Variational method in the study of intense laser beams propagation in plasma channels
强激光束在等离子体通道中传输的变分法研究

In an underdense plasma, the laser wave equation is given with higher-order-relativistic (HOR) effect. A variational methed is used to study HOR effect for intense laser beam propagation in plasma channel including diffraction, pre-formed plasma channel guiding and lower order relativistic effects. In the paraxial approximation, a potential well also exists for laser spot size. HOR effect decreases the amplitude of laser spot size oscillation, whereas accelerates its rate. Furthermore, it prevents the singularity of infinite intesity of laser beam when laser power is greater than (or equal to) the relativistic critical power. The condition of balance-solution of the beam spot size is also given.