Optimizing magnetically shielded solenoids

Abstract

An important consideration when designing a magnetostatic cavity for various applications is to maximize the ratio of the volume of field homogeneity to the overall size of the cavity. We report a design of a magnetically shielded solenoid that significantly improves the transverse field gradient averaged over a volume of 1000 cm³ by placing compensation coils around the holes in the mu-metal end caps rather than the conventional design in which the compensation coils are placed on the main solenoid. Our application is polarized ³He-based neutron spin filters, and our goal was to minimize the volume-averaged transverse field gradient, thereby the gradient induced relaxation time, over a ³He cell. For solenoids with end cap holes of different sizes, additional improvements in the field gradient were accomplished by introducing non-identical compensation coils centered around the non-identical holes in the end caps. The improved designs have yielded an overall factor of 7 decrease in the gradient in the solenoid, hence a factor of 50 increase in the gradient induced relaxation time of the ³He polarization. The results from both simulation and experiments for the development of several such solenoids are presented. Whereas our focus is on the development of magnetically shielded solenoids for ³He neutron spin filters, the approach can be applied for other applications demanding a high level of field homogeneity over a large volume.

FIG. 1.

Schematic of a MSS with round holes on the end caps. The neutron beam travels from right to left in this design. The MSS has the following components: (a) Co-netic mu-metal end caps; (b) the aluminum solenoid with a wall thickness of 2.4 mm for support of the copper winding; (c) Co-netic mu-metal cylinder; (d) copper winding; (e) compensation coils either attached to the end cap (design in this work) or wound on the main coil; (f) borated aluminum neutron shielding pieces attached to the upstream end cap and the downstream compensation coil (not visible).

FIG. 2.

Schematic (a and d) of end compensation and identical hole compensation configurations in a MSS and corresponding contour plots of the calculated normalized B_z profile (b and e) and the calculated ∣∂B_z/∂z∣/B profile (c and f) in the central plane (x = 0) for the region in which the ³He cell is contained. ∣∂B_z/∂z∣/B is in cm⁻¹. (a), (b) and (c) refer to the conventional end compensation approach. (d), (e) and (f) refer to the identical hole compensation approach. The mu-metal body and end cap is shown in black color. Long dotted lines close to the mu-metal cylinder body represent winding of the main solenoid, while the short ones represent winding of the compensation coils. The dashed black line box indicates a region in which the volume-averaged field gradient is the smallest and a ³He cell should be positioned. Note that the contour intervals between (b) and (e) and between (c) and (f) are the same, but the ranges are different for two schemes due to a significant difference in the gradient.

FIG. 3.

Schematic (a and d) of identical and non-identical hole compensation configurations and the corresponding contour plots of the calculated normalized B_z profile (b and e) and the calculated ∣∂B_z/∂z∣/B profile (c and f) in the central plane (x = 0) for the MSS Nyx. ∣∂B_z/∂z∣/B is in cm⁻¹. (a), (b) and (c) refer to the identical hole compensation approach. (d), (e) and (f) refer to the non-identical hole compensation approach. The mu-metal body and end cap is shown in black color. Long dotted lines close to the mu-metal cylinder body represent winding of the main solenoid, while the short ones represent winding of the compensation coils. A focusing neutron beam is drawn to show that the asymmetric hole sizes match the focusing condition. The dashed black line box indicates a region in which the volume-averaged field gradient is the smallest and a ³He cell should be positioned.

FIG. 4.

Calculated NVATGs (open red circles) and NLAGs (solid blue circles) for a 12 cm diameter, 10 cm long cylindrical cell, as a function of the number of turns of compensation coil for (a) Gemini with the end compensation and (b) Honesty with the non-identical hole compensation. The solid lines are to guide the eye.

FIG. 5.

The NVATG $\mid \overrightarrow{\nabla }{B}_{\perp }∕B\mid$ as a function of the diameter of the compensation coil locations for the MSS Gemini.

FIG. 6.

(A) Picture of the MSS Venus in which an RF coil and FID NMR coil can be seen and (B) 3D model of Venus with a 90 degree cut to show the detail of the compensation scheme. The MSS has the following components, (a) Co-netic mu-metal end cap, (b) compensation coil, (c) 3 mm diameter hole for access to the winding wire of the compensation coil, (d) 5 mm by 5 mm notch for access to the winding wire of the main coil, (e) Co-netic mu-metal body, and (f) the aluminum cylinder.

FIG. 7.

Measured normalized B_z field proles for different numbers of turns of compensation during optimization of the MSS Gemini with the identical hole compensation configuration. Fifteen turns of compensation coil (shown in a red solid line) were determined to yield the minimum NLAG. Lines are to guide the eye. Error bars are smaller than the data points. Throughout the paper error bars and uncertainties represent one standard deviation.