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The normalized emittance does not change as a function of energy and so can be used to indicate beam degradation if the particles are accelerated. For speeds close to the speed of light, where β = v / c {\displaystyle \beta =v/c} is close to one, the emittance is approximately inversely proportional to the energy.
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 ...
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]
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 ...
This implies that the smaller the beam size at the interaction point, the faster the rise of the beta function (and thus the beam size) when going away from the interaction point. In practice, the aperture of the beam line elements (e.g. focusing magnets) around the interaction point limit how small beta star can be made.
Beamstrahlung (from beam + bremsstrahlung) is the radiation from one beam of charged particles in storage rings, linear or circular colliders, namely the synchrotron radiation emitted due to the electromagnetic field of the opposing beam. [1] [2] Coined by J. Rees in 1978. [3]
A total of 177 quadrupole magnets (magnetic lenses) focuses the beam to provide a beam emittance of 5.5 nm rad. [1] 120 sextupole magnets correct the chromatic focusing errors of the quadrupoles. 73 horizontal and vertical beam steerers are used to continuously correct the position of the electron beam. Finally 24 skew quadrupole magnets are ...