Ultracold neutron accumulation in a superfluid-helium converter with magnetic multipole reflector

We analyze the accumulation of ultracold neutrons (UCNs) in a superfluid-helium converter vessel surrounded by a magnetic multipole reflector. We solved the spin-dependent rate equation, employing formulas valid for adiabatic spin transport of trapped UCNs in mechanical equilibrium. Results for saturation UCN densities are obtained in dependence of order and strength of the multipolar field. The addition of magnetic storage to neutron optical potentials can increase the density and energy of the low-field-seeking UCNs produced and serves to mitigate the effects of wall losses on the source performance. It also can provide a highly polarized sample of UCNs without need to polarize the neutron beam incident on the converter. This work was performed in preparation of the UCN source project SuperSUN at the Institut Laue–Langevin.

Figure 1

Schematic of the UCN accumulator comprised of a superfluid ${}^4\mathrm{He}$ converter with multipole magnet and system for UCN extraction. On the left a cut view is shown for $n=12$; filled (open) squares indicate electric current flowing into (out of) the plane. The neutron optical potentials are $V$ for the cylindrical inner surface over the length $L$, $\tilde{V}$ at the beam window and at the UCN valve, respectively, $\ge \tilde{V}$ for the UCN extraction system, and $V_{\mathrm{He}}\approx 18.5\mathrm{neV}$ in the superfluid.

Figure 2

Schematic of the magnetic and neutron optical potentials in the closed UCN accumulator shown in Fig. 1. In the upper figure, $V-V_{\mathrm{He}}>V_{\mathrm{m}R}$. Low-field-seeking (lfs) UCNs with total energy ${\epsilon }_0<\tilde{V}-V_{\mathrm{He}}$ are trapped (solid-line shade). High-field-seeking (hfs) UCNs with $0<{\epsilon }_0<V-V_{\mathrm{He}}-V_{\mathrm{m}R}$ are trapped, too (dashed-line shade), leading to polarization $P_{\infty }<1$ according to Eq. (9). The lower figure illustrates the situation $V-V_{\mathrm{He}}<V_{\mathrm{m}R}$ where hfs UCNs with ${\epsilon }_0>0$ are free to escape, hence $P_{\infty }=1$. Only hfs UCNs with ${\epsilon }_0<0$ (horizontal dotted shade) are trapped which, however, will stay in the regions with strong magnetic field when opening the UCN valve.

Figure 3

Saturated densities of low-field-seeking and high-field-seeking UCNs in a converter vessel with diameter 10 cm held at $0.5$ K and surrounded by a 12-pole and 8-pole magnet, respectively. Calculations employ Eq. (34) for $\tilde{V}=V=252$ neV (e.g., for a converter vessel made entirely of Be), and for various values of $f=W/V$. The solid lines show results for the best value of $f$ previously achieved for Be, while the upmost curves show the situation for unrealistically low $f$ for illustration. Values are given for an unpolarized differential neutron flux density of ${\mathrm{\Phi }}_{0.89\mathrm{nm}}={10}^9{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}{\mathrm{nm}}^{-1}$ at $\lambda =0.89$ nm, as available at the monochromatic beam position H172A at the ILL. A characteristic time constant ${\tau }_0$ is calculated for neutrons with velocity $v=\frac{3}{4}{v}_{max}$, including in Eq. (10) the rates ${\tau }_{\beta }^{-1}$, ${\tau }_{\mathrm{up}}^{-1}$, and the wall collisional losses calculated using Eq. (23) for $V_{\mathrm{m}R}=0$ and ${\epsilon }_0=\frac{9}{16}{V}_{\mathrm{trap}}$.

Figure 4

Saturated densities of low-field-seeking and high-field-seeking UCNs in converter vessels with diameter 10 cm, $V=252$ neV, $f=3\times {10}^{-5}$, $T=0.5$ K, and beam window and UCN valve (see Fig. 1) coated with three different materials with values of $\tilde{V}$ as indicated in the legend. The thicker of each pair of curves is for multipolarity $n=12$, the thinner is for $n=8$, and all values are given for ${\mathrm{\Phi }}_{0.89\mathrm{nm}}={10}^9{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}{\mathrm{nm}}^{-1}$ (unpolarized). The kinks visible for the two upper pairs of curves appear at field values corresponding to $V_{\mathrm{m}R}=\tilde{V}-V$. Densities of the hfs UCNs for $\tilde{V}\ge V$ are independent of $\tilde{V}$ but are smaller for the higher multipole order.

Figure 5

Saturated densities of low-field-seeking and high-field-seeking UCNs in converter vessels with diameter 10 cm, $V=252$ neV, $T=0.5$ K, $f=3\times {10}^{-5}$ (solid curves) or $f=2\times {10}^{-4}$ (dashed curves). Beam window and UCN valve (see Fig. 1) are coated with ${\mathrm{C}}^{11}\mathrm{BN}$ with $\tilde{V}=330$ neV. The magnetic multipole order is varied between $n=6$ and 24. Values are given for ${\mathrm{\Phi }}_{0.89\mathrm{nm}}={10}^9{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}{\mathrm{nm}}^{-1}$ (unpolarized).

Figure 6

Saturated density of low-field-seeking UCN in converter vessels with diameter 10 cm, $V=252$ neV, $T=0.5$ K, and surrounded by a 12-pole magnet. Solid curves are for $f=3\times {10}^{-5}$, dashed ones for $f=2\times {10}^{-4}$. $\tilde{V}-V_{\mathrm{He}}$ is varied between 60 neV and 311 neV. Values are given for ${\mathrm{\Phi }}_{0.89\mathrm{nm}}={10}^9{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}{\mathrm{nm}}^{-1}$ (unpolarized).