This paper reformulates laser–plasma wakefield acceleration in capillary discharges as coupled operators acting on modal representations of the laser field and plasma-density response. A transverse operator describes guiding and linear mode coupling; nonlinear, plasma-oscillation, and ponderomotive-source operators encode feedback and wake excitation. Linear evolution preserves modal invariant subspaces, whereas nonlinear interactions break them and mix modes. Expanding transverse and longitudinal fields in orthonormal bases makes energy transfer and the effects of complex geometries more explicit than in the original coupled partial differential equations. Bloch–Floquet analysis extends the framework to periodic plasma modulations. The authors also propose learning the expensive nonlinear and nonlocal operators from high-fidelity simulations with neural operators, yielding a differentiable reduced model for optimization and control. The work is primarily a mathematical and modeling framework; its claims about acceleration and computational savings require systematic validation against full simulations and experiments.
- Expressed coupled laser and plasma dynamics through four physically interpretable operators.
- Connected linear modal stability to invariant subspaces and nonlinear evolution to mode mixing.
- Represented transverse and longitudinal wakefield dynamics in a common modal framework.
- Incorporated periodic plasma structures through Bloch–Floquet analysis.
- Proposed neural-operator surrogates for nonlinear response and ponderomotive-source evaluations.