# Talk abstract

The Parker Problem for Coronal Heating: Magnetically Dominated MHD Turbulence in a Low~\beta Environment

### Abstract

Coronal loops are threaded by a strong magnetic field. As they are so

strongly magnetically dominated a first simplification in modeling

their dynamics is to neglect the velocity field. This is in fact supposed

to be very small in comparison with the Alfv\'en velocity associated

with the DC magnetic field. Setting the velocity equal to zero $u=0$ leads to a static force-free solution. The overall dynamics are then supposed to evolve through a series of equilibria, successively destabilized by magnetic reconnection. We simulate the Parker

problem in the framework of reduced MHD, modeling a coronal loop as an elongated Cartesian box threaded by a strong magnetic field,

whose footpoints are stirred by a velocity mimicking photospheric motions. We confirm that the velocity and magnetic field fluctuations induced in the computational box are very small compared with the strong axial magnetic field, and that velocity fluctuations are smaller than magnetic fluctuations. Both energy spectra develop well-defined

power-laws. We show that the presence of a small but finite velocity

field allows for transfers of energy among shells in Fourier space,

that would be impossible if $u=0$ exactly. We will discuss the properties of these energy fluxes and the differences with standard MHD turbulence characterized by equipartition of magnetic and kinetic energies.

strongly magnetically dominated a first simplification in modeling

their dynamics is to neglect the velocity field. This is in fact supposed

to be very small in comparison with the Alfv\'en velocity associated

with the DC magnetic field. Setting the velocity equal to zero $u=0$ leads to a static force-free solution. The overall dynamics are then supposed to evolve through a series of equilibria, successively destabilized by magnetic reconnection. We simulate the Parker

problem in the framework of reduced MHD, modeling a coronal loop as an elongated Cartesian box threaded by a strong magnetic field,

whose footpoints are stirred by a velocity mimicking photospheric motions. We confirm that the velocity and magnetic field fluctuations induced in the computational box are very small compared with the strong axial magnetic field, and that velocity fluctuations are smaller than magnetic fluctuations. Both energy spectra develop well-defined

power-laws. We show that the presence of a small but finite velocity

field allows for transfers of energy among shells in Fourier space,

that would be impossible if $u=0$ exactly. We will discuss the properties of these energy fluxes and the differences with standard MHD turbulence characterized by equipartition of magnetic and kinetic energies.