Turbulence in magnetized plasmas: Compressibility, cascade properties and diagnostics

This thesis presents an investigation on how magnetic fields and compressibility affect turbulence in astrophysical plasmas, and how these effects can be detected through observations. By combining numerical simulations of plasma turbulence with analytical tools, the research accomplishes three main goals: improving magnetic field measurements using polarized light, creating a method to identify different magnetohydrodynamic modes in synchrotron observations, and studying how fast magnetosonic waves transfer energy through turbulent plasmas. The first part develops a technique to measure magnetic field strength in turbulent regions using polarized spectral lines from atoms. This modified Davis-Chandrasekhar-Fermi (DCF) method accounts for how measurements are averaged across the line of sight, and produces reliable estimates of the magnetic field direction in the plane of the sky. In a novel approach, the DCF method is adapted to work with polarized spectral lines from the ground state alignment effect, which are less affected by dust alignment issues such as uncertainties in dust grain size, shape and composition. Tests using synthetic polarized line emissions from simulated turbulence show that the method performs as well as dust-based measurements while avoiding complications from dust alignment. The method remains stable across different turbulence properties, confirming its theoretical foundation and practical value for observational work. The second part presents a new statistical diagnostic to identify which types of magnetohydrodynamic waves dominate the energy in compressible turbulence using polarized synchrotron radiation. The modified synchrotron polarization analysis (SPA+) method relies on how the variance of the synchrotron emissivity varies with with respect to the mean magnetic field direction, which encodes information about the dominant MHD modes. Application of the SPA+ method to synthetic polarized synchrotron observations demonstrates its ability to recover the dominant MHD modes. The symmetric component of the signature function successfully separates regimes where \ waves dominate from those where compressible waves are stronger. Additionally, asymmetric features reveal the distinctive signature of the fast magnetosonic mode, enabling their direct detection for the first time in observations. In the final part of the thesis, the fast magnetosonic cascade is examined through dedicated simulations of decaying fast modes that isolate these waves in compressible turbulence. The simulations reveal that energy spectra are steeper than weak acoustic wave theory predicts, with a shock-dominated k^-2 spectra observed in the simulations. However, the cascade rate at the energy injection scale follows predictions from the weak acoustic picture, with the cascade time cas k^-1/2. This suggests that shocks and nonlinear effects steepen the spectrum, but are unable to terminate the cascade efficiently, which remains governed by weakly nonlinear interactions and acoustic-like energy cascade. These findings have important implications for understanding energy transfer and dissipation in astrophysical plasmas where fast modes can interact with and effectively scatter cosmic-rays. Overall, this work demonstrates how simulations and observational diagnostics together can illuminate the complex behavior of magnetized turbulent plasmas in astrophysics, opening new paths for better understanding of plasma properties through numerical simulations and observations.