We report the discovery of torsional Alfvénic oscillations in solar flares , which modulate the time evolution of the magnetic free energy E _ { f } ( t ) , while the magnetic potential energy E _ { p } ( t ) is uncorrelated , and the nonpotential energy varies as E _ { np } ( t ) = E _ { p } + E _ { f } ( t ) .
The mean observed time period of the torsional oscillations is P _ { obs } = 15.1 \pm 3.9 min , the mean field line length is L = 135 \pm 35 Mm , and the mean phase speed is v _ { phase } = 315 \pm 120 km s ^ { -1 } , which we interpret as torsional Alfvénic waves in flare loops with enhanced electron densities .
Most of the torsional oscillations are found to be decay-less , but exhibit a positive or negative trend in the evolution of the free energy , indicating new emerging flux ( if positive ) , magnetic cancellation , or flare energy dissipation ( if negative ) .
The time evolution of the free energy has been calculated in this study with the Vertical-Current Approximation ( Version 4 ) Nonlinear Force-Free Field ( VCA4-NLFFF ) code , which incorporates automatically detected coronal loops in the solution and bypasses the non-forcefreeness of the photospheric boundary condition , in contrast to traditional NLFFF codes .