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4.4 Free electrons and ions in gases

The behaviour of free electrons and ions in pure gases or their admixtures has been studied for most of the 20th century. The properties are important in proportional counters, ionization chambers, drift chambers and in the prediction of the electrical breakdown of gases. In this section it is assumed that the density of charged particles is sufficiently low that the probability of collisions between them are small compared to collisions with atoms or molecules.

4.4.1 Ionic mobility

The ionic mobility (μ) is defined as the velocity attained by an ion moving through a gas under unit electric field. A suitable unit is therefore m² s⁻¹ volt⁻¹. In general the mobility is a function of E/N and T, where E is the field strength and N, the Loschmidt constant, is the number of molecules m⁻³ at s.t.p. (see Ellis 1978), T is the Temperature. The unit of E/N is the Townsend (Td), 1 Td = 10⁻²¹ V m². Most early work was done using E/p where p is the gas pressure. For measurements around room temperature the effect of T is small but should be taken into account in calculating N. The mobility is constant at low values of E/N, the departure from constancy occurring when the ions attain drift velocities comparable with the agitation velocity of the gas molecule. Mobility can be critically dependent on gas purity, especially with the noble gases, because polar impurity molecules tend to cluster around the ion and so reduce its mobility. Many, but not all, early measurements were rendered quite useless by inattention to impurities. The mobility hardly varies with the charge of the ion, a doubly charged ion having practically the same mobility as a singly charged ion of either sign. The reduced mobility μ₀ m² s⁻¹ V⁻¹ is the value at a gas number density of 2.69 × 10²⁵ m⁻³. The mobility has been shown to vary as (gas number density)⁻¹ for pressures from 10 to 6 × 10⁶Nm⁻². The mobility of positive ions in gas mixtures is given by Blanc’s law (Blanc, 1908) μ = 1/∑_i f_i/μ_i where f_i is the fractional composition of the ith gas. All values in the table below are for μ₀. A dash indicates that either the particular ion does not exist or has not been examined. Where the mobility is not independent of E/N it is usual to take the mobility corresponding to the limit E = 0.

Modern techniques have shown that the number of ion species produced is much greater and more complex than was thought earlier. (See McDaniel (1964).) For example xenon ions Xeⁿ⁺ have been identified for n = 1 to 13.

Ionic mobilities for ions in their parent gas
 μ₀/(10⁻⁴ m² s⁻¹ volt⁻¹) at a gas number density of 2.69 × 10²⁵ m⁻³

Ionic mobilities for ions in various gases
 μ /(10⁻⁴ m² s⁻¹ volt⁻¹)

These values, from Tyndall (1938) are for gases at 293 K and 1.01 × 10⁵ N m⁻², and from Ellis et al. (1976) who also give details of the general theory. Later data is in Ellis (1978 and 1984).

J.W. Leake

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