Weak turbulence theory for collisional p

Plasma is an ionized gas where collective behavior tends to dominate individual particle interactions, often leading to a treatment of plasmas as collisionless. However, the importance of the discrete nature of particles and the associated spontaneous electromagnetic fluctuations is frequently overlooked. The weak turbulence theory, a perturbative nonlinear approach developed over several decades from the late 1950s to the early 1980s, traditionally does not account for discrete particle effects in plasma descriptions. This paper addresses the shortcomings of the existing literature by demonstrating how noneigenmode fluctuations can alter the kinetic equations governing particle interactions. The research introduces a generalized particle kinetic equation that incorporates the Balescu-Lénard-Landau collision integral, alongside a modified wave kinetic equation accounting for both collisional damping and the bremsstrahlung emissions from plasma normal modes. This advancement provides a more complete framework for understanding collisional plasmas, emphasizing the role of noneigenmode contributions in the statistical behavior of plasma dynamics.