Torsional Alfvénic Oscillations Discovered in the Magnetic Free Energy During Solar Flares

Abstract: We report the discovery of torsional Alfv\'enic 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 $L=135\pm35$ Mm, and the mean phase speed is $v_{phase} =315 \pm 120$ km s$^{-1}$, which we interpret as torsional Alfv\'enic 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 {\sl 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.