Neutron lifetime measurements and effective spectral cleaning with an ultracold neutron trap using a vertical Halbach octupole permanent magnet array

Ultracold neutron (UCN) storage measurements were made in a trap constructed from a 1.3-T Halbach octupole permanent (HOPE) magnet array aligned vertically, using the TES port of the PF2 source at the Institut Laue-Langevin. A mechanical UCN valve at the bottom of the trap was used for filling and emptying. This valve was covered with Fomblin grease to induce nonspecular reflections and was used in combination with a movable polyethylene UCN remover inserted from the top for cleaning of above-threshold UCNs. Loss from UCN depolarization was suppressed with a minimum 2-mT bias field. Without using the UCN remover, a total storage time constant of $(712\pm 19)\mathrm{s}$ was observed; with the remover inserted for 80 s and used at either 80 cm or 65 cm from the bottom of the trap, time constants of $(824\pm 32)\mathrm{s}$ and $(835\pm 36)\mathrm{s}$ were observed. Combining the latter two values, a neutron lifetime of ${\tau }_{\mathrm{n}}=(887\pm 39)\mathrm{s}$ is extracted after primarily correcting for losses at the UCN valve. The time constants of the UCN population during cleaning were observed and compared to calculations based on kinetic theory as well as Monte Carlo studies. These calculations are used to predict above-threshold populations of $\sim 5\%,\sim 0.5\%$, and $\sim {10}^{-12}\%$ remaining after cleaning in the no-remover, 80-cm remover, and 65-cm remover measurements. Thus, by using a nonspecular reflector covering the entire bottom of the trap and a remover at the top of the trap, we have established an effective cleaning procedure for removing a major systematic effect in high-precision ${\tau }_{\mathrm{n}}$ experiments with magnetically stored UCNs.

Figure 1

Schematic and photo of the first phase experiments with the HOPE magnetic trap performed on the PF2-TES port using a mechanical UCN piston valve for filling and emptying.

Figure 2

(Main plot) Contour plots of the UCN potential energy $U_{\mathrm{pot}}\left(\vec{r}\right)$ in the trapping region on vertical slices passing through $\rho =0$. On the left for $\varphi =0$ and on the right for $\varphi =7.5^{\circ }$ (see text). Zero potential is defined to be at $z=0$ and $\rho =0$. The aperture for the UCN piston valve at the bottom of the trap and the epoxy on the magnet sidewall is not shown. The location of the Fomblin grease on the valve piston, valve seat, and magnet sidewall is shown with lines in a color to match that of $U_{\mathrm{Fomblin}}$. (Left) Zoomed into the bottom left-hand corner of the main plot (i.e., the $\varphi =0$ slice). The trapping potential $U_{\mathrm{trap}}=84\mathrm{neV}$, shown as the solid black line, is defined by the height of the Fomblin grease on the sidewall. This contour is $5\mathrm{cm}$ lower when $\varphi =7.5^{\circ }$. The contours of the two remover potentials $U_{\mathrm{rm}}$ for $h_{\mathrm{PE}}=80\mathrm{cm}$ and $65\mathrm{cm}$ are also shown. These contours are $2\mathrm{cm}$ and $0.5\mathrm{cm}$ lower when $\varphi =7.5^{\circ }$, respectively.

Figure 3

(Blue line) The effective volume $V_{\mathrm{eff}}$ of the trapping configuration with no PE remover versus the total energy $E_{\mathrm{tot}}$. When the remover is in place, UCNs with $E_{\mathrm{tot}}>U_{\mathrm{rm}}$ experience a reduced $V_{\mathrm{eff}}$. (Green circles with error bars) The measured $N_{0,\mathrm{slow}}$, the number of UCNs initially loaded into the trap with $E_{\mathrm{tot}}<U_{\mathrm{rm}}$, for different PE remover heights. (Green dashed line) The green points fitted with Eq. (9) to determine the shape of the integral UCN spectrum $N_0(E_{\mathrm{tot}}<U_{\mathrm{rm}})$. The relationship between $V_{\mathrm{eff}}\left(E_{\mathrm{tot}}\right)$ and $N_0(E_{\mathrm{tot}}<U_{\mathrm{rm}})$ is described in the text near Eq. (9).

Figure 4

The effective loss area $A_{\mathrm{eff}\mathrm{loss}}\left(E_{\mathrm{tot}}\right)$ normalized by $f_{\mathrm{Fomblin}}$ for the Fomblin grease at the bottom and sidewall. The loss time constant from both these surfaces ${\tau }_{\mathrm{walls}}^{-1}$, also normalized by $f_{\mathrm{Fomblin}}$, is also shown. All these quantities assume kinetic theory.

Figure 5

The effective loss area $A_{\mathrm{eff}\mathrm{loss}}\left(E_{\mathrm{tot}}\right)$ for the epoxy on the trap sidewall and for the PE UCN remover, placed at two different heights $h_{\mathrm{PE}}$. The epoxy is assumed to have the same $U_{\mathrm{opt}}$ and $f$ as the PE.

Figure 6

The count rate at the UCN detector during several measurement procedures for $t_{\mathrm{hold}}\ge 35\mathrm{s}$. The details of a procedure and the cause of the peaks are described in the text.

Figure 7

Storage curves for the no remover and $h_{\mathrm{PE}}=80\mathrm{cm}$ measurements. The vertical dashed line is shown to indicate $t_{\mathrm{clean}}=80\mathrm{s}$, the time when the PE remover was raised. The zoomed-in regions are to show details for short $t_{\mathrm{hold}}$. The solid lines are from fits with a sum of two exponential decays (see text).

Figure 8

Analyses of the storage curves by fitting with a single exponential decay with time constant ${\tau }_{1\text{−}\exp }$ and scanning the starting $t_{\mathrm{hold}}$ of the fit. The vertical dashed line is used to indicate $t_{\mathrm{clean}}=80\mathrm{s}$, the time when the remover was raised. For comparison, the ${\tau }_{\mathrm{slow}}$ values extracted from the sum of two exponential decay fits are also shown in these plots as horizontal green lines, with the dashed lines being the $\pm 1\sigma$ range.

Figure 9

The calculated cleaning time constants ${\tau }_{\mathrm{clean}}\left(E_{\mathrm{tot}}\right)$ using kinetic theory [Eq. (10)] and Monte Carlo (MC) simulations. There are no losses at the sidewall in the MC simulations hence the kinetic theory calculations with no sidewall loss are also plotted for comparison.

Figure 10

Calculated relative number of UCNs with energy $U_{\mathrm{rm}}<E_{\mathrm{tot}}<U_{\mathrm{rm}}+30\mathrm{neV}$, denoted by $N(t_{\mathrm{hold}},U_{\mathrm{rm}}<E_{\mathrm{tot}}<U_{\mathrm{rm}}+30\mathrm{neV})$, remaining in the trap during cleaning (i.e., when $t_{\mathrm{hold}}<t_{\mathrm{clean}}=80\mathrm{s}$) using ${\tau }_{\mathrm{clean}}\left(E_{\mathrm{tot}}\right)$ from kinetic theory for the PE remover at 80 and $65\mathrm{cm}$ including the sidewall loss, and for no remover (i.e., sidewall loss only). The measured $E_{\mathrm{tot}}^{2.5}$ UCN spectrum is used in these calculations. The numbers are normalized to unity at $t_{\mathrm{hold}}=0$. The dashed lines are single exponential fits between $20\mathrm{s}<t_{\mathrm{hold}}<40\mathrm{s}$ (fit region indicated by the vertical dash-dotted lines) used to estimate ${\tau }_{\mathrm{fast}}$.

Figure 11

The calculated number of the UCNs with $U_{\mathrm{trap}}<E_{\mathrm{tot}}<U_{\mathrm{trap}}+10\mathrm{neV}$ remaining during the cleaning process (i.e., $t_{\mathrm{hold}}\le 80\mathrm{s}$) normalized to the initial number of UCNs with $E_{\mathrm{tot}}<U_{\mathrm{rm}}$. The latter is approximately constant to $\sim 10\%$ during cleaning because of the long ${\tau }_{\mathrm{tot}}$ for well-trapped UCNs $\left(E_{\mathrm{tot}}<U_{\mathrm{trap}}\right)$. This is done for all three remover configurations using the measured $E_{\mathrm{tot}}^{2.5}$ UCN spectrum and based on the kinetic theory and a simplified MC study. This plot is used to estimate the fraction of above-threshold UCNs remaining after cleaning to study the effectiveness of a cleaning procedure.

Figure 12

The observed total storage time constants for the three remover configurations for $t_{\mathrm{hold}}>80\mathrm{s}$ (i.e., after cleaning) with statistical error bars $\left({\sigma }_{\mathrm{stat}}\right)$. The extracted neutron lifetimes ${\tau }_{\mathrm{n}}$, assuming effective cleaning, are plotted next to these values. The error bars have the statistical error and the total systematic error combined in quadrature $\left[{({\sigma }_{\mathrm{stat}}^2+{\sigma }_{\mathrm{sys}}^2)}^{1/2}\right]$. These values are compared with the Particle Data Group (PDG) values [63, 64].

Figure 13

The total storage time constant ${\overline{\tau }}_{\mathrm{tot}}$ when scanning the bias field solenoid current. The measurements were made in earlier angled-trap experiments (see text) before Fomblin grease was applied on the valve piston and valve seat (“without Fomblin”) and after Fomblin grease was applied (“with Fomblin”). The dashed lines are used to guide the eye only.

Figure 14

Schematic of the next phase measurements of the HOPE project with full 3D magnetic trapping. The movable components are shown with the green arrows and nominal “flow” of UCNs into and out of the shown parts of the setup are indicated by the red arrows. The superconducting upper end coil is only used if focusing of the charged neutron decay products onto a detector is required (not discussed in this paper).