Towards precision quantitative measurement of radiation reaction within the classical radiation-dominated regime

Radiation reaction (RR) is a fundamental yet incompletely validated process in laser-particle interactions, since it lacks quantitatively definitive experimental verifications, especially the transition from classical to quantum regime. Herein, we propose a novel experimental scenario for investigating radiation RR within the classical radiation-dominated regime (CRDR), via the collision of a high-intensity petawatt-class laser with a tens-of-MeV electron beam from a LINAC. This approach enables access to a distinct parameter regime wherein RR dominates electron dynamics while quantum effects remain modest. Numerical simulations demonstrate that three key observables exist for identifying the RR within this CRDR regime: (i) quantitative measurement of energy spectra to validate the quantum correction factor; (ii) control of the collision time delay with charge-counting to map intensity dependence of RR; and (iii) verification of large angle ($90^\circ$) photon emission under the recoil condition $2\gamma \gtrsim a_0$. These experimental measurements will establish the benchmarks for RR models spanning the classical-to-quantum regime, thereby providing critical insights into fundamental strong-field quantum electrodynamics.