current frequency $f$, measured using the circuit in the inset. A controllable current source drove a sense resistor $R_s$ in series with the ZS coil (modeled as a lumped $RL$ circuit with resistance $R$ and self-inductance $L$). The measured impedance $Z(f)= R_s V_\text{coil}/V_s$ (red dots) was fit with the $RL$ series impedance $Z(f)=\sqrt{R^2+4\pi^2f^2L^2}$ (pink curve) to obtain $R = 26.5(3)$ m$\Omega$ and $L=19.1(1)~\mu$H.