12.5 Choice of the Gas Pressure 427
path of the particles are balanced to a certain degree by some advantages in the
measuring accuracy, and we want to review them here. We note in passing that the
wall thickness of a vessel must increase in proportion to the over-pressure it has
to hold.
We have stated in (2.85) that for the mobility tensor the electric and magnetic
fields scale with the gas density. One would therefore like to discuss the gas density
always in connection with the corresponding change of the electric and magnetic
field strengths, thus keeping the drift-velocity vector constant. But in practice an in-
crease of the relevant field strength is easy in the electric and difficult in the magnetic
case. Therefore, we proceed by specifying the magnetic field first, the gas density is
discussed next, and then the electric fields are adjusted accordingly. The gas density
is varied by changing the pressure, since one usually works at room temperature.
Let us consider the various consequences of a change of the gas pressure by a
factor p > 1, say from 1 bar to p bar. Table 12.10 contains a summary of the most
important effects.
12.5.1 Point-Measuring Accuracy
In measurement accuracy, insofar as it is limited by diffusion, one gains by increas-
ing the pressure – unless the limitation is in the diffusion transverse to the magnetic
field, and
ωτ
1. Therefore, we distinguish between the following:
(a) Longitudinal diffusion or
ωτ
1: For the width of the diffusion cloud one
gains a factor l/
√
p (2.61, 63), and in the accuracy to find the centre of the
cloud one gains another factor 1/
√
p, because the statistical fluctuations vary
with 1/
√
N
tot
, where N
tot
is the total number of electrons in the diffusion cloud.
Therefore, the over-all gain is a factor 1/p.
(b) Transverse diffusion with
ωτ
1: For the width of the diffusion cloud one
loses a factor
√
p according to (2.61, 63, 72). The statistical fluctuations com-
pensate this; therefore, the over-all factor is 1.
The contributions to the measurement accuracy that arise from the driftpath varia-
tions have statistical fluctuations that vary with 1/
√
N
eff
(see (1.73) and Sect. 7.2.3).
As the pressure is increased, N
eff
increases as well, but only slowly. For the purpose
of the present estimates we take N
eff
proportional to
√
p (Figs. 1.22 and 1.23). The
situation would change where declustering occurred in any important measure. The
drift-path variations are partly due to the wire geometry, i.e. constant when p varies,
but partly they have a pressure dependence of their own. This is the case for the wire
E ×B effect. Here we refer to the angle at which the electrons approach the wires in
their immediate neighbourhood (Sect. 7.3.1). The tangent of the effective Lorentz
angle
ψ
will decrease roughly proportional to 1/p,asp increases. A smaller angle
ψ
will reduce the drift-path variations. Depending on how important the wire E ×B
effect is in comparison to the other drift-path variations, we may say in summary
that the contributions to the measurement accuracy that arise from the drift-path
variations decrease as a function of p which is somewhere between 1/p and 1/p
0.25
.