(c) For the case with coaxial flow, a thin transition layer between(a)and (b) may be necessary for accuracy, but will be ignored in our analysis 3. Constricted Arc With No flow The typical arrangement is a strongly water-cooled cylindrical enclosure, made of mutually insulated copper segments, with the arc burning along its centerline(Fig. 1) Copper Insulators Water Cooling R P Arc Buffer Gas elelelelelelo Constricted Arc Fig. 1. Constricted Arc Except for the near-electrode regions, the arc properties are constant along its length. In a cross-section, the axial electric field E= E is independent of radius as well, and er small. The Ohmic dissipation rate is j E per unit volume, or oE, since j=OE. Here o varies strongly inside the arc, from zero at rRa to a maximum o at the centerline; as a rough approximation, we take -o as a representative average, and so the amount of heat deposited ohmically per unit length is zR E. This heat must be conducted to 16.522, Space Propulsion Lecture 11-12(c) For the case with coaxial flow, a thin transition layer between (a) and (b) may be necessary for accuracy, but will be ignored in our analysis. 3. Constricted Arc With No Flow The typical arrangement is a strongly water-cooled cylindrical enclosure, made of mutually insulated copper segments, with the arc burning along its centerline (Fig. 1). Fig. 1. Constricted Arc Except for the near-electrode regions, the arc properties are constant along its length. In a cross-section, the axial electric field E = Ex is independent of radius as well, and Er is small. The Ohmic dissipation rate is r j . r E per unit volume, or σE2 , since . Here r j = σ r E σ varies strongly inside the arc, from zero at r=Ra to a maximum σ c at the centerline; as a rough approximation, we take 1 2 σ c as a representative average, and so the amount of heat deposited ohmically per unit length is 1 2 πRa 2 σ cE2 . This heat must be conducted to 16.522, Space Propulsion Lecture 11-12 Prof. Manuel Martinez-Sanchez Page 2 of 18