By Stanley Humphries Jr.

Addresses the subjects very 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 adequate 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 rules at the back of sleek beam purposes resembling stochastic cooling, high-brightness injectors and the loose electron laser. Designed to provide scholars with the serious considering talents precious for the simplifications and problem-solving insights designated to collective physics difficulties. Serves as an self sufficient reference or because the better half publication to ideas of Charged Particle Acceleration to supply a programmed advent to the sphere of particle acceleration.

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68) where . Because of the axial bunching, Ti' is larger than Ti. 7. 69) implies that the density of orbit vectors of a collisionless group of particles is constant in a frame of reference moving with the vectors through phase space. If we view the collection of vector points as a fluid, Eq. 69) states that the fluid is locally incompressible. In fluid dynamics, relationships like Eq. 69) are called Lagrangian equations — they are defined in a frame of reference that moves with the fluid. 52 Phase-space description of charged-particle beams Charged-particle beams Often, the Lagrangian viewpoint is not the most convenient form.

Under this condition, the theory of linear algebra states that two-dimensional transformations preserve elements of area. 40) Extension of the derivation to six-dimensional phase space orbit vectors leads to the conclusion that the hypervolume occupied by a collection of particles is conserved over each time step. 41) 42 Phase space description of charged-particle beams Charged Particle Beams The symbol D/Dt denotes the convective derivative. In fluid dynamics, convection denotes moving along with fluid.

46) in the limit that . The units of n(x,y,z) are particles/m3. We can write an analog for Eq. 45) in continuous form. Again, consider a one-dimensional distribution. 47) If we extend the integration limits on the right hand side of Eq. 47) over all velocities, then the left hand side equals N(x). Substituting in Eq. 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.