Particles are charged by unipolar ions in the absence of an electric field. The collision of ions and particles occurs due to the random thermal motion of ions. If every ion that collides with a particle is retained, the rate of charging with respect to time is as follows:
For an initially uncharged particle, integrating this equation gives the number of charges gained due to diffusion charging as follows:
ndce2Ni 2kT '
k = the Boltzman constant T = the absolute temperature e = the charge of one electron
Here, c is the mean thermal speed of the ions and for a Maxwellian distribution is given by v8kT/7rmwhere m is the ionic mass.
When both field and diffusion charging are significant, adding the values of the n calculated with Equations 5.17(11) and 5.17(13) is not satisfactory; adding the charging rates due to field and diffusion charging is better and gives an overall rate. This process yields a nonlinear differential equation with no analytic solution and therefore has to be solved numerically. An overall theory of combined charging agrees with experimental values but is computationally cumbersome.
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