Electrostatic-Probe Studies in a Flame Plasma

Simple theoretical considerations have yielded an approximate formula for the ion current per unit length I_i to a cylindrical probe (radius r_p, bias voltage V) immersed in a collision‐dominated moving plasma (subsonic velocity=v_f, electron density=n_e, ion mobility=μ_i). $$I_i=\frac{{\text{2(πμ}}_i{\epsilon }_0{)}^{\text{1/3}}{\mathrm{(n}}_e{\mathrm{ev}}_f{\mathrm{V)}}^{\text{2/3}}}{[\log {\mathrm{(I}}_i{\text{/2n}}_e{\mathrm{ev}}_f{r}_p{\mathrm{)]}}^{\text{2/3}}}\mathrm{\hspace{0.17em}(}\mathrm{mks})$$ where e is the electronic charge. This relation has been checked with a propane/air flame and a moving probe; it is found to be correct within ±50% over several decades of probe voltage, probe‐flame velocity and flame ionization. A more favorable choice of μ_i in the above expression improves the agreement between theory and experiment to ±30%. Measurements of sheath thickness obtained from the mutual interference of two adjacent probes support the basic tenets of the theoretical model. It is concluded that, in many instances of probe measurements in flames and other collision‐dominated plasmas, the velocity‐dependent approach adopted in this paper will be necessary since very large errors can arise if the usual static continuum plasma formulas are used. (Errors of up to a factor of 100 have been reported.)