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Resonant upconversion through a sixth order relativistic nonlinearity resulting in a unique resonance was recently proposed [Malkin and Fisch, Phys. Rev. E 108, 045208 (2023)]. The high order resonance is a unique non-integer multiple of a driving pump frequency resulting in a frequency upshift by a factor of ≈3.73. We demonstrate the presence, unique requirements, and growth of this mode numerically. Through tuning waves to high amplitude, in a mildly underdense plasma, the six-photon process may grow more than other non-resonant but lower order processes. The growth of the high frequency mode remains below the nonlinear growth regime. However, extending current numerical results to more strongly coupled resonances with longer pulse propagation distances suggests a pathway to significant upconversion. 

Observing collective effects originating from the interplay between quantum electrodynamics and plasma physics might be achieved in upcoming experiments. In particular, the generation of electron–positron pairs and the observation of their collective dynamics could be simultaneously achieved in a collision between an intense laser and a highly relativistic electron beam through a laser frequency shift driven by an increase in the plasma density increase. In this collision, the radiation of high-energy photons will serve a dual purpose: first, in seeding the cascade of pair generation; and, second, in decelerating the created pairs for detection. The deceleration results in a detectable shift in the plasma frequency. This deceleration was previously studied considering only a small sample of individual pair particles. However, the highly stochastic nature of the quantum radiation reaction in the strong-field regime limits the descriptive power of the average behavior to the dynamics of pair particles. Here, we examine the full kinetic evolution of generated pairs in order to more accurately model the relativistically adjusted plasma density. As we show, the most effective pair energy for creating observable signatures occurs at a local minimum, obtained at finite laser field strength due to the trade-off between pair deceleration and the relativistic particle oscillation at increasing laser intensity. For a small number of laser cycles, the quantum radiation reaction may re-arrange the generated pairs into anisotropic distributions in momentum space, although, in the one-dimensional simulations considered here, this anisotropy quickly decreases.