When magnetic nux penetrates a type-II superconduct or, it does so as
quantized flux lines or vortex lines, so called because each is surrou
nded by a supercurrent vortex. Interactions between such vortices lead
to a very rich and well characterized phenomenology for this 'mixed s
tate'. But an outstanding question remains: are individual vortex Line
s 'strong', or can they easily be cut and made to pass through one ano
ther? The concept of vortex cutting was originally proposed to account
for dissipation observed in superconducting wires oriented parallel t
o an applied magnetic field, where the vortex lines and transport curr
ent should be in a force-free configuration(1-6). Previous experiments
, however, have been unable to establish the vortex topology in the fo
rce-free configuration or the size of the energy barrier for vortex cu
tting. Here we report magneto-optical images of YBa2Cu3O7-delta sample
s in the force-fi-ee configuration which show that thousands of vortex
lines can twist together to form highly stable structures. In some ca
ses, these 'vortex twisters' interact with one another to produce wave
-like dynamics. Our measurements also determine directly the current r
equired to initiate vortex cutting, and show that it is much higher th
an that needed to overcome the pinning of vortices by material defects
. This implies that thermodynamic phases of entangled vortices(7-10) a
re intrinsically stable and may occupy a significant portion of the mi
xed-state phase diagram for type-II superconductors.