Comprehensive understanding of nonlocal transport is mandatory for many applications of laser–plasma interaction physics, such as inertial confinement fusion and modeling of astrophysical phenomena in the laboratory. Theoretical description is important for guiding numerical simulations and experiments. In this article, an analytic approach is developed: by using a simple integral differential model, we calculate the preheating of plasma upstream of the heat front associated with nonlocal transport. A detailed comparison of various transport configurations as a function of the boundary conditions and the nonlinearity parameter is presented in the context of laser–plasma interaction. Three important results are demonstrated in this paper. First, analytical expressions for all possible self-similar solutions of local nonlinear transport are obtained. Second, a systematic comparison of various nonlocal kernels and forms of the delocalization length is performed. Third, an analytic expression for the temperature profile upstream of the heat front is obtained.

对于激光-等离子体相互作用物理学的许多应用，如惯性约束聚变和实验室中的天体物理现象建模，必须全面了解非局域传输。理论描述对于指导数值模拟和实验很重要。在本文中，开发了一种分析方法：通过使用简单的积分微分模型，我们计算了与非局部传输相关的热前沿上游等离子体的预热。在激光-等离子体相互作用的背景下，详细比较了各种输运配置作为边界条件和非线性参数的函数。本文展示了三个重要的结果。首先，获得所有可能的局部非线性输运自相似解的解析表达式。其次，对各种非局部内核和离域长度的形式进行了系统比较。第三，获得了热锋上游温度分布的解析表达式。