Page 223 - Fundamentals of Magnetic Thermonuclear Reactor Design

Vacuum and Tritium System Chapter | 6 205

pumping system structure and geometry optimisation, spacecraft ambient air
modelling, and so on.
An original concept summarised later allows removing these restrictions. It
is based on a set of differential and integral characteristics of a vacuum system.
The differential characteristics include the statistically determined molecule–
surface interaction parameters (e.g. the accommodation, reflection, sticking,
condensation and stimulated gas release coefficients) and local characteristics
(such as the molecular concentration and incident molecular flow density).
The integral characteristics describe the molecular continuum interaction
with certain surfaces. The key integral characteristics are the followings:

l The capture coefficient of a sorbent, such as a vacuum surface-action pump.
l The return coefficient reflecting the possibility of return to the VS ‘area of
departure’ for a population of molecules.
These characteristics allow the construction of a closed system of equations
describing, unconditionally, a rarefied gas behaviour.
An integral method of kinetic analysis, developed as an extension of the
concept presented, is premised on using the integral form of the kinetic equa-
tion. The components in the right side of the equation describe
l thermal desorption/diffusion flows coming through the vacuum chamber wall,
l gas flows from local in-chamber sources, and
l integral flows of molecules reflected by the surface, and molecules emitted
by the surface as a result of stimulated desorption.
The resultant integral equation for the density of a molecular flow hitting an
elemental site inside the chamber is the basis for determining the characteristics
of a system under analysis. Assuming that the latter has m surfaces with deter-
mined parameters, we can take the range of integration as a composition of m
parts and transform the initial integral equation into a linear algebraic system of
equations. Equation coefficients and ‘elemental’ molecular concentration values
under assumed diffuse and isotropic scattering of molecules by the walls have
been computed for typical geometrical structures.
Any structural or geometrical complication of a VS design quickly leads to
a computational intractability. This problem can be circumvented by using the
equivalent surface method, which is a logical model and a computational algo-
rithm for estimating molecular flows in multi-component vacuum system, and
for their design optimisation.
This method implies that actual components of a system under design are
substituted by simply shaped gas-kinetic equivalents. These equivalents are
attributed characteristics that are inferred from the identity of the actual system
and its model’s molecular characteristics. For example, a sorbent’s inlet cross
section is taken to be the sorbent’s equivalent surface. The latter is attributed
the ability of ‘interacting’ with molecular flows, which the substituted sorbent
possesses. A characteristic attributed with respect to a chamber to be evacuated