Magnetic island merger as a mechanism for inverse magnetic energy transfer

Abstract

Magnetic energy transfer from small to large scales due to successive magnetic island coalescence is investigated. A solvable analytical model is introduced and shown to correctly capture the evolution of the main quantities of interest, as borne out by direct numerical simulations. Magnetic reconnection is identified as the key mechanism enabling the inverse transfer, and setting its properties: Magnetic energy decays as [˜ over t][superscript −1], where [˜ over t] is time normalized to the (appropriately defined) reconnection timescale, and the correlation length of the field grows as [˜ over t][superscript 1/2]. The magnetic energy spectrum is self-similar, and evolves as ∝[˜ over t][superscript −3/2]k[superscript −2,] where the k dependence is imparted by the formation of thin current sheets.