Reconnections of vortex loops in turbulent superfluid helium: Rates of the breakdown and fusion processes

Kinetics of merging and breaking down of vortex loops is an important part of vortex tangle dynamics. Another part is the motion of individual lines, which obeys the Biot-Savart law in the presence of friction force and of applied external velocity fields if any. In the present work, we evaluate the coefficients of the reconnection rates A(l (1),l (2),l) and B(l,l (1),l (2)). Quantity A is a number (per unit time and unit volume) of events, when two loops with lengths l (1)and l (2) collide and form a single loop of length l = l (1) + l (2). Quantity B(l,l (1),l (2)) describes the rate of events, where a single loop of length l breaks down into two daughter loops of lengths l (1) and l (2). These quantities ave evaluated as the average number of zeroes of vector S (s) (xi (2),xi (1),t) connecting two points on the loops at xi (2) and xi (1) at time t. Statistics of the individual loops is taken from the Gaussian model of vortex tangle.