Investigation of classical radiation reaction with aligned crystals

Classical radiation reaction is the effect of the electromagnetic field emitted by an accelerated electric charge on the motion of the charge itself. The self-consistent underlying classical equation of motion including radiation-reaction effects, the Landau-Lifshitz equation, has never been tested experimentally, in spite of the first theoretical treatments of radiation reaction having been developed more than a century ago. Here we show that classical radiation reaction effects, in particular those due to the near electromagnetic field, as predicted by the Landau-Lifshitz equation, can be measured using presently available facilities, in the energy emission spectrum of $10$-$\text{GeV}$ electrons crossing a $0.5$-$\text{mm}$ thick diamond crystal in the axial channeling regime. Our theoretical results demonstrate the feasibility of the suggested setup, e.g., at the CERN Secondary Beam Areas (SBA) beamlines