By Stanley Humphries Jr.

Addresses the themes very important to realizing high-power accelerators and high-brightness charged particle beams. provides a unified description of charged particle beams that's specific sufficient to be used as a textual content and complete sufficient to face as a reference. This remedy of particle beam physics prepares scholars to learn the literature and to take advantage of accelerators successfully. Describes the fundamental rules in the back of glossy beam functions comparable to stochastic cooling, high-brightness injectors and the unfastened electron laser. Designed to provide scholars with the serious pondering abilities invaluable for the simplifications and problem-solving insights exact to collective physics difficulties. Serves as an self sufficient reference or because the significant other booklet to ideas of Charged Particle Acceleration to supply a programmed advent to the sector of particle acceleration.

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12). To illustrate the phase dynamics of high energy particles, we shall consider the relativistic harmonic oscillator. Here, the change of kinetic energy of a particle moving in the linear force of Eq. 3) is comparable to or greater than the rest energy. We must account for a change in the relativistic mass factor, (. 3. Representation of particle motions in phase-space. (a) Longitudinal motion (z-vz) of protons accelerated by an axial electric field, Ez = 105 V/m. 3 m. applicable to the transverse oscillation of charged particles in beams.

As time advances, the shapes of individual segments change, but their net area remains constant. Adjacent segments always share the same boundary particles. In the smooth force limit, the segments cannot overlap or exchange particles. 11 illustrates these facts. In the figure, an applied force of the form Fx = -kx acts on particles. They initially occupy an irregular phase space area. Plots of the evolution of the rectangular boundaries at three later times are shown. Note that the boundaries between segments are always straight lines.

A form of the Boltzmann equation that includes only electromagnetic forces, the Vlasov equation, is often encountered in charged particle beam physics. 9 shows a region of phase space occupied by a one-dimensional beam distribution. The function f(x,vx,t) represents the density of orbit vector points at a particular time. Suppose we measure f near an orbit vector point [xo(to),vxo(to)] at time to. 69) states that the measurements always give the same value if we follow the orbit vector as it moves with time, or Here, we seek an alternate equation that prescribes how f varies in time at a constant position in phase space, (x, vx).