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Interactions between unidirectional quantized vortex rings

We have used the vortex filament method to numerically investigate the interactions between pairs of quantized vortex rings that are initially traveling in the same direction but with their axes offset by a variable impact parameter. The interaction of two circular rings of comparable radii produce outcomes that can be categorized into four regimes, dependent only on the impact parameter; the two rings can either miss each other on the inside or outside, or they can reconnect leading to final states consisting of either one or two deformed rings. The fraction of of energy went into ring deformations and the transverse component of velocity of the rings are analyzed for each regime. We find that rings of very similar radius only reconnect for a very narrow range of the impact parameter, much smaller than would be expected from geometrical cross-section alone. In contrast, when the radii of the rings are very different, the range of impact parameters producing a reconnection is close to the geometrical value. A second type of interaction considered is the collision of circular rings with a highly deformed ring. This type of interaction appears to be a productive mechanism for creating small vortex rings. The simulations are discussed in the context of experiments on colliding vortex rings and quantum turbulence in superfluid helium in the zero temperature limit.