Physics
Parallel Beam
A parallel beam is a type of light beam that consists of rays that are parallel to each other. In physics, parallel beams are often used in experiments and calculations to simplify the analysis of light interactions with objects. They are also used in medical imaging techniques such as X-rays and CT scans.
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eBook - PDFSynchrotron Radiation and Free-Electron Lasers
Principles of Coherent X-Ray Generation
- Kwang-Je Kim, Zhirong Huang, Ryan Lindberg(Authors)
- 2017(Publication Date)
- Cambridge University Press(Publisher)
1 Preliminary Concepts In this chapter we look at some physics of particle and radiation beams in the parax- ial approximation. A paraxial beam is one that is well-collimated along its propagation direction, which we take to be the z axis. For a relativistic electron beam to be paraxial means that the angle between ˆ z and the velocity vector of a typical electron is small, so that v z |v ⊥ | and v z ≈ c. In the case of electromagnetic radiation, a paraxial beam is one that can be characterized by a small angular divergence, which is equivalent to saying that the angle between the optical axis ˆ z and a typical ray is small. The simi- larity between particle trajectories and optical rays runs even deeper than is suggested here, and we will see several other similar characteristics between paraxial particle and radiation beams in what follows. In the first section we cover certain essential points regarding paraxial particle beams. We start by introducing the relativistic electron phase space, and continue with a very brief description of electron beam transport and linear particle optics. This discussion will be self-contained but rather incomplete, covering only those beam properties and dynamics that are required for subsequent study of X-ray generation from relativistic beams; interested readers can consult any of the numerous texts on accelerator physics, some of which we list in the References. We conclude this section with a brief introduc- tion to the particle distribution function on phase space, which will be essential to the treatment of FEL dynamics in Chapters 3, 5, and 6. The second section introduces paraxial wave optics, starting with a treatment of diffraction and certain geometrical optics that will parallel the particle beam physics from the previous section.
eBook - PDF- Naftaly Menn(Author)
- 2004(Publication Date)
- Academic Press(Publisher)
In most cases experienced in practice, 1 2 1 ♦ Geometrical Optics in the Paraxial Area Figure 1.1 Optical beams: (a) parallel, (b,c) homocentric and (d) non-homocentric. imaging systems are based on lenses (exceptions are the imaging systems with curved mirrors). The functioning of any optical element, as well as the whole system, can be described either in terms of ray optics or in terms of wave optics. The first case is usually called the geometrical optics approach while the second is called physical optics. In reality there are many situations when we need both (for example, in image quality evaluation, see Chapter 2). But, since each approach has advantages and disadvantages in practical use, it is important to know where and how to exploit each one in order to minimize the complexity of consideration and to avoid wasting time and effort. This chapter is related to geometrical optics, or, more specifically, to ray optics. Actually an optical ray is a mathematical simplification: it is a line with no thick-ness. In reality optical beams which consist of an endless quantity of optical rays are created and transferred by electro-optical systems. Naturally, there exist three kinds of optical beams: parallel, divergent, and convergent (see Fig. 1.1). If a beam, either divergent or convergent, has a single point of intersection of all optical rays it is called a homocentric beam (Fig. 1.1b,c). An example of a non-homocentric beam is shown in Fig. 1.1d. Such a convergent beam could be the result of different phenomena occurring in optical systems (see Chapter 2 for more details). Ray optics is primarily based on two simple physical laws: the law of reflection and the law of refraction. Both are applicable when a light beam is incident on a surface separating two optical media, with two different indexes of refraction, n 1 and n 2 (see Fig. 1.2). The first law is just a statement that the incident angle, i , is Figure 1.2 Reflection and refraction of radiation.
- C. Bradley Moore(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
5 Molecular Beams PHILIP R. BROOKS CHEMISTRY DEPARTMENT RICE UNIVERSITY HOUSTON, TEXAS I. Introduction A. Intrinsic Properties B. Extrinsic Properties: Scattering C. Scope of This Chapter II. Interaction of Light with a Beam III. Beam-Laser Accomplishments A. Intrinsic Properties B. Extrinsic Properties: State Preparation C. Beam Properties IV. Speculation A. Spectroscopy B. Scattering v. Summary References I. INTRODUCTION 139 140 142 143 143 149 149 154 155 156 156 158 159 159 A molecular beam is a group of molecules which move collision free in an otherwise high vacuum in the same direction within the geometrical confines of a beam. The essential feature of a beam is the absence of collisions; this makes practicable many studies of molecular properties. One can obtain spectra with no collision or Doppler broadening or one can study the result of a single bimolecular collision on chemical reactivity without the mitigating effects of wall collisions. In these respects a molecular beam may almost be regarded as a fourth state of matter. 139 140 PHILIP R. BROOKS We restrict our attention to beams of neutral molecules near thermal energies (E ~ 1 kcal/mole IOt.I 300 em -1; V IOt.I 500 m/sec), Because of the requirement that the beam be collision free, beam densities must be kept low. Typical densities are ;s 10 12 em 3 which corresponds to the density of a gas at P ;S 3 x 10-5 Torr, normally regarded as a high vacuum. In principle beams can be formed of a wide variety of stable, metastable or reactive atoms, molecules, or free radicals. Detection techniques are the limiting factor and vary from experiment to experiment.
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