Cascade of magnetic energy as a mechanism of coronal heating

A statistical model is defined for the quasi-static evolution of the motion of photospheric structures through a cascade process. Since the magnetic footprints move slowly, the coronal field can adapt to changing boundary conditions as free magnetic energy is transported over timescales significantly smaller than those of the movements of the footprints. The energy is transported as coronal loops are shredded into increasingly finer segments by randomly changing velocity gradients in the photosphere, a process which is stochastic. Numerical computations are provided which show that the magnetic energy is transferred to larger wavenumbers by a cascade process. Application of the model to coronal heating is discussed. 34 references