Velocity-Space Signatures of Ion Cyclotron Damping Across Ion Plasma Beta Regimes

Ion cyclotron damping (iCD) is a key mechanism for dissipating electromagnetic wave energy in weakly collisional space plasmas. We use Liouville mapping combined with the field-particle correlation technique to reveal the velocity-space signature of iCD. This non-self-consistent approach efficiently captures the velocity-space distribution of how particles exchange energy with waves. We identify two features for iCD: (i) a quadrupolar energization pattern in the perpendicular $(v_x, v_y)$ plane, and (ii) localized energy transfer near the $n = 1$ resonance in gyrotropic $(v_\parallel, v_\perp)$ space. Importantly, these signatures remain largely unchanged across a wide range of ion plasma beta, with minimal variation near the resonant velocity. This is the first study to systematically examine how the iCD velocity-space signature evolves with plasma beta, serving as a practical reference for detecting iCD in spacecraft observations across diverse $\beta_i$ environments.