Extension of the KAEC code with quadratic kinetic particle compression: Numerical implementation and benchmark applications

Energetic particles (EPs), primarily generated by external heating and fusion reactions, play a key role in magnetically confined plasmas. Their kinetic effects can destabilize toroidicity-induced Alfvén eigenmodes (TAEs). To capture the EP contribution, the quadratic kinetic particle compression (QKPC) term is formulated based on the gyrokinetic theory. The gyrokinetic equation is derived in terms of the invariants of motion: energy E, magnetic moment μ, and toroidal canonical momentum Pϕ and solved using numerically computed orbits of confined particles. This work extends the eigenvalue code KAEC [Yu et al., Phys. Plasmas 16, 072505 (2009)], originally developed without EP drive, by incorporating the QKPC term into the Alfvén wave equation. The extended model enables nonperturbative calculation of TAEs, including finite drift orbit width and finite Larmor radius effects for both passing and trapped EPs. The developed code has been successfully verified, including linear simulations of EP-driven TAEs in good agreement with established codes.