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Extra info for CAS-CERN Accelerator School - Cyclotrons and Linacs [and applications]

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Fig. 6 Disc-loaded linac (schematic) Fig. 7 DTL linac (schematic) Fig. 01, a very convenient accelerator is the radio-frequency quadrupole, RFQ. This widespread accelerator will be treated in some detail in Section 9. 4, a convenient structure is the side-coupled linac, SCL [6], shown schematically in Fig. 9. Its particularity is that in addition to accelerating cells it also contains coupling cells, placed sidewise. The field vector Ez is in phase opposition in adjacent accelerating cells. The coupling cells form another chain of oscillators and the SCL is therefore a 'biperiodic structure'.

5: Fig. 5 Dispersion diagram of periodic structures i) the working point of the TW mode is usually around point A (phase advance per period of the structure ≅ π /2; the phase velocity ≅ c, the group velocity corresponds to the tangent to the curve at point A); ii) the working points of the SW mode must have phase advances of 0 or π, modulo 2 π (as for example points B and C); it is only at these points that the direct (full line) and reflected wave (dotted line) have the same phase velocity, so they can both be used to accelerate particles.

2 Dispersion (Brillouin) diagram for empty cavities The plotted curve is a hyperbola and the slope of the radius vector from the origin to a point on the curve gives the phase velocity ν ph = ω /k ; all the points above the asymptote, for which νph = c, have ν ph > c. The slope of a point on the hyperbola gives the group velocity [2] νg = dω . dk The lowest frequency for which the boundary conditions are satisfied is ω c. At this frequency the phase advance k, as well as the group velocity, are zero, whilst the phase velocity is infinite.

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CAS-CERN Accelerator School - Cyclotrons and Linacs [and applications]


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