Beam energy scaling of a stably operated laser wakefield accelerator

Summary form only given. A simple theory for the study of stability and beam energy scaling of laser wake field accelerators (LWFA) was derived on the basis of the balance between the ponderomotive force due to the laser pulse and the restoring force due to the background ions. The theoretical analysis shows that the curvature of the accelerating structure is proportional to the relativistic plasma wavelength, which determines the beam energy scaling of a stably operated LWFA. Two dimensional particle-in-cell simulations were performed that demonstrate the fluctuation of the maximum energy gain of an accelerated electron bunch due to the unstable accelerating structure, which length is dynamically oscillating between the plasma wavelength and the relativistic plasma wavelength within a range of the laser intensity. The unstable accelerating structure can be stabilized by varying the laser intensity or reducing the plasma density. The simulation results reveal the existence of the parameter space for stable operations of a LWFA. The comparisons between the energy scaling law derived by the simple theory, the numerical results, and previous experimental results with self-guided laser pulses show good agreement and prove the simple theory can provide a good estimation of the beam energy for designing a new LWFA experiment.