The transport properties of Li
ions in
helium have received much interest owing to the relative
simplicity of this particular ion-atom system, which has allowed
the calculation of highly accurate ab initio interaction
potentials. These can be used in conjunction with transport
theory to give ``ab initio'' transport coefficients, which can
be compared directly with experiment.
However the results from experiment were confusing.
Skullerud et al.[1986] measured the ratio of 
of transverse
diffusion to mobility,
and found that their data is in significant disagreement
with values of 
calculated from the potential of
Viehland [1983], which was based on the data of
Gatland et al.[1977]. Furthermore, a highly accurate ab
initio potential calculation by Senff and Burton [1986]
yielded 
values that agrees with the measured values
within the stated uncertainty of 2%.
Furthermore, there was considerable discrepancy amongst the
mobility values of Takata [1975], Gatland et al.
[1977] and Cassidy and Elford [1985], even
allowing for
the slightly different experimental conditions under which the
experiments were performed. The differing data were finally
reconciled by explicitly recognizing the possibility that the
experiments were no longer described by a second order diffusion
equation of the form (
).
Two different ad hoc methods of eliminating the effects due to
the breakdown of this description
were applied by England and Elford [1987] and
Løvaas et al. [1988], and yielded transport data in
agreement with the ab initio calculations.
These effects are known as end-effects, because
the diffusion equation is expected to hold in the bulk of a
homogeneous neutral gas, with a uniform field, and any
departures from this state occur at the ends of the apparatus.
England and Elford [1987] assume that the end effects in time of flight mobility measurements take the form of a power series in the inverse of the drift length. By fitting this power series to their mobility measurements at different drift distances, they eliminated the end effects by extrapolating to infinite drift distance.
Løvaas et al. [1988] assume that the end effects
induce a distortion to the basic gaussian solution
() that can be written as a series in Hermite
polynomials, similar to the solution of the transport equation
() given by Skullerud [1974]. By
truncating the series at third order, they obtain expressions
for the mean and variance of the drift time. By comparing these
values at different drift distances, they can obtain values for
the transport coefficients.
In the case of lithium ions in helium, the transport properties are now
considered to be well understood. However, it has highlighted a deficiency in
the conventional transport theory based on the diffusion equation
(), which needs to be overcome if the correction
methods employed are to be understood. In this chapter, I develop a
non-hydrodynamic theory of time-of-flight experiments which provides
theoretical underpinning to the methods of England and Elford, and to those of
Løvaas et al.. These results have been reported in Standish
[1987] However, I have not treated the effects due to the
distortion of the field near the shutter, nor the effects of absorption onto
the apparatus, which are considered to be a significant contribution to the
total end-effect. Much work remains to be done in this area before there is
full understanding of end-effects.