8 Accelerator Engineering and Technology: Accelerator Technology
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diffuse) between the surfaces. Its precise determination can be quite tedious, apart
from the few simple geometrical cases of flat plates, nested cylinders and nested
spheres.
8.3.4.3 Gas Conduction
Since J. Dewar’s invention (1898) of the cryogenic vessel which bears his name,
evacuated envelopes provide the best insulation against heat transport in gaseous
media. At low pressure, convection becomes negligible and only residual gas
conduction is at work. This process operates in two distinct regimes, depending
upon the value of the mean free path of gas molecules relative to the typical
distance d between the cold and warm surfaces.
The mean free path of gas molecules, as predicted by kinetic theory, scales with
the square root of temperature and inversely with pressure and the square root of
molar mass. It therefore becomes large at low pressure, high temperature and for
light gas species.
When is much less than d corresponding to higher pressure, the probability
of interaction of a given molecule with others before it travels distance d is high
(viscous regime), and heat diffuses as in any continuous medium:
Q = k(T )AdT /dx.
(8.31)
Note that the thermal conductivity k(T) of the gas is independent of pressure.
When is much greater than d at low pressure, the molecular regime prevails
and the heat transfer between two surfaces at temperatures T 1 and T 2 is given by
Kennard’s law:
Q = A α(T ) ) P (T 2 − T 1 ) ,
(8.32)
where Ω is a parameter depending upon the gas species, and α is the “accommodation coefficient” representing the thermalization of molecules on the surfaces;
its value depends on T 1 , T 2 , the gas species and the geometry of the facing surfaces.
Note that the conductive heat flux in molecular regime is proportional to pressure P
and independent of the spacing between the surfaces (and therefore not amenable to
the concept of thermal conductivity). Typical values of heat flux by gas conduction
at cryogenic temperature are given in Table 8.14.
8.3.4.4 Multilayer Insulation
Multi-layer insulation (MLI) is based on n multiple reflecting shields wrapped
around the cryogenic piece of equipment to be insulated, with the aim of benefiting
from the n + 1 reduction factor in radiative heat in-leak. In practice, this is
implemented in the form of aluminium or aluminized polymer films, with low
395
diffuse) between the surfaces. Its precise determination can be quite tedious, apart
from the few simple geometrical cases of flat plates, nested cylinders and nested
spheres.
8.3.4.3 Gas Conduction
Since J. Dewar’s invention (1898) of the cryogenic vessel which bears his name,
evacuated envelopes provide the best insulation against heat transport in gaseous
media. At low pressure, convection becomes negligible and only residual gas
conduction is at work. This process operates in two distinct regimes, depending
upon the value of the mean free path of gas molecules relative to the typical
distance d between the cold and warm surfaces.
The mean free path of gas molecules, as predicted by kinetic theory, scales with
the square root of temperature and inversely with pressure and the square root of
molar mass. It therefore becomes large at low pressure, high temperature and for
light gas species.
When is much less than d corresponding to higher pressure, the probability
of interaction of a given molecule with others before it travels distance d is high
(viscous regime), and heat diffuses as in any continuous medium:
Q = k(T )AdT /dx.
(8.31)
Note that the thermal conductivity k(T) of the gas is independent of pressure.
When is much greater than d at low pressure, the molecular regime prevails
and the heat transfer between two surfaces at temperatures T 1 and T 2 is given by
Kennard’s law:
Q = A α(T ) ) P (T 2 − T 1 ) ,
(8.32)
where Ω is a parameter depending upon the gas species, and α is the “accommodation coefficient” representing the thermalization of molecules on the surfaces;
its value depends on T 1 , T 2 , the gas species and the geometry of the facing surfaces.
Note that the conductive heat flux in molecular regime is proportional to pressure P
and independent of the spacing between the surfaces (and therefore not amenable to
the concept of thermal conductivity). Typical values of heat flux by gas conduction
at cryogenic temperature are given in Table 8.14.
8.3.4.4 Multilayer Insulation
Multi-layer insulation (MLI) is based on n multiple reflecting shields wrapped
around the cryogenic piece of equipment to be insulated, with the aim of benefiting
from the n + 1 reduction factor in radiative heat in-leak. In practice, this is
implemented in the form of aluminium or aluminized polymer films, with low