Quantifying the Expanding and Cooling Effects into the Double Adiabatic Evolution of the Solar Wind Through the Expanding Box Model

One of the fundamental problems in space physics is the expansion dynamics of the solar wind, strongly correlated with collective plasma reactions, such as wave instabilities that tend to relax kinetic anisotropies. The expansion is in general described through the double adiabatic or Chew-Goldberger-Low (CGL) theory, which sets the main ideas and plasma expansion’s major role in describing plasma cooling/heating dynamics. Here, using the expanding box model (EBM) we revisit the CGL description including plasma expansion. Our primary objective is to isolate the expanding effects into the conservation of the double adiabatic invariants, a key aspect of the CGL theory. Following the same approximations and assumptions as in EBM and CGL theory, we developed a CGL-like description in which the expansion modifies the conservation of the double adiabatic invariants. Our results show that the double adiabatic equations are no longer conserved if plasma cooling is introduced through the EBM, with explicit dependence on expanding parameters, magnetic field profiles, and velocity gradients. Solving the equations for different magnetic field and density profiles (obtained self-consistently through the equations), we compute the evolution of temperature anisotropy and plasma beta, which deviates from CGL predictions and empirical observations. This deviation is attributed to the plasma cooling effect induced by the expansion of the plasma. The results suggest that heating mechanisms even play a major role in counteracting plasma cooling during expansion.