The relativistic Doppler effect offers a fundamental means of frequency upconverting electromagnetic radiation.
In 1993, Esarey et al.<sup>1</sup> mentioned the possibility of scattering light at fast moving electrons to upconvert its
frequency. For the process to be efficient, one needs to have a highly compressed bunch of electrons, since only
then the scattering process can become coherent. The condition for coherency is, that the scale length of the
electron bunch or its density gradient needs to be on the order of the wavelength to be generated or smaller. This
is much tinier than what can be reached by commonly known techniques, including conventional accelerators as
well as laser-plasma accelerators.
Therefore, electrons are extracted from a small droplet or a thin foil by a highly relativistic driver laser
(a<sub>0</sub> = eA<sub>0</sub>/mc<sup>2</sup> ⪆⪆ 1). The electron bunch becomes accelerated and at the same time compressed by the forces of
the laser field. The acceleration can be achieved either by the relativistic ponderomotive force of a conventional
laser pulse, as suggested in,<sup>6</sup> or by the longitudinal field on the optical axis of a radially polarized pulse, as
suggested in.8 In both cases, the bunch is compressed because of the fundamental snowplough effect of the
co-moving force, i.e. the laser pulse. Spacecharge forces are counteracting the compression, thus limiting the
amount of charge to be compressed. Nevertheless, in a wide range of parameters the edges of the electron bunches
density profile remain sharp, enabling coherent Thomson scattering.
We use analytic models and PIC simulations to describe and analyze thoroughly the effects occurring and
finally estimate the conversion efficiency that can be reached by this scheme. Techniques to increase the efficiency
and gain further control over the generated radiation are suggested and discussed. Reaching best possible control
over temporal envelope of the driver pulse appears to be the most important issue here.