Physics and Engineering of Radiation Detection

154 Chapter 3. Gas Filled Detectors

is actually the change in the electric field inside the active volume. Hence the drift
of electrons and ions both contribute to the overall output pulse. This implies that
understanding the drift of positive charges is as important in a chamber as the
negative electrons.
In the presence of externally applied electric field, ions move toward the negative
electrode with a drift velocity that is much lower than that of electrons. The distri-
bution of these ions can be fairly accurately characterized by a Gaussian distribution
of the form

dN=

N

√

4 πDt

e−(x−tvd)

(^2) / 4 Dt
dx, (3.2.6)
wherevdis thedriftvelocity of ions, which is actually the velocity of the cloud
of ions moving along the electric field lines. This velocity is much lower than the
instantaneous velocity of ions.tis the ion drift time. Drift velocity is an important
parameter, since it tells us how quickly we should expect the ions to reach the
cathode and get collected. It has been found that as long as no breakdown occurs
in the gas, this velocity remains proportional to the ratio of electric field and gas
pressure.
vd=μ+

E

P

(3.2.7)

HereE is the applied electric field,P is the pressure of the gas, andμ+is the
mobility of ions in the gas. Mobility depends on the mean free path of the ion in
the gas, the energy it looses per impact, and the energy distribution. In a given gas,
it therefore remains constant for a particular ion. Table 3.2.1 gives the mobility,
diffusion coefficient, and mean free paths of several ions in their own gases.

Table 3.2.1: Mean free pathλ, diffusion coefficientD, and mobilityμof ions in
their own gas under standard conditions of temperature and pressure.

Gas λ(× 10 −^5 cm) D(cm^2 /s) μ(cm^2 s−^1 V−^1 )

H 2 1.8 0.34 13.0

He 2.8 0.26 10.2

Ar 1.0 0.04 1.7

O 2 1.0 0.06 2.2

H 2 O 1.0 0.02 0.7

A useful relationship between mobility and diffusion coefficient given by

μ+=

e

kT

D+, (3.2.8)

is known as Nernst-Einstein relation. Herekis the Boltzmann’s constant andTis
the absolute temperature.