Numerical simulations of waves and turbulence in coronal loops: observables and spectra
We investigate numerically the time evolution of velocity and magnetic field fluctuations in a coronal loop, focusing on the dynamics due to both phase mixing and turbulent cascade. The intensity, doppler velocity and non-thermal broadening are synthesized from numerical results in order to establish if the upcoming Multi-slit Solar Explorer (MUSE) mission could reveal the presence of those phenomena in the solar corona through its unprecedented high-resolution spectroscopic observations. The loop is represented by a cylindrical pressure-balanced magnetic structure with a transverse density and magnetic field inhomogeneity. The initial perturbation is a superposition of a torsional Alfv\'en wave and a transverse turbulent component with different tunable weights. In order to reconstruct plasma emission features we calculate moments of the Fe IX 171 \AA\ spectral line. 2D maps obtained by integrating the emission along the assumed line of sight are calculated for the emission intensity $I_0$, the Doppler shift $I_1$ and the non-thermal broadening $I_2$, for several values of the model parameters. Finally, we simulate MUSE spectrograph by considering a resolution of $312$ km $\times$ $312$ km. We observe how intensity maps show the formation of longitudinal threads. The generation of small-scale fluctuations mainly takes place in the inhomogeneity region at the loop boundary, where the effects of phase mixing and non-thermal broadening are stronger. 1D power spectra of intensity and Doppler shift maps are calculated and compared with the corresponding spectra of density and line-of-sight velocity component. The agreement observed between the spectral indexes of the intensity power spectra at MUSE resolution and the one computed from the full 3D density field indicates that spectra of $I_0$ can be used to infer information on the spectrum of density inside a loop.