  We propose an innovative method to shift the transversal position of the
focal point of an optical cavity keeping it actively stabilized. Our cavity is
a 4 mirrors bow-tie cavity and the spatial shift of the resonant mode is
obtained by properly rotating the two curved mirrors by piezo actuators. This
method allows us to move the transversal position of the cavity focal point of
$135 \mu m$ in a time of $50 ms$, keeping the resonance condition of the cavity
by means of the Pound-Drever-Hall technique. We propose to use this technique
for the generation of 2-color X-rays via Inverse Compton Scattering (ICS). This
technique exploits the large average power stored in the high finesse cavity by
shifting the laser beam with respect to the electron beam trajectory, hence
controlling the spatial superposition of the electron and photon beams in the
interaction region. Arranging two cavities assembled one on top of the other,
with different collision angle with the electron beam, allows the generation of
X-ray bursts of different energies just by swiftly moving the two cavities,
switching the two focal points onto the electron beam trajectory, thus
activating in sequence two different ICS spectral lines.
