In the present paper, we study the wakes known as the donut wake which is generated by Laguerre-Gauss (LG) laser pulses. Effects of the special spatial profile of a LG pulse on the radial and longitudinal wakefields are presented via an analytical model in a weakly non-linear regime in two dimensions. Different aspects of the donut-shaped wakefields have been analyzed and compared with Gaussian-driven wakes. There is also some discussion about the accelerating-focusing phase of the donut wake. Variations of longitudinal and radial wakes with laser amplitude, pulse length, and pulse spot size have been presented and discussed. Finally, we present the optimum pulse duration for such wakes.
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