He₂^* cluster tracking velocimetry technique

Another technique that we are developing is based on tracking small He₂^* clusters created in He II via neutron-³He absorption reactions. A compelling reason for developing this technique is that it will produce full-space velocity-field information that can hardly be obtained using the tracer-line tracking method. Knowing the full-space velocity field is essential in visualizing eddy structures and large-scale flow patterns that in some cases can control the flow properties [1]. In the past, many efforts were devoted in developing PTV methods for mapping the normal-fluid velocity field by tracking seeded micron-sized tracers [1-4]. However, these methods all have inherent issues since the tracer motion can be affected by both the normal fluid and the vortices. Our He₂^* cluster tracking technique will provide an ultimate solution to the long-lasting quest for unambiguous normal-fluid velocity field measurement.

Figure 1: (a) Schematic diagram showing the neutron-³He absorption reaction that leads to the creation of a cluster of about 10⁴ He₂^* molecules. (b) A fluorescence image of a cloud of about 10³ He₂^* molecules, produced by pulsing a needle source in He II [9]. We expect higher fluorescent light intensity from the clusters as they comprise more He₂^* molecules.

³He atoms that exist in He II as impurity particles can absorb neutrons (see the reaction schematic in Fig. 1 (a)) [5]. The absorption cross-section σ depends on the energy of the incident neutrons and can be quite large for thermal neutrons that have spins aligned with the ³He atoms (i.e. σ ~ 10^-20 cm²) [6]. This reaction produces two charged particles, a proton (¹H) and a tritium (³H), that move back to back with a total kinetic energy of 764 keV [7]. The two particles have sufficient energies to ionize and excite ground state ⁴He atoms along their tracks in He II , which leads to the generation of He₂^* molecules. The total length of the two tracks is about 80 μm, evaluated based on the known energy deposition rate of ¹H and ³H in helium [7]. We also estimate that more than 10⁴ molecules are produced, considering the fraction of the kinetic energy that goes to the generation of He₂^* molecules [8]. Therefore, every n-³He absorption event in He II creates a cluster of about 10⁴ He₂^* molecules. Imaging these clusters should be feasible since we have already demonstrated high-quality fluorescence imaging of tiny clouds of He₂^* molecules in He II (see Fig. 1 (b)) [9]. Due to the small molecular diffusion (~ 10 μm during typical drift time), every cluster can be treated as a single tracer, and a spatial resolution of a few tens of microns is achievable. Tracking these clusters will allow us to map out the full velocity field.

In order to study the generation of He₂^* clusters in He II as well as to characterize their size and intensity distributions, we have established a collaboration with a group of researchers at Nagoya University (i.e. Prof. Shimizu, Prof. Tsuji, Prof. Wada, et al.) to conduct experiments using the J-PARC neutron facility in Japan [10]. Our plan is to pass a thermal neutron beam with a suitable flux (i.e. ~10⁴/cm² per pulse) through a He II filled cell (see Fig. 2). By adjusting the concentration of ³He impurity, we will be able to tune the number density of the resulted He₂^* clusters. For instance, even with a ³He concentration as low as 50 ppm (part per million), about 10² clusters will be produced per 1 cm³ volume of He II, sufficient for velocity-field mapping purpose. This work will also lead to a sensitive mechanism for neutron detection.

Reference:

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