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Small scale magnetic fields (magnetic elements) are ubiquitous in the solar photosphere. Their interaction can provide energy to the upper atmospheric layers, and contribute to heat the solar corona. In this work, the dynamic properties of magnetic elements in the quiet Sun are investigated. The high number of magnetic elements detected in a supegranular cell allowed us to compute their displacement spectrum (∆r) 2 ∝ τ γ (being γ > 0, and τ the time since the first detection), separating the contribution of the network (NW) and the internetwork (IN) regions. In particular, we found γ = 1.27 ± 0.05 and γ = 1.08 ± 0.11 in NW (at smaller and larger scales, respectively), and γ = 1.44 ± 0.08 in IN. These results are discussed in light of the literature on the topic, as well as the implications for the build up of the magnetic network.

Magnetohydrodynamics (MHD) wave propagation inside the Sun's atmosphere is closely related to the magnetic field topology. For example, magnetic fields are able to lower the cutoff frequency for acoustic waves, thus allowing the propagation of waves that would otherwise be trapped below the photosphere into the upper atmosphere. In addition, MHD waves can be either transmitted or converted into other forms of waves at altitudes where the sound speed equals the Alfvén speed. We take advantage of the large field-of-view provided by the IBIS experiment to study the wave propagation at two heights in the solar atmosphere, which is probed using the photospheric Fe 617.3 nm spectral line and the chromospheric Ca 854.2 nm spectral line, and its relationship to the local magnetic field. Among other things, we find substantial leakage of waves with five-minute periods in the chromosphere at the edges of a pore and in the diffuse magnetic field surrounding it. By using spectropolarimetric inversions of Hinode SOT/SP data, we also find a relationship between the photospheric power spectrum and the magnetic field inclination angle. In particular, we identify well-defined transmission peaks around 25• for five-minute waves and around 15• for three-minute waves. We propose a very simple model based on wave transmission theory to explain this behavior. Finally, our analysis of both the power spectra and chromospheric amplification spectra suggests the presence of longitudinal acoustic waves along the magnetic field lines.

The study of the spatiotemporal scales on which small magnetic structures are organized, may be approached by determining how magnetic elements are transported by convective motions. The process involved is diffusion. Several works explored the topic, both by simulations and observations. In order to constrain the diffusion process, we analyze the displacement of magnetic elements in time, and the evolution of the mutual distance between magnetic element pairs. We take advantage of Hinode high spatial resolution data of a quiet Sun region at the disk center. The large field of view (∼ 50 Mm) and the long duration of observations (over 25 hours without interruption at a cadence of 90 seconds) allowed us to investigate the turbulent flows at unprecedent high spatial and time scales.

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