next up previous contents index
Next: Model Calculation Up: End Effects in Previous: Lithium ion -

Nonhydrodynamic Contributions to End-Effects in Time-of-Flight Swarm Experiments

Let us consider an experiment where the time at which the centroid arrives at the collector is measured. This is not the same thing as measuring the time at which the peak collector current occurs. We will deal with the experiment in which the peak collector current is measured in the next section.

The distance travelled by the centroid in time t can be found by integrating :

 

If we measure the times and at two different drift distances and , and then extract the   drift velocity from the ratio , as Løvaas et al. [1988] do, then the non-hydrodynamic effects are completely eliminated. However, if we just take the ratio of drift length to drift time, then a correction needs to be made to take into account the term. Inverting (gif) to get t as a function of , the measured value of the drift velocity is obtained by dividing by the time (since all vectors in the system must be proportional to we can treat them as scalar quantities):

 

England and Elford [1987] supposed that the correction due to all the end effects is a power series in :

 

Equation (gif) is exactly this form, the correction being just the sum of a geometric series:



Russell Standish
Thu May 18 11:43:52 EST 1995