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本文从能量守恒定律出发，对应于等梯度加速结构，推导出瞬时束流负载一般解的解析表达式．特别对应于热阴极微波枪做为注入器的情形，此时脉冲内电流随时间线性增加，首次给出这时的束负载效应的解析公式．对北京自由电子激光器的加速器系统，给出数值计算结果，可以看到由于脉内电流的增长导致脉内束能量下降的程度。
In this paper, starting from the law of conservation of energy, corresponding to the gradient acceleration structure, an analytical expression of the general solution to the instantaneous beam current load is deduced. Especially corresponding to the case of a hot cathode microwave gun as an injector, the current in the pulse increases linearly with time. For the first time, the analytic formula of the beam loading effect at this time is given. For the Beijing free electron laser accelerator system, the numerical calculation results are given, and it can be seen that the energy of the pulse in the pulse decreases due to the increase of the in-pulse current.