Vectorial velocity filter for ultracold neutrons based on a surface-disordered mirror system

We perform classical three-dimensional Monte Carlo simulations of ultracold neutrons scattering through an absorbing-reflecting mirror system in the Earth's gravitational field. We show that the underlying mixed phase space of regular skipping motion and random motion due to disorder scattering can be exploited to realize a vectorial velocity filter for ultracold neutrons. The absorbing-reflecting mirror system proposed allows beams of ultracold neutrons with low angular divergence to be formed. The range of velocity components can be controlled by adjusting the geometric parameters of the system. First experimental tests of its performance are presented. One potential future application is the investigation of transport and scattering dynamics in confined systems downstream of the filter.

Figure 1

Schematic view of the ARMS proposed as a filter for the vectorial velocity $\vec{v}$. The system consists of a glass mirror (bottom) and a rough glass plate with surface disorder inducing large-angle disorder scattering and absorption (top). The incident neutron beam leaves the neutron guide through a collimator [for the position of the spacers, see Fig. 8].

Figure 2

A typical surface of the rough upper mirror measured with the scanning electron microscope (SEM). To produce an SEM image the surface was coated with Ni, making the sample electrically conductive. (The measurement was performed at the USTEM facility [25].) The disorder has amplitude $A\sim 3\mu$m and a correlation length $l_{\mathrm{cor}}\sim 2\mu$m.

Figure 3

The projection of the Poincaré surface of section onto the $(p_z,z)$ plane of the phase space for neutron transport consists of a regular island [red (gray) area at the center] representing skipping trajectories, and of an irregular part of chaotic scattering trajectories induced by the surface disorder with roughness amplitude $A$. The yellow (light gray) area with $z$ ranging from $W$ to $W+A$ indicates the region where neutrons scatter off the upper surface.

Figure 4

Velocity distribution $f\left(v_x\right)$ measured by time of flight at the ILL facility for a straight, 2-m long cylindrical neutron guide with 4-cm radius (beamline UCN at PF2).

Figure 5

A sample distribution of 3000 trajectories undergoing chaotic scattering in the top view of the absorbing-reflecting mirror system (ARMS). The trajectories enter with initial conditions $y=0$ and $v_y=0$. Color scale in arbitrary units.

Figure 6

Monte Carlo simulations for the components of the vectorial velocity distribution after passing the ARMS with parameters discussed in Sec. 3a. (a) Distribution of the absolute value of the total velocity $f\left(v\right)$; (b)–(d) distributions of the components $f\left(v_x\right)$, $f\left(v_y\right)$, and $f\left(v_z\right)$; (e), (f) angular distributions $f\left({\theta }_y\right)$ and $f\left({\theta }_z\right)$. The total distributions (solid red lines) can be decomposed into gravitational skipping (dotted blue line) and chaotic scattering (dashed green line) trajectories. Vertical lines correspond to analytical results for the band pass of the velocity components (15, 16, 17). The parameters of the filter are as follows: $W=250\mu$m, $l_x=l_y=10$ cm, $A=3\mu$m, $l_{\mathrm{cor}}=2\mu$m.

Figure 7

Projection of the Poincaré section $x=l_x$ onto the ($v_z$, $z$) plane for the filter system with (a) $l_x=0.1$ m and (b) $l_x=0.2$ m. Only the regular island is visible since the trajectories in the chaotic sea are spread out over a large volume in the phase space resulting in a much reduced density in the projected surface of section compared to the regular island. The structure in the island (a) is due to nonuniform velocity and position distributions at the ARMS entrance. Due to the large number of bounces, the distribution in the island (b) is more homogeneous.

Figure 8

Trajectories representing the limiting velocities for transmission. (a) The solid red line corresponds to the trajectory with minimal forward velocity $v_x$, the dashed blue line to the one with maximal $v_x$. (b) The solid red lines correspond to the trajectories launching with the largest angle ${\theta }_y$ still reflected by the spacers (thick black lines top and bottom); the dashed lines display the same for the case without spacers.

Figure 9

Dependence of the fraction of chaotic scattering $F_c$ (solid line), skipping $(1-F_c)$ (dashed line) trajectories, and the total transmission probability $T$ through the neutron filter (dotted-dashed line) as a function of (a) the filter length $l_x$; (b) the slit width $W$; (c) the amplitude $A$; and (d) the correlation length $l_{\mathrm{cor}}$ of the surface disorder. The parameters of the filter (unless stated otherwise) are as follows: $W=250\mu$m, $l_x=l_y=10$ cm, $A=3\mu$m, $l_{\mathrm{cor}}=2\mu$m.

Figure 10

Classical trajectory Monte Carlo simulations for the filter as in Fig. 6, however, with twice the length $l_x=20$ cm and without spacers. Distributions of (a) the absolute value of the total velocity $f\left(v\right)$; (b)–(d) the velocity components $f\left(v_x\right)$, $f\left(v_y\right)$, and $f\left(v_z\right)$; (e), (f) angular distributions $f\left({\theta }_y\right)$ and $f\left({\theta }_z\right)$ (solid line). Contributions from gravitational skipping and chaotic scattering trajectories are indicated by dotted blue and dashed green lines, respectively. Vertical lines correspond to analytical results for the velocity band pass [see Eqs. (15, 16, 17)]. The parameters of the filter are as follows: $W=250\mu$m, $l_y=10$ cm, $A=3\mu$m, $l_{\mathrm{cor}}=2\mu$m.

Figure 11

The side view of the experimental setup.

Figure 12

The neutron transmission rate through the ARMS as a function of the collimator opening $W_{\mathrm{col}}$. (a) The experimental (blue squares) and calculated (red circles) data. (b) The calculated data (red circles) and its decomposition into chaotic scattering (blue squares) and gravitational skipping (green triangles) contributions. The horizontal dashed line shows a saturation of the amount of gravitational skipping trajectories.

Figure 13

The $z$-coordinate distribution of the detected neutrons measured with a track detector. (a) The experimental (blue squares) and calculated (red circles) data. (b) The calculated data (red circles) and its decomposition into chaotic scattering (blue squares) and gravitational skipping (green triangles) contributions. A horizontal dashed line corresponds to the background noise in the experiment. The light blue (light gray) area shows the contribution of neutrons with predominantly chaotic scattering trajectories.