First Principle Description of Plasma Expansion using the Expanding Box Model. Implications for CGL Theory in the Solar Wind.

Multiscale modeling of expanding plasmas is crucial for understanding the dynamics and evolution of various astrophysical plasma systems. In this context, the Expanding Box Model (EBM) was used to add the expansion into the kinetic equations, allowing us to describe plasma physics in a new system of reference non-expanding and co-moving with the plasma. This system allows us to maintain a constant volume through non-inertial forces, and its interpretation is fundamental to describing plasma physics.

We have employed the EBM formalism to incorporate the expanding properties of the system into the plasma dynamics, which mainly affects transverse coordinates (i.e., y y/o z). Coordinate transformations were introduced within the co-moving frame system to obtain the modified Vlasov equation. Our main goal is to develop a plasma physics theory through a novel first principle description in the expanding frame, which is fundamentally based on the (collisionless) Vlasov equation for the evolution of the velocity distribution functions. Based on this, the expanding moments, such as the continuity, momentum, and energy equations, can then be derived, and an MHD model of the plasma expansion can be developed. Finally, coupling the obtained moments and Maxwell equations, a CGL-like plasma description is developed in the EB frame to study the evolution of macroscopic quantities (temperature, magnetic field, parallel beta, and anisotropy).

Our results show the expansion affecting the kinetic and fluid equations through non-inertial and fictitious forces in the transverse directions, which contain all the information related to the expansion. These are thus reflected by the equations derived for the expanding moments of the distribution function, including density, bulk (drift) velocity, and pressure (or temperature). Furthermore, we developed an ideal expanding-MHD model based on these modified moments, providing a new interpretation and comparison with the existing results when expansion is considered. The EBM modifies the conservative form of the two adiabatic invariants in the CGL approximation. Equations are solved for radially decreasing magnetic fields and density profiles to study the relations between plasma parallel beta and anisotropy within the expansion.