  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.
