Abstract
An accelerated charged particle emits electromagnetic radiation. If the driving force is sufficiently strong, the radiated energy becomes comparable to the kinetic energy of the particle and the back-action of the emitted radiation (radiation reaction) significantly alters the dynamics of the particle. The Landau-Lifshitz (LL) equation has been proposed as the classical equation to describe the dynamics of a charged particle in a strong electromagnetic field when the effects of radiation reaction are taken into account. Hitherto, the experimental problem in validating the LL equation has been to achieve sufficiently strong fields for radiation reaction to be important without quantum effects being prominent. Notwithstanding, here we provide a quantitative experimental test of the LL equation by measuring the emission spectrum for a wide range of settings for 50 GeV positrons crossing aligned silicon single crystals near the $(110)$ planar channeling regime as well as 40 GeV and 80 GeV electrons traversing aligned diamond single crystals near the $\langle100\rangle$ axial channeling regime. The experimental spectra are in remarkable agreement with predictions based on the LL equation of motion with small quantum corrections for recoil and, in case of electrons, spin and reduced radiation emission, as well as with a more elaborate quantum mechanical model. Our experiment clearly shows the inadequacy of the Lorentz force as the sole agent of force on the particles in the classical limit, due to its absence of radiative energy loss in describing the dynamics of high-energy charged particles in strong electromagnetic fields like those in aligned single crystals.
Highlights
The Lorentz force accounts for the dynamics of charged particles moving in the presence of electromagnetic fields and represents a cornerstone of classical electrodynamics [1,2]
We investigated the necessity of radiation reaction for several unique cases near the classical limit in aligned crystals
The energy losses are moderate in the planar channeling regime for 50 GeV positrons so it could be expected that the spectra obtained neglecting radiation-reaction effects would be roughly adequate, but the experiments and simulations clearly show that this is not the case
Summary
The Lorentz force accounts for the dynamics of charged particles moving in the presence of electromagnetic fields and represents a cornerstone of classical electrodynamics [1,2]. This fundamental relation is complemented by Maxwell’s equations, which describe the evolution of the electromagnetic field due to charged particles in motion. Under typical experimental conditions the energy radiated by a charged particle is negligible compared to its kinetic energy, such that the radiation can be safely neglected in determining the dynamics of the particle It was realized already at the beginning of the twentieth century [3,4,5] that if the particle undergoes large accelerations, the amount of energy radiated becomes
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