Extending the theory of near-marginal wave-particle instabilities for a time-dependent turbulent effective scattering

In a burning plasma, destabilization of Alfvén eigenmodes (AEs) by fast ions may lead to increased energetic particle (EP) transport and decreased confinement. The dynamics of this energy exchange depends on the "effective scattering"– a combination of collisions and background turbulence which replenishes the gradient of resonant particles to further drive the AEs. Previous theory has generally assumed a constant effective scattering. In a real tokamak, turbulence levels may be modified over time by shearing due to zonal flows, L-H transitions, and other factors, resulting in a time-dependent effective scattering. We investigate the analytical implications of a time-dependent effective scattering on the Berk-Breizman cubic equation, and show that the equation becomes time-local only when the time derivative of the collisionality, divided by the square of the collisionality, is small. We derive the first-order correction for a slowly varying collisionality. We also discuss explicit solutions to the Landau-Stuart equation with a time-dependent effective scattering, and show a path forward for experimental validation. Lastly, we discuss corrections to the quasilinear transport theory in terms of modifications to its resonant structure.