3.2. Diffusion and Drift of Charges in Gases 153
dxat a distancexfrom the center of the initial charge distribution after timet.D
is generally reported in dimensions ofcm^2 /sand is an important quantity since it
can be used to determine the standard deviation of the linear as well as the volume
distribution of charges through the relations
σx =√
2 Dt (3.2.4)
and σv =√
6 Dt. (3.2.5)Electrons, owing to their very small mass, diffuse much faster. This can also be
deduced by comparing the thermal velocities of electrons and ions, which usually
differ by two to three orders of magnitude. The diffusion coefficient for electrons is,
therefore, much different from that of the ions in the same gas. Since the diffusion
coefficient has mass and charge dependence, therefore for different ions it assumes
values that may differ significantly from each other. Further complications arise
due to its dependence on the gas in which the ion is moving. Since in radiation
detectors we are concerned with the movement of ions that are produced by the
incident radiation therefore we restrict ourselves to the diffusion of ions in their own
gas. Addition of admixture gases in the filling gas can also modify the diffusion
properties, in which case the correct value of the diffusion coefficient, corresponding
to the types and concentrations of the gases used, should be sought. The values of
diffusion coefficients for different gases and gas mixtures have been experimentally
determined and reported by several authors (see Table.3.2.1).
A.1 DiffusioninthePresenceofElectricField
In the presence of electric field the diffusion is no longer isotropic and therefore can
not be described by a scalar diffusion coefficient. The diffusion coefficient in this
case is a tensor with two non-zero components: a longitudinal componentDLand
a transverse componentDT. For many gases, the longitudinal diffusion coefficient
DLis smaller than the transverse diffusion coefficientDT(39).
3.2.B DriftofChargesinElectricField................
In a gaseous detector, the Maxwellian shape of the energy distribution of charges
can not be guaranteed. The reason is the applied bias voltage that creates electric
field inside the active volume. The electrons, owing to their small mass, experience
a strong electric force and consequently their energy distribution deviates from the
pure Maxwellian shape. On the other hand, the distribution of ions is not signifi-
cantly affected if the applied electric field is not high enough to cause discharge in
the gas (39). The electrons behave quite differently than ions in the presence of
electric field and therefore we must study the two types of charges separately.
B.1 DriftofIons...........................
In a gaseous detector the pulse shape and its amplitude depend not only on the
motion of electrons but also of ions. The ions are positively charged and much
heavier than electrons and therefore move around quite sluggishly. In most gaseous
detectors, specially ionization chambers, the output signal can be measured from the
positive or from the negative electrode. In both cases, however, what is measured