New insight into short wavelength solar wind fluctuations from Vlasov theory

The nature of solar wind (SW) turbulence below the proton gyroscale is a topic that is being investigated extensively nowadays. Although recent observations gave evidence of the dominance of Kinetic Alfv\'en Waves (KAW) at sub-ion scales with $\omega\omega_{ci}$) is more relevant. Here, we propose to study key properties of the short wavelength plasma modes under realistic SW conditions, typically $\beta_i\gtrsim \beta_e\sim 1$ and for high oblique angles of propagation $80^\circ\leq \Theta_{\bf kB}<90^\circ$ as observed from the Cluster data. The linear properties of the plasma modes under these conditions are poorly known, which contrasts with the well-documented cold plasma limit and/or moderate oblique angles of propagation ($\Theta_{\bf kB} <80^\circ$). Based on linear solutions of the Vlasov kinetic theory, we discuss the relevance of each plasma mode (fast, Bernstein, KAW, whistler) in carrying the energy cascade down to electron scales. We show, in particular, that the shear Alfv\'en mode extends at scales $k\rho_i\gtrsim1$ following either a whistler mode ($\omega>\omega_{ci}$) or a KAW mode (with $\omega