Validity of using Elsässer variables to study the interaction of compressible solar wind fluctuations with a coronal mass ejection

Alfvénic fluctuations, as modelled by the non-linear interactions of Alfvén waves of various scales, are seen to dominate solar wind turbulence. However, there is also a non-negligible component of non-Alfvénic fluctuations. The Elsässer formalism, which is central to the study of Alfvénic turbulence due to its ability to differentiate between parallel and anti-parallel Alfvén waves, cannot strictly separate wavemodes in the presence of compressive magnetoacoustic waves. In this study, we analyse the deviations generated in the Elsässer formalism as density fluctuations are naturally generated through the propagation of a linearly polarised Alfvén wave. The study was performed in the context of a coronal mass ejection (CME) propagating through the solar wind, which enables the creation of two solar wind regimes, pristine wind and a shocked CME sheath, where the Elsässer formalism can be evaluated. In these two regimes we studied the deviations of the Elsässer formalism in separating parallel and anti-parallel components of Alfvénic solar wind perturbations generated by small-amplitude density fluctuations. We used an ideal 2.5D magnetohydrodynamic (MHD) model with an adiabatic equation of state. An Alfvén pump wave was injected into the quiet solar wind by perturbing the transverse magnetic field and velocity components. This wave subsequently generates density fluctuations through the ponderomotive force. A CME was injected by inserting a flux-rope modelled as a magnetic island into the quasi-steady solar wind. The presence of density perturbations creates an approximately 10 reflection coefficient for the Alfvén waves as well as a deviation of approximately 0.1 in the cross helicity in regions containing both parallel and anti-parallel fluctuations.