When the Use cumulative space charge density check box is cleared, the contribution of the charged particles to the space charge density in the surrounding domain is overwritten at each iteration of the Bidirectionally Coupled Particle Tracing study step. If this check box is selected, then instead the space charge density contribution is computed as a cumulative average over successive iterations of the solver sequence. This often leads to more robust and consistent statistical convergence of the bidirectionally coupled model.

While the number of iterations taken by the solver sequence is less than or equal to the specified Number of iterations β, then the contribution of the particles to the space charge density is updated at each iteration by scaling the newly computed charge density contribution by a factor less than 1. This reduces the probability that the charge density will be overestimated. During the ramping-up iterations, the new value of the cumulative space charge density is

After the ramping-up iterations are complete (iter > β), the cumulative space charge density at each subsequent iteration is

where wj is the weight of each iteration. The weights are determined by the option selected from the Weights for subsequent iterations list:

The benefit of using an Arithmetic sequence or Geometric sequence is that the early iterations have a reduced impact on the solution. Therefore, if the first few iterations have very large relative error, this early error will attenuate more quickly than when using Uniform weighting.