An investigation of the spatiotemporal dynamics of a quadruple Gaussian laser beam via plasma in the presence of an external magnetic field characterized by ponderomotive and relativistic nonlinearities is presented. The moment theory approach is used to study the second-order nonlinear differential equation analytically and numerically. The evolution of the beam width parameter determines the pulse dynamics, in both time and space. The spatial evolution at different pulse times of a quadruple Gaussian laser beam in a relativistic ponderomotive magnetized plasma is reported. The effects of initial laser parameters, such as lateral beam separation, laser intensity, external magnetic field, plasma density, and time factor on self-focusing, are studied. Strong periodic self-focusing is observed for a gradual increase in the magnetic field, plasma density, and time factor, whereas an increase in beam intensity shows reversal effects. The phenomenon of self-trapping is also observed for different values of lateral beam separation and magnetic field. A three-dimensional portrait of the normalized intensity as a function of the normalized radial co-ordinate and lateral beam separation is well illustrated. It is useful in studying inertial confinement fusion.

中文翻译：

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相对论磁动磁化等离子体中四倍高斯光束的时空动力学特征。

提出了在存在以质动力和相对论非线性为特征的外部磁场的情况下，通过等离子体对四倍高斯激光束的时空动力学的研究。矩理论方法用于分析和数值研究二阶非线性微分方程。光束宽度参数的变化决定了时间和空间上的脉冲动力学。报道了相对论互感磁化等离子体中四倍高斯激光束在不同脉冲时间的空间演化。研究了初始激光参数（如横向光束分离，激光强度，外部磁场，等离子体密度和时间因子）对自聚焦的影响。观察到强烈的周期性自聚焦，磁场逐渐增加，等离子体密度和时间因子，而光束强度的增加则显示出反向作用。对于横向束分离和磁场的不同值，也观察到自陷现象。很好地示出了归一化强度作为归一化径向坐标和横向束分离的函数的三维肖像。在研究惯性约束融合方面很有用。