Account of near-cathode sheath in numerical models of high-pressure arc discharges

Abstract

Three approaches to description of separation of charges in near-cathode regions of high-pressure arc discharges are compared. The …rst approach employs a single set of equations, including the Poisson equation, in the whole interelectrode gap. The second approach employs a fully non-equilibrium description of the quasi-neutral bulk plasma, complemented with a newly developed description of the space-charge sheaths. The third, and the simplest, approach exploits the fact that a signi…cant power is deposited by the arc power supply into the near-cathode plasma layer, which allows one to simulate the plasma-cathode interaction in the …rst approximation independently of processes in the bulk plasma. It is found that results given by the di¤erent models are in a generally good agreement, and in some cases the agreement is even surprisingly good. It follows that the predicted integral characteristics of the plasma-cathode interaction are not strongly a¤ected by details of the model provided that the basic physics is right.

Gas tungsten arc models including the physics of the cathode layer: remaining issues

“…It implies that assumption (A6) is verified, as checked for free burning arcs in [11]. For GTA applications, the cathode tip end radius is one order of magnitude less than the arc attachment radius, r tip ≈ 10 −4 m. If r tip is used to define the characteristic length, then λ r < r tip and assumption (A6) should still be satisfied.…”

“…A problem with these approaches was their poor ability to predict both the electric potential and the temperature field in good agreement with experimental measurements [10]. In particular, approaches accounting for a self-consistent modelling of the cathode sheath are known to predict sheath voltage drop and plasma column voltage in good agreement with experimental data over a broad range of current intensity spanning from high intensity discharge lamps to free burning arcs [10,11]. However, an underestimation of the arc temperature was observed by Baeva et al [12] applying a model that takes into account thermal and chemical non-equilibrium in the plasma column (model hereinafter referred to as the original fully non-equilibrium (FNE) model).…”

“…The second numerical approach combines cathode layer and plasma column. The plasma column is then modeled with a two-temperature plasma (2T-plasma) model assuming chemical equilibrium (another possible alternative is a local thermal equilibrium or LTE-plasma [11]). The cathode layer is, as in [14], made of a space-charge layer (or sheath), a Knudsen layer, and an ionization layer (or pre-sheath).…”

“…But the ionization layer is treated as part of the cathode boundary since it cannot be described by a plasma column that assumes chemical equilibrium. These approaches were compared two by two by Benilov et al [11] computing free burning arc test cases in one-space dimension and two-space dimension (with an hemispherical cathode). At atmospheric pressure and for a current density larger than about 5 × 10 7 A m −2 the three approaches provide calculation results in good agreement since the introduction of a cathode boundary layer and its sub-division in up to three sub-layers is valid in the context of free burning arc [11].…”

“…Numerical results are presented in the sequel to illustrate the effect of some modelling assumptions. Modelling assumptions specific to the FNE-approach by Baeva et al [11,14], and to the approach developed by Pekker at al. [19,20], are also addressed.…”