The Physics Analysis of a Gas Attenuator with Argon as a Working Gas (Rev. 1) Page: 4 of 18
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presented in this report can serve for a general orientation only, not for getting exact
numerical values of various parameters.
2. The absorption properties of Argon
The absorption properties of argon  are illustrated by Fig.1 where the
attenuation factor A is shown for various beam energies. The other relevant parameters
for argon are presented in Table 1.
Table 1. Some parameters of argon
Atomic Atomic Collision Density at Sound speed Viscosity,
number radius cross- section normal at normal at 0 C 
A=40 ra =0.98 A 6=1.21-10-5 po= 1.78 so=320 m/s -=2.1.10-4
cm2 10-3 g/cm3 g/s-cm
Figure 2 shows the line density of argon required to reach an attenuation of 104.
Assuming that the length of the main attenuation cell is L=6 m, one sees that, to reach the
highest attenuation of A=104, one has to have the pressures in this cell in the range
between - 2 torr and - 60 torr.
3. Evaluation of the gas throughput
The mean free path for the argon atoms, evaluated as
where n is the particle density, and 6 is the collision cross-section, see Table 1. In the
pressure range 0.1 torr<p<100 torr, X lies between a few hundred microns and a fraction
of a micron (Fig. 3). This means that the gas flow is collisional in the sense that the mean
free path is much shorter than the orifice radius a. This, in turn, means that the gas
exhaust through each of the orifices will occur in a hydrodynamic manner (not in a
Knudsen manner); the discharge through each of the orifices can then be evaluated by Eq.
(14) of Ref. :
2(2 \2(y -1)
Q = ra2son , (3)
where the quantities bearing a subscript "0" refer to the attenuation cell, and y is the
adiabatic index (y-5/3 for argon). For further reference, we present also the local sound
speed (the flow velocity) at the sonic transition point,
s* = so ~ - 0.87so (4)
and the gas density at this point,
n* = no ~0.65no (5)
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Ryutov, D D; Bionta, R M; McKernan, M A; Shen, S & Trent, J W. The Physics Analysis of a Gas Attenuator with Argon as a Working Gas (Rev. 1), report, January 3, 2006; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc879188/m1/4/: accessed December 18, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.