By D. A. Edwards
The 1st part bargains with the movement of a unmarried particle below the impression of digital and magnetic fields. the fundamental language of linear and round accelerators is built. the primary of section balance is brought in addition to part oscillations in linear accelerators and synchrotrons. provides a therapy of betatron oscillations through an day trip into nonlinear dynamics and its program to accelerators. the second one part discusses depth based results, quite area cost and coherent instabilities. comprises tables of parameters for a variety of accelerators that are utilized in the various difficulties supplied on the finish of every bankruptcy.
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Extra resources for An Introduction to the Physics of High Energy Accelerators
The quality factor, or Q, of the cavity is defined as the ratio of the stored energy to the energy lost in one radian of an oscillation. 14) and the relation JA = - J l . 52, the stored energy is a little over 25% of the energy that would be associated with the field E , filling the entire volume V . We next calculate the losses due to the ohmic heating in the cavity wall. 15) where J is directed radially inward or outward on the end plates, and is parallel to the axes on the inner surface of the cylinder.
38) We can now address the question of whether or not a particle initially near to the ideal particle in energy and phase remains so as it proceeds through the accelerator. We will illustrate the principle for the case of a circular accelerator. For a linear accelerator, the argument is nearly identical; only a few words need be changed. The natural first step is to apply the difference equations to a variety of initial conditions. 15. Application of the difference equations for synchrotron motion for five initial conditions.
If, on the other hand, we use excursion of*time of passage, A t , rather than excursion of phase of passage, A 4 , then A 4 = wrf A t and in A E-At coordinates the area becomes A T ~= TAB -, ? 74) which is a constant. Of course E and t are well known to be a canonically conjugate pair. The area in phase space which contains the particles of a bunch is termed the longitudinal ernittance. It is to be hoped that this emittance is smaller than the area of the entire stable region. 75) As noted earlier, such a bucket is referred to as a stationary bucket, since the ideal particle is not accelerated in this case.
An Introduction to the Physics of High Energy Accelerators by D. A. Edwards