Abstract: Crucial aspects related to energy transport and dissipation into heat within the higher layers of the solar atmosphere remain poorly understood. An essential parameter for characterizing energy flow and its direction is the Poynting flux, primarily used in solar physics to estimate the upward energy generated by plasma motion in the photosphere.

This study presents a three-dimensional mapping of magnetic energy transport within a numerically simulated solar atmosphere for the first time. By computing the Finite Time Lyapunov Exponent of the energy velocity (defined as the ratio of Poynting flux to magnetic energy density), we pinpoint the sources and destinations of magnetic energy flow across the solar atmosphere. The energy mapping indicates the presence of energy transport barriers limiting the flow of magnetic energy from the photosphere to the upper atmosphere, suggesting that estimates of energy upflow from photospheric motion may overestimate energy reaching the chromosphere and corona. Our investigation shows that vortices act as energy channels, breaching these barriers and significantly changing energy mapping (sources and deposition location of energy). Magnetic energy generated by the vortices is continuously transported upward as a Poynting flux vortex, with a portion of the energy concentrated around vortices and the remaining energy moving into higher atmospheric layers. Also, our results show an increase in magnetic energy availability about three times higher than before the vortices were established. Moreover, our research demonstrates that the presence of vortices gives rise to conditions characterized by significant magnetic and velocity field gradients at small scales, facilitating the dissipation of magnetic energy and the heating of the plasma.