By D. A. Edwards
The 1st part offers with the movement of a unmarried particle less than the effect of digital and magnetic fields. the elemental language of linear and round accelerators is constructed. the main of part balance is brought in addition to part oscillations in linear accelerators and synchrotrons. offers a remedy of betatron oscillations by means of an day trip into nonlinear dynamics and its software to accelerators. the second one part discusses depth established results, quite area cost and coherent instabilities. contains tables of parameters for a variety of accelerators that are utilized in the varied difficulties supplied on the finish of every bankruptcy.
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Extra resources for An Introduction to the Physics of High Energy Accelerators
76 during this process. Suppose that our simple pillbox cavity were filled with a material of relative permeability K , = p / p o . 4 will now contain a factor of K , on the right hand side. Now we need a mechanism for varying K , through the acceleration cycle. 9 shows one approach to providing tunability while retaining the material-free passage for the beam. K. 4 Accelerating Structures Though the discussion of the preceding section may be useful to illustrate the principles of acceleration in a large accelerator, in fact a single cavity is seldom sufficient to provide the requisite energy gain per turn in a synchrotron and surely not sufficient to produce the final energy of a linac.
18 in that these dynamical variables change by rather small amounts from turn to turn. 39) dAE -= eV(sin 4 dn - sin 4$). 41) provided that we assume a constant accelerating voltage and sufficiently small dE,/dn. 43) or, 1 d4 2 dn -(-) + 771w,7eVc2 (cos 4 v2Es + 4 sin 4s)= constant. 44) + This is formally identical to the expression for the total “energy” T V = U,where the first term on the left is the “kinetic energy” T, and the second term is the “potential energy” V. We can therefore make an energy level diagram where horizontal lines indicating the total “energy” of the particle are drawn in addition to the “potential energy” function V .
Both came into prominance as the principal approaches to high energy acceleration just after World War 11. In the case of the linac, radar components could be easily adapted to build the first of the big linacs. In the case of the synchrotron, the invention of the phase focusing principal in 1945 coupled with significant government support for research in particle physics made possible the construction of a first generation of synchrotrons, which came into operation in about 1950. 1 ACCELERATION METHODS Our limited goal in this part of the chapter is to provide an elementary picture of the mechanisms of acceleration on which to base the discussion of longitudinal stability in linear accelerators and synchrotrons.
An Introduction to the Physics of High Energy Accelerators by D. A. Edwards