By Professor Helmut Wiedemann Dr. (auth.)
Particle Accelerator Physics
Particle Accelerator Physicsis an in-depth and complete advent to the sphere of high-energy particle acceleration and beam dynamics.
Part I gathers the elemental instruments, recalling the necessities of electrostatics and electrodynamics in addition to of particle dynamics in electromagnetic fields.
Part II is an in depth primer in beam dynamics, partially III through the advent and outline of the most beam parameters. half IV is dedicated to the therapy of perturbations in beam dynamics. half V discusses the main points of charged particle accleration. half VI and half VII introduce the extra complicated subject matters of coupled beam dynamics and the outline of very extreme beams. half VIII is an exhaustive remedy of radiation from speeded up fees and introduces very important assets of coherent radiation akin to synchrotrons and free-electron lasers. half IX collects the appendices accumulating worthy mathematical and actual formulae, parameters and devices. options to many end-of-chapter difficulties are given.
This textbook is acceptable for a thorough two-semester direction beginning on the complicated undergraduate point.
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However, the objective of canonical transformations is to express the problem at hand in as many cyclic variables as possible. Any form of generating function that achieves this goal is therefore appropriate. To illustrate the use of generating functions for canonical transformation, we will discuss a few very general examples. 106) and i = 1, 2, . . , N the identities ∂G = P¯ i , ∂qi ∂G q¯i = + ¯ = qi . 110) ∂G = Pz . ∂z Similarly, relations for the transformation from rectangular to polar coordinates are derived from the generating function G = −Px r cos ϕ sin ϑ − Py r sin ϕ sin ϑ − Pz r cos ϑ .
Einstein’s point of view is expressed in the following quote: “It is not good to introduce the concept of the mass of a moving body M = γm0 for which no clear deﬁnition can be given. It is better to introduce no other mass concept than the ‘rest mass’ m0 . ” In this book, we take the rest mass m0 as an invariant. γ= Photon 4-Vector An analogous 4-vector can be formulated for photons using deBroglie’s re˜ = (ckx , cky , ckz ,iω). Since the energy– lations p = k and E = ω for ck momentum 4-vector is derived from the canonical momentum, we will have to modify this 4-vector when electromagnetic ﬁelds are present.
73) Noting that γdτ = dt , the extension to the Lagrange function in the presence of electromagnetic ﬁelds is L = −mc2 1 − β 2 + eAv − eφ . 75) where p is the ordinary momentum. 74) is consistent with L = T − V , where the potential V = eφ − eAv . 18). 76b) ∂A results with r˙ = v and dA dt = ∂t + (v ∇) A in an expression for the ordinary momentum p ∂A dp = −e + e [v × (∇ × A)] − e ∇φ . 77) dt ∂t Converting potentials to ﬁelds, we may recover the Lorentz force F L = F L = eE + e (v × B) . 78) 22 1 Of Fields and Forces individual particle trajectory y s z ideal beam path x y x ρ0 Fig.