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abstract:
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The transverse motion of a relativistic charged particle in a radio-frequency linear accelerator (rf linac) is examined. The spatially averaged equations of motion derived for the motion in a periodic accelerating cavity system, and solved exactly in the ultra-relativistic limit. These soluction, along with an impulse treatment of the transients at the entrance and exit and exit of the linac cavities, allow derivation of a linear transport matrix throuigh the cavity. This generalized matrix is imporved over previously derived results in that it is applicable to both travelling and standing wave structures, allows for arbitrary injection phase and spatial harmonic content of the rf fields, and is more accurate in approximating the exact charged particle motion.
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