Treatment of beam loading effects in a standing wave accelerator

ILC (International Linear Collider) is e+ e- linear collider in the next high energy program promoted by ICFA. In ILC, an intense positron pulse in a multi-bunch format is generated by impinging electron beam on a target. The generated positron is captured by a standing wave accelerator in a solenoid focusing. By employing the accelerator with a large aperture, an enough amount of positron can be captured, even with a limited accelerator gradient. However, the heavy beam loading up to 2 A perturbs the field gradient and profile along the longitudinal position. We present the theoretical treatment of the beam loading effect in the standing wave acceleration based on a multi-cell model. Based on the model, we have obtained the expected gradient which is lower than the single cell model. The compensation of the transient beam loading effect is not perfect, but enough for practical use. (author)