By Andrzej Wolski
Particle accelerators are crucial instruments for clinical learn in fields as various as excessive power physics, fabrics technology and structural biology. also they are usual in and medication. generating the optimal layout and reaching the easiest functionality for an accelerator is dependent upon an in depth figuring out of many (often complicated and infrequently sophisticated) results that make certain the houses and behaviour of the particle beam. Beam Dynamics in excessive power Particle Accelerators offers an creation to the strategies underlying accelerator beam line layout and research, taking an strategy that emphasizes the splendor of the topic and leads into the improvement of a variety of robust concepts for figuring out and modeling charged particle beams.
Readership: Undergraduate scholars who're trying to find an advent to beam dynamics, and graduate scholars and researchers within the box.
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Extra info for Beam Dynamics in High Energy Particle Accelerators
Sample text
Middle: quadrupole. Bottom: sextupole. Fields on the left are normal (an = 0); those on the right are skew (bn = 0). Co-ordinate axes are shown only for the normal quadrupole field, but similar axes apply for all fields. The view of each field is that of a beam travelling in the +z direction. 73). Conventionally, a pure multipole with ϕn = 0 or ϕn = π is known as a normal multipole, while a pure multipole with ϕn = ±π/2 is known as a skew multipole (see Fig. 3). The units of Cn depend on the order of the multipole.
Before we describe how to do this, we shall give expressions for the vector potential A and the magnetic field B in terms of the generalised gradients: these expressions will be useful for studies of the effect of a given three-dimensional magnetic field on the beam dynamics in an accelerator. The scalar and vector potentials are related by: B = ∇ × A = −∇φmag . 115)). 135) leads to the relationships: ∂φmag ∂Az = −r , ∂θ ∂r ∂Az ∂Ar 1 ∂φmag − = , ∂r ∂z r ∂θ ∂φmag ∂Ar =r . 133), the vector potential has components: ∞ ∞ Ar = m=−∞ =0 (−1) +1 |m|!
Hence, to generate a pure multipole field in a magnet containing material of infinite permeability, we just need to shape the material so that its surface follows a surface of constant magnetic scalar potential for the required field. e. 61): − ∂ ∂ +i ∂y ∂x φmag = By + iBx = Cn (x + iy)n−1 . 64) where: x + iy = reiθ . 64) is indeed the potential for a pure multipole of order n can be shown as follows. 66) where rˆ and θˆ are unit vectors in the directions of increasing r and θ, respectively. 66) that: −∇φmag = x ˆ sin ((n − 1)θ − ϕn ) |Cn | rn−1 +ˆ y cos ((n − 1)θ − ϕn ) |Cn | rn−1 .