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Calculate RMS emittance of the original beam: = If the length of the quadrupole is short compared to its focal length f = 1 / K {\displaystyle f=1/K} , where K {\displaystyle K} is the field strength of the quadrupole, its transfer matrix Q {\displaystyle Q} can be approximated by the thin lens approximation:
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 ...
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.
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.
Beam divergence usually refers to a beam of circular cross section, but not necessarily so. A beam may, for example, have an elliptical cross section, in which case the orientation of the beam divergence must be specified, for example with respect to the major or minor axis of the elliptical cross section.
Euler–Bernoulli beam theory (also known as engineer's beam theory or classical beam theory) [1] is a simplification of the linear theory of elasticity which provides a means of calculating the load-carrying and deflection characteristics of beams. It covers the case corresponding to small deflections of a beam that is subjected to lateral ...
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 steradian then the source would have a luminous intensity of 2 candela.
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