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Either π/2 or 2π/3 modes are used. For the former a phase shift of 2π is obtained over four cells while for the latter it needs three cells. 101 Fig. 19 Operating point for vp = c For an acceleration to take place one chooses the fundamental space harmonic such that: βo = ω c π 2 or βod = 2π 3 The fundamental is the only one to give a net accelerating field since the higher space harmonics have no effect on the average. Hence, most of the particle dynamics in a travelling wave structure can be treated only using the fundamental space harmonic which can be calculated, for any structure having cylindrical symmetry, with the help of powerful computer codes like LALA or SUPERFISH.
Clearly the length of the drift tubes will soon become prohibitive at higher energies unless the input RF frequency is increased. Higher-frequency power generators only became available after the second world war, as a consequence of radar developments. However at higher frequencies the system, which is almost capacitive, will radiate a large amount of energy; as a matter of fact if one considers the end faces of the drift tubes as the plates of a capacitor, the displacement current flowing through it is given by I = ω CV where C is the capacitance between the drift tubes, V the accelerating voltage and ω the angular frequency in use.
97 cm. As the waves propagate in such a structure, part of the input power is dissipated into the walls and the remaining power will lead to a smaller accelerating field. Hence the accelerating gradient decreases continuously along the structure. 01. 6(2a)2[ cm ] = 72MΩ / m while Q is practically independant of (2a) and equal to 15000. 2 Constant-gradient structure In order to compensate for the variation of the accelerating field along the structure, due to power dissipation, it is possible to lower the group velocity from cell to cell, by changing the geometry for the same operating frequency.
CAS-CERN Accelerator School - Basic (general) Accelerator Physics