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

TL;DR

The paper addresses the challenge of quantitatively validating radiation reaction (RR) and tracing the classical-to-quantum transition in strong-field QED. It proposes a CRDR experiment in which a petawatt-class laser collides with tens-of-MeV electron beams, and analyzes predictions using the LL equation and a semi-classical modification that incorporates the quantum correction factor $g(χ_e)$. The study identifies three key observables—electron energy spectra, collision-time control via charge counting, and large-angle photon emission under RR—as robust signatures for RR in CRDR, supported by 3D-PIC simulations indicating $χ_e ightarrow ext{O}(10^{-2}-10^{-1})$ and $R_c ightarrow ext{O}(0.1)$. The results show measurable differences between classical and semi-classical RR predictions and demonstrate tunable RR strength through time-delay and energy adjustments, providing benchmarks across the classical-quantum boundary and advancing SFQED understanding. The work outlines a clear path for precision RR testing at TDLI and discusses future upgrades toward access to SFQED regimes with higher $χ_e$.

Abstract

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 $2γ\gtrsim a_0$. 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.

Figures (6)

• Figure 1: (a) Schematic of the proposed radiation reaction experiment at TDLI. The linear accelerator provides an electron bunch with a central energy of 10-90 MeV and an energy spread of 0.1%, which collides with a 3 PW laser. The laser is focused by an Off-Axis Parabola (OAP) with an $f$-number of 2. After the collision, the electron energy spectrum is diagnosed by a high-precision magnetic spectrometer, while the $\gamma$-ray is diagnosed using CsI (Cesium Iodide) detectors and a spectrometer. (b) The single particle trajectories calculated based on the LL and MLL models respectively, as well as the envelope of correction factor $g(\chi_e)$ during the electron motion. (c) Adjusting the time delay between the electron bunch and the laser pulse can change the charge number participating in the reaction and the energy spectrum after the collision. (d) The trajectories of electrons with different initial energies $E_{e^-}$ after colliding with the laser, as well as the radiation angle for the electron bunch with $E_{e^-}=30\ \rm MeV$.
• Figure 2: 3D-PIC simulation results of a 3 PW laser colliding with the 90 MeV linac electron bunch. (a-b) Snapshots of electron density distribution $\rho_e$ and the laser field $E_x$ in the polarized plane at time $t = 88\, \rm T_0$ and $t = 100\,\rm T_0$, respectively. The inset of (a) shows the initial transverse distribution of the electron bunch. The inset of (b) amplifies the laser field $E_x$ near the focus. (c) Distribution of $\chi_e$ at $t = 100\,\rm T_0$. The color bar represents the electron energy. Each point represents an individual electron. (d) Distribution of $R_c$ and $\chi_e$ for every electron at $t = 100\,\rm T_0$. The color bar represents the laser dimensionless parameter $a_0$ experienced by each electron. The black dashed lines show the variation of $R_c$ with $\chi_e$ when $\gamma =$ 175, 120 and 75. The red line shows the Gaunt factor $g(\chi_e)$ at different $\chi_e$. (e) The electron energy spectrum after the collision. The gray line shows the spectrum without RR. The orange and blue lines represent the spectrum calculated based on the LL and MLL model, respectively. The inset shows the bunch divergence distribution before and after the collision. (f) The photon spectrum calculated using the two models. The inset shows the divergence angles of photons in the $yz$ plane (upper) and $xz$ plane (lower), respectively
• Figure 3: Simulation results by tuning the time delay between the laser pulse and the electron bunch. (a) The maximum $R_{c}$ in collisions of a laser at various defocusing positions $z-z_{focus}$ with a 90 MeV electron bunch. The black dashed lines shows the laser waist radius $w_0$ and the red line is the peak $a_0$ during the laser evolution. The blue solid and dashed lines show the final electron energy after the collision versus defocusing position of laser, as calculated by the LL and MLL models, respectively. (b) The electron spectrum after the collision at different time delays. The circular and triangular dots represent the total electron charge in different energy intervals. The red lines represent the Gaussian curve fitting. (c) The maximum $\chi_e$ and the minimal $g(\chi_e)$ during the interaction at different time delays. (d) The trajectory of an electron in head-on collision with laser. (e) The photon energy spectrum with a detection lower limit of 50 keV. The solid lines represent the spectrum without time delay, while the dashed lines represent the results with a 600 fs delay. The inset shows the critical photon energy versus the time delay.
• Figure 4: Simulation results with different initial longitudinal momentum $p_z$ for the LL model. (a) For different $p_z$, the black dots represent the minimal longitudinal momentum $p'_z$ of the electron bunch after the collision. The blue and yellow regions are separated by $p'_z = 0$. The gray dashed line indicates $p_z = \gamma$, and the orange lines represent the range of electron energies after the collision. (b-e) The single electron's trajectory calculated via particle tracking code. The initial electron energy is 10 MeV in (b) and (c), and 30 MeV in (d) and (e). The black dashed lines in (e) represents the instantaneous $p_z < 0$.
• Figure 5: (a-e) The photon radiation results for different initial electron energies in the $xz$ plane. (f-g) The photon angle distribution for $E_{e^-} = 10\, \rm MeV$ (f) and $E_{e^-} = 30\, \rm MeV$ (g), based on the LL model. The inset in (g) shows the distribution around $90^{\circ}$, for cases with and without RR. (h) The black line shows the ratio of the minimum electron energy after collision to its initial value, and the critical photon energy is shown by the red line.