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 parmeters) 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. In 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-homed 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 tails which create background particles in a detector. In 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.
- Research Organization:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- AC03-76SF00515
- OSTI ID:
- 82539
- Report Number(s):
- SLAC-PUB-95-6684; CONF-9410219-25; ON: DE95013398; TRN: 95:017196
- Resource Relation:
- Conference: Beam instrumentation workshop, Vancouver (Canada), 2-6 Oct 1994; Other Information: PBD: Sep 1994
- Country of Publication:
- United States
- Language:
- English
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