By Helmut Wiedemann

This ebook offers an in-depth and complete advent to the sphere of high-energy particle acceleration and beam dynamics. this is often the 1st glossy and finished textbook within the box. It starts off via collecting the fundamental instruments, recalling the necessities of electrostatics and electrodynamics in addition to of particle dynamics in electromagnetic fields. It contains insurance of complex subject matters of coupled beam dynamics. there's an exhaustive remedy of radiation from sped up fees. Appendices assemble invaluable mathematical and actual formulae, parameters and devices, and options to the numerous end-of-chapter difficulties are given.

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444 12. four. 2 Statistical Alignment and box mistakes . . . . . . . . . . . . . . . . 445 12. five Dipole box mistakes and Dispersion functionality . . . . . . . . . . . . . . . . 450 12. five. 1 Self repayment of Perturbations . . . . . . . . . . . . . . . . . . 451 12. five. 2 Perturbations in Open delivery traces . . . . . . . . . . . . . . . 452 12. 6 Dispersion functionality in better Order . . . . . . . . . . . . . . . . . . . . . . . 454 12. 6. 1 Chromaticity in greater Approximation . . . . . . . . . . . . . . . 456 12. 7 Nonlinear Chromaticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458 12. eight Perturbation tools in Beam Dynamics . . . . . . . . . . . . . . . . . . 463 12. eight. 1 Periodic Distribution of Statistical Perturbations . . . . . . 464 12. eight. 2 Periodic Perturbations in round Accelerators . . . . . . . . 467 12. eight. three Statistical the right way to evaluation Perturbations . . . . . . . . 469 thirteen Hamiltonian Resonance thought . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479 thirteen. 1 Resonances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479 thirteen. 1. 1 Resonance stipulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480 thirteen. 1. 2 Coupling Resonances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484 thirteen. 1. three Resonance Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485 thirteen. 2 Nonlinear Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487 thirteen. three Resonant phrases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490 thirteen. four Resonance styles and Stop-Band Width . . . . . . . . . . . . . . . . . . 492 thirteen. four. 1 part integer cease band . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493 thirteen. four. 2 Separatrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495 thirteen. five common Stop-Band Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497 thirteen. 6 Third-Order Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498 thirteen. 6. 1 Particle movement in part house . . . . . . . . . . . . . . . . . . . . . 501 Contents XXIII 14 Hamiltonian Nonlinear Beam Dynamics . . . . . . . . . . . . . . . . . . . 503 14. 1 greater Order Beam Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503 14. 1. 1 Multipole error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503 14. 1. 2 Nonlinear Matrix Formalism . . . . . . . . . . . . . . . . . . . . . . . . 507 14. 2 Aberrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512 14. 2. 1 Geometric Aberrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514 14. 2. 2 Filamentation of part house . . . . . . . . . . . . . . . . . . . . . . . 520 14. 2. three Chromatic Aberrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523 14. 2. four Particle monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526 14. three Hamiltonian Perturbation concept . . . . . . . . . . . . . . . . . . . . . . . . . 528 14. three. 1 song Shift in greater Order . . . . . . . . . . . . . . . . . . . . . . . . . 534 half V Acceleration 15 Charged Particle Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 541 15. 1 Preinjector and Beam training . . . . . . . . . . . . . . . . . . . . . . . . . 541 15. 1. 1 Prebuncher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 541 15. 1. 2 Beam Chopper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544 15. 2 rf-Waveguides and Cavities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545 15. 2. 1 Wave Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545 15. 2. 2 oblong Waveguide Modes . . . . . . . . . . . . . . . . . . . . . . 547 15. 2. three Cylindrical Waveguide Modes . . . . . . . . . . . . . . . . . . . . . . . 551 15. three Linear Accelerator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554 15. three. 1 simple Waveguide Parameters . . . . . . . . . . . . . . . . . . . . . . . 555 15. three. 2 Particle catch in a Linear Accelerator box .

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