针对空泡机制中的双束等离子体尾波电子加速设计，给出了能够快速得到被加速束流在最大加速距离下的相对能散的预测公式。通过加速初始时刻束流纵向分布以及束流所处位置的纵向尾波场可得到束流最终相对能散。该预测公式不仅可应用于驱动束流与被加速束流初始能量相同的情况，还可应用于两个束流初始能量不相同的情况。由该预测公式得到的束流相对能散与被加速束流和驱动束流的初始能量的比值有关，而与两个束流初始能量的数值无关。利用准静态近似的粒子网格模拟程序QuickPIC对理论进行了模拟验证，模拟结果与理论预期结果一致。

We measured the parameter reproducibility and radial electron density profile of capillary discharge waveguides with diameters of 650 $\mathrm{\mu} \mathrm{m}$ to 2 mm and lengths of 9 to 40 cm. To the best of the authors’ knowledge, 40 cm is the longest discharge capillary plasma waveguide to date. This length is important for $\ge$10 GeV electron energy gain in a single laser-driven plasma wakefield acceleration stage. Evaluation of waveguide parameter variations showed that their focusing strength was stable and reproducible to $<0.2$% and their average on-axis plasma electron density to $<1$%. These variations explain only a small fraction of laser-driven plasma wakefield acceleration electron bunch variations observed in experiments to date. Measurements of laser pulse centroid oscillations revealed that the radial channel profile rises faster than parabolic and is in excellent agreement with magnetohydrodynamic simulation results. We show that the effects of non-parabolic contributions on Gaussian pulse propagation were negligible when the pulse was approximately matched to the channel. However, they affected pulse propagation for a non-matched configuration in which the waveguide was used as a plasma telescope to change the focused laser pulse spot size.