Using the two-dimensional model, we compute the ensemble average Andreev reflection coefficient of a flux of thermal quasiparticles in 3He-B incident upon the system of point vortices, each moving in the flow field generated by all other vortex points. In the case where the initial positions of all point vortices are random, such a vortex gas can be regarded as a (somewhat crude) two-dimensional model of a real, three-dimensional vortex tangle. On the other hand, in the case where vortices and antivortices are arranged in pairs, a random system of such pairs models, in two dimensions, a gas of three-dimensional vortex rings. Of particular interest is the change of the average Andreev reflection coefficient with the transition from a gas of vortex-antivortex pairs to a random system of point vortices. Our study is particularly motivated by the experimental observation at Lancaster University of the transition from a gas of vortex rings to a dense tangle. The question which we ask is whether a gas of vortex rings and a dense tangle have a different Andreev signature. We found that, due to the partial screening, a transition from the gas of vortex-antivortex pairs to the random point vortex gas is associated with the several-fold increase of the reflection coefficient. We note that these results, although consistent with observations at Lancaster, should be regarded as qualitative rather than quantitative.
Sergeev, Y. A., Barenghi, C. F., & Dijk, P. J. V. (2010). Two-dimensional model of interactions between thermal quasiparticles and turbulent structures in 3He-B. EPL, 90(5). https://doi.org/10.1209/0295-5075/90/56003