Thermal scaling laws of the optical Bragg acceleration structure

The temperature distribution and heat flow in the planar optical Bragg acceleration structure, fed by a train of high-power laser pulses, are analyzed. Dynamic analysis of a high-repetition rate train of pulses indicates that the stationary solution is an excellent approximation for the regime of interest. Analytic expressions for the temperature and heat distributions across the acceleration structure are developed. Assuming an accelerating gradient of 1  GV/m and a loss factor similar to that existing in communication optical fibers 1   dB/km (tan⁡δ∼10^-11), the temperature increase is less than 1 K and the heat flow is of the order of 1   W/cm², which is 3 orders of magnitude lower than the known technological limit for heat dissipation. Obviously, using materials with a significantly higher loss tangent may lead to unacceptable temperatures and temperature gradients as well as confinement difficulties and phase mismatch.