Exact periodic solutions of the Liouville equation and the "snake" of density in JET

The "snake" is a persistent density perturbation at the rational q-surfaces after pellet injection. Together with other phenomena (density pinch and profile resiliancy) it can be traced back to the extremum of an action functional for line-vortices in 3D. In a field theoretical formulation this leads to the Liouville equation. We provide explicit method of calculating solutions to the Liouville eq. on periodic domains and obtain, in particular, localised perturbations similar to the experimentally observed "snakes".