Abstract
Andreev scattering of thermal excitations is a powerful tool for studying quantized vortices and turbulence in superfluid $^{3}\mathrm{He}\text{\ensuremath{-}}\mathrm{B}$ at very low temperatures. We write Hamilton's equations for a quasiparticle in the presence of a vortex line, determine its trajectory, and find under which conditions it is Andreev reflected. To make contact with experiments, we generalize our results to the Onsager vortex gas and find values of the intervortex spacing in agreement with less rigorous estimates.
Highlights
The use of Andreev scattering as a visualization technique of ultra–low temperature turbulence requires to find out exactly what happens to a single quasiparticle which moves in the velocity field of a vortex, which is what we set out to do
To apply our result to experiments, we consider for simplicity a system of random parallelantiparallel vortices (i.e. a system of vortex points in the (x, y)-plane; such a system is known as the Onsager vortex gas)
Starting from Hamilton’s equations, we have calculated the trajectories of quasiparticles which move in the velocity field of a quantized vortex in 3He-B and determined the Andreev reflection point
Summary
Superfluid turbulence consists of a disordered tangle of quantized vortex filaments which move under the velocity field of each other[1, 2]. Questions which are currently addressed concern (i) the existence of a Kolmogorov energy cascade at length scales larger than the typical intervortex spacing[4, 5], (ii) the existence of a Kelvin wave cascade at length scales smaller than the Kolmogorov length[6, 7, 8, 9] followed by (iii) acoustic emission at even shorter length scales[10, 11], (iv) the possible existence of a bottleneck[12, 13] between the Kolmogorov cascade and the Kelvin wave cascade, (v) the nature of the fluctuations of the observed vortex line density[14, 15, 16, 17] and (vi) their decay[18, 19], (vii) whether there are two forms of turbulence[20], a structured one, which consists of many length scales (Kolmogorov turbulence), and an unstructured, more random one (Vinen turbulence), (viii) the effects of rotation on turbulence[21, 22, 23, 24] Most of these questions refer to the important limit T /Tc ≪ 1, where fundamental distinctions between a perfect Euler fluid and a superfluid becomes apparent[25].
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