Theoretical investigation on optical self action effects of intense q-Gaussian laser beams interacting with collisionless plasmas with axial density ramp has been presented. Emphasis are put on investigating the dynamics of beam width and axial phase of the laser beam. Effect of the ellipticity of the cross section of the laser beam also has been incorporated. Using variational theory based on Lagrangian formulation nonlinear partial differential equation (P.D.E) governing the evolution of beam amplitude has been reduced to a set of coupled ordinary differential equations for the beam widths of the laser beam along the transverse directions. The evolution equation for the axial phase of the laser beam has been obtained by the Fourier transform of the amplitude structure of the laser beam from coordinate space to \((k_x, k_y)\) space. The differential equations so obtained have been solved numerically to envision the effect of laser-plasma parameters on the propagation dynamics of the laser beam.

强q光自作用效应的理论研究提出了高斯激光束与无碰撞等离子体相互作用的轴向密度梯度。重点放在研究光束宽度和激光束轴向相位的动力学上。还结合了激光束横截面的椭圆度的影响。使用基于拉格朗日公式的变分理论，将控制光束幅度演变的非线性偏微分方程（PDE）简化为一组沿横向方向的光束宽度的耦合常微分方程。通过对激光束的振幅结构从坐标空间到\（（k_x，k_y）\）进行傅立叶变换，得到了激光束轴向相位的演化方程。空间。如此获得的微分方程已被数值求解，以设想激光等离子体参数对激光束传播动力学的影响。