By Stanley Humphries Jr.
Addresses the themes important to realizing high-power accelerators and high-brightness charged particle beams. provides a unified description of charged particle beams that's exact sufficient to be used as a textual content and entire sufficient to face as a reference. This remedy of particle beam physics prepares scholars to learn the literature and to exploit accelerators successfully. Describes the elemental principles in the back of sleek beam functions akin to stochastic cooling, high-brightness injectors and the loose electron laser. Designed to provide scholars with the severe pondering abilities important for the simplifications and problem-solving insights certain to collective physics difficulties. Serves as an autonomous reference or because the significant other publication to rules of Charged Particle Acceleration to supply a programmed creation to the sphere of particle acceleration.
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48) The three-dimensional generalization of Eq. 49) The average velocity of a one-dimensional discrete distribution is calculated by taking a weighted sum over the distribution. Again, we divide phase space into elements with dimensions )x and )vx. The average velocity at position x is the sum over all elements at x of vx times the probability that a particle is in the element. 51) The extension to a one-dimensional continuous distribution function is straightforward. 53) Note that the denominator in Eq.
3 discussed finite-difference methods to calculate particle orbits by advancing in small time steps, )t. We will concentrate on the leapfrog method that sequentially advances position and velocity. In this context, the spatial coordinates of a particle orbit are defined at times t, t+)t, t + 2)t,... while the velocity coordinates are defined at t+)t/2, t + 3)t/2,..... The first step is to find the change in the spatial positions of particles at time t = t + )t. 30) where i is the index number of particles within the group.
Another consequence is that the trajectories of particles influenced by smooth forces never cross in phase space. As two trajectories approach, the forces acting on both particles becomes almost identical. The implication is that the trajectories of particles in phase space are laminar. The trajectories follow non-intersecting streamlines, as shown in Fig. 2a. Particle 22 Phase space description of charged-particle beams Charged Particle Beams orbits plotted in configuration space clearly do not have this property (Fig.