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The condition of propagation hence corresponds to: 0 ≤ cos β d ≤ 1 Fig. 18 Brillouin diagram for a slow wave structure At βd = π the phases in two successive cells are opposite (π mode) and one gets a standing wave pattern in the combination of all the space harmonics. The calculation of the real fields in loaded structures which would take careful account of all boundary conditions is tedious. Generally a reasonably accurate description of the dispersion curve, relating β to k, is obtained by an equivalent transmission line analysis or a coupled resonators chain analysis.

Wideroe, to avoid the limitation of electrostatic devices due to voltage superposition. The proposed scheme, later on (early 1930's) improved by E. Lawrence and D. Sloan at the Berkeley University, is shown on Fig. 2. Fig. 2 Wideroe-type accelerator 82 An oscillator (7 MHz at that time) feeds alternately a series of drift tubes in such a way that particles see no field when travelling inside these tubes while they are accelerated in between. c. field. This scheme does not allow continuous acceleration of beams of particles.

Persico, E. E. A. Y. 1968 P. Lapostolle, A. Septier (Editors), Linear Accelerators, North Holland Publishing Company, Amsterdam 1970 P. B. Wilson, High Energy Electron Linacs: Applications to Storage Ring RF Systems and Linear Colliders, SLAC PUB 2884. Y. A. Loew, Elementary Principles of Linear Accelerators, SLAC PUB 3221. Y. M. A. Teplyakov, Linear Ion Accelerator With Spatially Homogeneous Strong Focusing, Pribory i. H. R. E. A. Swenson, RF Quadrupole Beam Dynamics, IEE Transactions on Nuclear Science, Vol.

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CAS-CERN Accelerator School - Basic (general) Accelerator Physics

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