Probing Space-time Distortion with Laser Wake Field Acceleration and X-ray Free Electron Lasers

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.