  Petawatt class femtosecond lasers and x-ray free electron lasers (XFEL) open
up a new page in research fields related to space and vacuum physics. One of
fundamental principles can be explored by these new instruments is the
equivalence principle, saying that gravitation and acceleration should be
treated equivalently. If it is true this must lead to the appearance of the
Unruh effect analogous to Hawking's black hole radiation. It says that a
detector moving with a constant acceleration $w$ sees a boson's thermal bath
with its temperature $T_w=\hbar w/2\pi k_B c$. Practical detection of the Unruh
effect requires extremely strong acceleration and fast probing sources. Here we
demonstrate that x-rays scattering from highly accelerated electrons can be
used for such detection. We present two, feasible for the Unruh effect, designs
for highly accelerated systems produced in underdense plasma irradiated by high
intensity lasers pulses. The first is Thomson scattering of a XFEL pulse from
plasma wave excited by an intense laser pulse. Properly chosen observation
angles enable us to distinguish the Unruh effect from the normal Doppler shift
with a reasonable photon number. The second is a system consisting of electron
bunches accelerated by a laser wake-field, as sources and as detectors, which
move in a constantly accelerating reference frame (Rindler space) and are
probed by x-ray free electron laser pulses. The numbers of photons is shown to
be enough to observe reproducible results.
