Modeling and Control of the High-Voltage Terminal of a Tandem Van de Graaff Accelerator

This paper presents a mathematical model derived from an equivalent electrical circuit to describe the dynamic behavior of the high-voltage terminal of a tandem Van de Graaff accelerator. Two approaches are presented for modeling the transit time of the current flowing through the corona needles. The first one considers an equivalent self-inductance in the corona triode, whereas, in the second one, the transit time is represented by a delay in the corona current. The validation of the proposed models was carried out through experimental tests developed at the National Nuclear Research Institute of Mexico. Furthermore, two strategies for controlling the slow variations of the terminal voltage limited by the slow response of the control loop based on corona discharge are evaluated: a Proportional–Integral–Derivative controller and a sliding mode controller. The Root-Mean-Squared Error calculation leads to the conclusion that both control strategies are suitable for regulating the voltage at the accelerator potential terminal. However, the sliding mode controller leads to an overshoot-free response and a shorter settling time.