Practical design approach for trapezoidal modulation of a radio-frequency quadrupole

Abstract

Trapezoidal modulation of quadrupole electrodes offers additional benefits to the concept of a radiofrequency quadrupole (RFQ). Because of the significant increase of the effective shunt impedance, RFQs with trapezoidal modulation have a reduced interelectrode voltage or resonator length as compared to conventional RFQs with sinusoidal modulation. This feature is especially valuable for RFQs operating in cw mode, since it reduces the required rf power. We develop a detailed procedure for the design of RFQ electrodes with trapezoidal modulation. With our design procedure and by properly choosing the trapezoidal cell parameters, we can easily control the peak surface fields in the RFQ to the same level as for sinusoidal cell modulation. The procedure is applied to the design of the electrodes for the ReA3 RFQ at Michigan State University.

Перспективные Технологии Для Прикладных Резонансных Ускорителей Заряженных Частиц И Примеры Их Использования (Обзор)

“…9). Благодаря использованию источника ионов с высокой степенью обдирки [180], эффективного дизайна ускорителя типа RFQ с трапецеидальной формой электродов [181,182] и высокоградиентных четвертьволновых резонаторов c несколькими трубками дрейфа удалось добиться компактного размера ускорителя в 16 m для пучков урана, ускоренных до 285 MeV. Снижение ВЧ-потерь в резонаторах позволило избежать использования сверхпроводящих структур, несмотря на непрерывный режим работы ускорителя, и значительно сократить стоимость конструкции благодаря отсутствию сложной и дорогой системы рефрижераторов для жидкого гелия [183].…”

Novel deuteron RFQ design with trapezoidal electrodes and double dipole four-vane structure

“…It had a step-like pole-tip profile which was soon replaced by trapezoidal modulation with a simple piecewise linear profile [19]. Recently, a sinusoidal junction for the acceleration gap has been proposed and developed to provide a positional and tangential continuity with the adjacent cells (TSINE) [20]. The longitudinal pole-tip profiles of horizontal R x and vertical R y in the acceleration gap satisfy: successfully implemented in some RFQs [7,21].…”

750 MHz radio frequency quadrupole with trapezoidal vanes for carbon ion therapy

“…While other transitions may be used, we adopted the trapezoidal cell geometry proposed in Ref. [23]. From here on, the sinusoidal junction is denoted as the accelerating gap with length g. Furthermore, we let r 0 identify the mid-cell aperture, a the min-imum aperture, m the modulation factor, and L the cell length (Fig.…”

“…The electric field of trapezoidal vanes cannot be described by the two-term or eight-term potential function used by the available RFQ design codes [18,[24][25][26][27][28], parmteq [18] being the most common. Previously, 3D simulation code was employed to design RFQs with trapezoidal electrodes, taking the electrode geometry directly into account [23,[29][30][31][32][33][34]. While this procedure delivers highly accurate results, it is also time-consuming, as for each parameter change new simulations have to be performed to solve the Laplace equation.…”