Influence of finite-k_perp pump Alfvén wave on PDI development

Determine how the perpendicular wavenumber k_perp associated with a finite-perpendicular-scale pump Alfvén wave influences the development of parametric decay instability (PDI), to extend existing PDI theory beyond the k_perp=0 plane-wave assumption and explicitly account for the pump’s finite perpendicular scale.

Background

Parametric decay instability (PDI) of Alfvén waves has been extensively studied, but most theoretical treatments assume plane waves with zero perpendicular wavenumber (k_perp=0). Some prior theoretical and numerical work allows finite k_perp for parent or child waves, yet a systematic theory for a pump wave with finite perpendicular scale has not been developed.

In both laboratory and space plasmas, Alfvén waves often possess significant finite perpendicular scale (large k_perp), arising from finite antenna size in experiments or transverse gradients, resonance absorption, and turbulent cascade in low-beta regions such as the solar corona. Understanding how a pump wave’s finite k_perp affects PDI is therefore essential for assessing the conditions for PDI excitation and its relevance in realistic three-dimensional open systems.