Measurements in Phase Spaces

Abstract

In general, the motion of particles can be described by the Hamiltonian formalism based on the well-known Hamiltonian equations. Assuming an ensemble of N identical, non-interacting particles, the Hamiltonian of a particle depends only on six coordinates in so-called phase space. Here the assumption of non-interacting may be a particular case, but it is a very common one. Therefore, the N particles will occupy a six-dimensional volume in the phase space, determined by their distribution over the six coordinates. For the following reasons, measurement of phase space distributions are important for the accelerator designer, physicist, operator, and, last but not least also for the experimentalist: