ISSN:
1089-7623
Source:
AIP Digital Archive
Topics:
Physics
,
Electrical Engineering, Measurement and Control Technology
Notes:
For the analytical and numerical description of the emittance of a particle beam in cylindrical symmetric transport and accelerator systems often the rr′ plane is used, yielding a sectional emittance ε (r, r′). In contrast, emittance measurements are mostly taken as the projectional emittance ε (x, x′). As could be shown earlier, the description of a cylindrical symmetric beam in the projectional xx′ plane of phase space results in the presence of lines for each ring of particles, connecting the two corresponding points, with which the same beam is described in the rr′ plane. There is a very special intensity distribution along these lines, both for straight as well as for skew trajectories. It is shown here that the theoretically obtained density distribution along such a line is a weight function for the intensity measured with a slit of width Δx. For one particle it can also be interpreted as a probability function for the particle being at a certain position x0. In view of Liouville's theorem, the case of the two-dimensional emittance in cylindrical symmetric systems is discussed, where this law of conservation is, due to the coupling of the x and y planes, not generally applicable. It is shown here that for an emittance measurement performed in the xx′ plane, care has to be taken when choosing the slit width, since a small Δx yields a good spatial resolution, but increases the risk of missing information in the center of each connecting line. © 1997 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.1148280
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