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. 2025 May 26;15:18378. doi: 10.1038/s41598-025-01904-4

Table 3.

Boundary conditions32.

Governing equations Ground electrode boundary Needle electrode boundary Open boundary
Electron transport equation Outflow fluxInline graphic Flux of secondary electrons Inline graphic
Positive ion transport equation Zero densityInline graphic Outflow fluxInline graphic Inline graphic
Negative ion transport equation Outflow fluxInline graphic Zero densityInline graphic Inline graphic
Poisson equation Ground potential Positive DC potential Zero chargeInline graphic