Summary
We investigate analytically the stability regions of the transverse motion of particles in radio-frequency quadrupole accelerators, under diverse physical assumptions. It turns out that in the case where a nontrivial solution for the longitudinal equation is considered, the corresponding equation for the transverse motion shows the new property that its stability region contains a sequence of narrow instability stripes.
Riassunto
Si studiano, analiticamente, le regioni di stabilità della equazione del moto trasversale di particelle in acceleratori a radiofrequenza quadrupolare, in diverse condizioni fisiche. Si trova che nel caso in cui si consideri una soluzione non banale della equazione per il moto longitudinale, la corrispondente equazione del moto trasversale possiede una regione di stabilità contenente una successione di strette strisce di instabilità.
Реэюме
Мы аналитически исследуем области устойчивости поперечного движения частиц в радиочастотных квадрупольных ускорителях при раэличных фиэических предположениях. Окаэывается, что в случае, когда рассматривается нетривиальное рещение для продольного уравнения, соостветствуюшее уравнение для поперечного движения обнаруживает новое свойство: область устойчивости содержит последовательность уэких полос неустойчивости.
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Leo, M., Leo, R.A., Mancarella, G. et al. Stability boundaries for the equations of the transverse motion of particles in a radio-frequency quadrupole device. Nuov Cim A 102, 781–794 (1989). https://doi.org/10.1007/BF02730751
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DOI: https://doi.org/10.1007/BF02730751