Contained modes in mirrors with sheared

In this report, we investigate the phenomenon of contained modes in mirrors subjected to sheared rotation, particularly focusing on the implications of E × B rotation on wave propagation. The objective is to discern how a fixed azimuthal perturbation observed in the laboratory frame translates into a wave in the rotating plasma frame. By recognizing that the rotation frequency varies radially, we apply a comprehensive analysis rooted in Doppler shift principles to understand the implications of varying wave frequencies across different radii. Our methodology combines theoretical analysis with simulations to illustrate the behavior of waves in the presence of a sheared rotation profile. Results indicate that these Doppler shifts are significant, leading to a deeper understanding of wave dynamics in rotating systems. This understanding is critical for advancing the design and functionality of plasma confinement in fusion reactors. This research contributes to ongoing efforts in plasma physics and offers insights that could enhance the efficiency of future fusion energy systems.