Beam Distributions Beyond RMS

The beam is often represented only by its position (mean) and the width (rms = root mean squared) of its distribution. To achieve these beam parameters in a noisy condition with high backgrounds, a Gaussian distribution with offset (4 parameters) is fitted to the measured beam distribution. This gives a very robust answer and is not very sensitive to background subtraction techniques. To get higher moments of the distribution, like skew or kurtosis, a fitting function with one or two more parameters is desired which would model the higher moments. h this paper we will concentrate on an Asymmetric Gaussian and a Super Gaussian function that will give something like the skew and the kurtosis of the distribution. — This information is used to quantify special beam distribution. Some are unwanted like beam tails (skew) from transverse wakefields, higher order dispersive aberrations or potential well distortion in a damping ring. A negative kurtosis of a beam distribution describes a more rectangular, compact shape like with an over-compressed beam in z or a closed to double-horned energy distribution, while a positive kurtosis looks more like a “Christmas tree” and can quantify a beam mismatch after filamentation. Besides the advantages of the quantification, there are some distributions which need a further investigation like long flat tis which create background particles in a detector. h particle simulations on the other hand a simple rms number might grossly overestimate the effective size (e.g. for producing luminosity) due to a few particles which are far away from the core. This can reduce the practical gain of a big theoretical improvement in the beam size.