Mass attenuation length

The energy loss of photons in matter can be characterized by the cross section of the process and also by the mean free path of photons between interactions. The latter can be expressed in units of surface density, and then it is called mass attenuation length. Photon attenuation lengths for various elements are shown inO Fig. 8.13 as taken from Bichsel et al. (2002). 

The photon mean free path (mass attenuation length) as a function of photon energy for various absorbers (Bichsel et al. 2002). The photon intensity after traversing the absorber of thickness X is / = /oexp(-x/A)... 

Absorption coefficients define the X-ray attenuation effect from a given solids. We use both mass absorption coefficients, //m, and linear absorption coefficients, p, with these being related by ju = j.umpx, where p is the density of a given solid and x is the X-ray path length. The mass absorption for any material can be calculated from the elemental mass absorption coefficients by the relation pm = Z/ / where the f and the are the weight fraction and linear absorption coefficients, respectively, for each element in the material. 

It can be seen that the pulse decay strongly depends on cycle time (tperi d) and reactor bed length. If the periodic time is very long the system reaches a so-called quasisteady state in periodic operation and very short periods (see curve (a) in Fig. 4.9) lead to a merging of pulses. The choice of pulsing frequency can be influenced, e.g. by pulse attenuation characteristic, mass storage in catalyst particles and reaction kinetics. 

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