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One of the most fundamental methods of measuring beam emittance is the quadrupole scan method. The emittance of the beam for a particular plane of interest (i.e., horizontal or vertical) can be obtained by varying the field strength of a quadrupole (or quadrupoles) upstream of a monitor (i.e., a wire or a screen). [4]
One dimensional position-momentum plot, showing the beam ellipse described in terms of the Courant–Snyder parameters. In accelerator physics, the Courant–Snyder parameters (frequently referred to as Twiss parameters or CS parameters) are a set of quantities used to describe the distribution of positions and velocities of the particles in a beam. [1]
Emittance is a common quantity in beam physics which describes the volume of a beam in phase space, and is normally conserved through typical linear beam transformations; for example, one may transition from a beam with a large spatial size and a small momentum spread to one with a small spatial size and a large momentum spread, both cases retaining the same emittance.
The equations below assume a beam with a circular cross-section at all values of z; this can be seen by noting that a single transverse dimension, r, appears.Beams with elliptical cross-sections, or with waists at different positions in z for the two transverse dimensions (astigmatic beams) can also be described as Gaussian beams, but with distinct values of w 0 and of the z = 0 location for ...
In optics, the complex beam parameter is a complex number that specifies the properties of a Gaussian beam at a particular point z along the axis of the beam. It is usually denoted by q . It can be calculated from the beam's vacuum wavelength λ 0 , the radius of curvature R of the phase front , the index of refraction n ( n =1 for air), and ...
Etendue is the product of geometric extent and the squared refractive index of a medium through which the beam propagates. [1] Because angles, solid angles, and refractive indices are dimensionless quantities, etendue is often expressed in units of area (given by dS). However, it can alternatively be expressed in units of area (square meters ...
The luminous intensity (in candelas) is a measure of how bright the beam in a particular direction is. If a lamp has a 1 lumen bulb and the optics of the lamp are set up to focus the light evenly into a 1 steradian beam, then the beam would have a luminous intensity of 1 candela. If the optics were changed to concentrate the beam into 1/2 ...
The two main ways of using radiation damping to reduce the emittance of a particle beam are the use of undulators and damping rings (often containing undulators), both relying on the same principle of inducing synchrotron radiation to reduce the particles' momentum, then replacing the momentum only in the desired direction of motion.
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