An Introduction to the Physics of High Energy Accelerators by D. A. Edwards

By D. A. Edwards

The 1st part offers with the movement of a unmarried particle lower than the effect of digital and magnetic fields. the fundamental language of linear and round accelerators is built. the primary of section balance is brought besides part oscillations in linear accelerators and synchrotrons. provides a remedy of betatron oscillations through an day trip into nonlinear dynamics and its program to accelerators. the second one part discusses depth based results, rather house cost and coherent instabilities. comprises tables of parameters for a range of accelerators that are utilized in the varied difficulties supplied on the finish of every bankruptcy.

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We do not explore the technology of accelerating structures; that is a rich subject in itself. But we do conclude with a few remarks on the sorts of accelerating structures that are employed in practice. 1 DC Accelerators The first accelerator in the modern sense was the electrostatic accelerator that Cockcroft and Walton used to demonstrate the disintegration of lithium nuclei upon bombardment with protons. 1. Cockcroft-Walton preaccelerator at the Fermi National Accelerator Laboratory. This device provides negative hydrogen ions at 750,000 eV kinetic energy for subsequent occeleration through the Fermilab facility.

The surface resistivity is the bulk resistivity divided by the skin depth of the material at the frequency of interest. Surface resistivity therefore has units of ohms. 19) where Z o is the impedance of free space, ( p o / ~ J 1 / *The . 20) ACCELERATION METHODS ___ 27 but we note that the second term vanishes when evaluated at the first root of 1,. 21) For copper surfaces in the 400 MHz region, this expression gives Q of order lo4 for the geometry that we are using. The Q is one figure of merit for a cavity.

51) dE, = eVsin4,. 54) dES = eVsin+,. 55) = Upon subtracting, we find dE dES r ( E ) - - T ( E , ) =~eV( sin dt + - sin 4,). 56 becomes d - ( T A E ) =eV(sin+ dt - sin+,). 58) The conversion of the phase equation to employ time as the independent variable is straightforward. 59) d -(TAE) dt = T( eV cos +, )A+ =T ~ A + . 50. Note that since A contains rl while p contains cos +,, then either A > 0 and p < 0 or A < 0 and p > 0. = PHASE STABlLlM 43 A standard approach to solving a second order differential equation of this sort is to choose a trial solution of the form AC#J= uu and pick u such that the first derivative term is zero in the equation for u.

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