text: The classical limit of non-linear inverse Compton scattering, also called non-linear Thomson scattering and multiphoton Thomson scattering, is a special case of classical synchrotron emission driven by the force exerted on a charged particle by intense electric and magnetic fields. Practically, a moving charge emits electromagnetic radiation while experiencing the Lorentz force induced by the presence of these electromagnetic fields. The calculation of the emitted spectrum in this classical case is based on the solution of the Lorentz equation for the particle and the substitution of the corresponding particle trajectory in the Liénard-Wiechert fields. In the following, the considered charged particles will be electrons, and gaussian units will be used.
  The component of the Lorentz force perpendicular to the particle velocity is the component responsible for the local radial acceleration and thus of the relevant part of the radiation emission by a relativistic electron of charge , mass  and velocity . In a simplified picture, one can suppose a local circular trajectory for a relativistic particle and can assume a relativistic centripetal force equal to the magnitude of the perpendicular Lorentz force acting on the particle: <math display="block">
  \gamma \dfrac{m v^2}{\rho}=e\sqrt{\left(\mathbf{E}+\dfrac{\mathbf{v}}{c}\times\mathbf{B}\right)^2-\left(\dfrac{\mathbf{E}\cdot\mathbf{v}}{v}\right)^2}
   and  are the electric and magnetic fields respectively,  is the magnitude of the electron velocity and  is the Lorentz factor . This equation defines a simple dependence of the local radius of curvature on the particle velocity and on the electromagnetic fields felt by the particle. Since the motion of the particle is relativistic, the magnitude  can be substituted with the speed of light to simplify the expression for . Given an expression for , the model given in Example 1: bending magnet can be used to approximately describe the classical limit of non-linear inverse Compton scattering. Thus, the power distribution in frequency of non-linear Thomson scattering by a relativistic charged particle can be seen as equivalent to the general case of synchrotron emission with the main parameters made explicitly dependent on the particle velocity and on the electromagnetic fields.