Phase space measurements by a finite-width slit

Summary form only given. A general method has been developed for correcting the width and the height of a beamlet´s density profile, which are in general wider and higher than those of the original distribution function due to the finite slit width. Force-free drift motion of particles between the slit plane and the detector plane is assumed. It is found that the density profile of the beamlet on the detector plane can be expressed by a function which is an integral of the beam distribution with respect to x´. From this function (which is a function of x with slit width w and standard deviation of the distribution function σ as parameters), one can find σ and the height of the distribution function in terms of w and the FWHM (full width at half maximum) and height of the measured beamlet density profile. This analysis was carried out for a few commonly used beam distribution functions, such as the Maxwellian, Bennett, waterbag, and Kapchinskij-Vladimirskij distributions