The laser pulse can be used to accelerate electrons in plasma in the so called bubble regime [1]. The bubble regime can be reached when the laser energy is above some threshold value that is defined by the pulse duration [2]. For a 1 kJ laser, the pulse duration must be below 300 fs to form the bubble. For longer laser pulses, a self-modulation regime of electron acceleration will set in. Electrons accelerated in plasma wiggle in the transverse fields of the ion channel. This wiggling leads to betatron radiation that is similar to synchrotron emission in conventional accelerators [3-10].  According to the formula electrons accelerated to a few GeV energies will emit photons in the range 102…103 keV. The assumed kJ-class laser is sufficient to accelerate electrons to such energies or above.

The betatron source is highly collimated. The photons are expected to have angular divergence on the order of  that is less than 1 mrad.  

The laser-plasma interaction must be studied using particle-in-cell methods. Because the acceleration distance  is expected to be large, the Lorentz-boosted PIC framework will be required.

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