or, rearran 4 1+J1+ 2 which shows how Tc eventually increases linearly with I, but its variation is faster at low current The field itself follows from(4). Define a non-dimensional field E'= E (14) E and then 2 which indicates a decreasing field(and voltage )as the current increases These results are summarized in Fig. 2. calculated with 1=1/4 The negative slope of the line E'=f() is typical of arc discharges, and creates some difficulties in their operation. We note first that the increase ofe as I decreases does not continue indefinitely; below some current level, the thermal power input to the electrodes(particularly the cathode) is insufficient to sustain the electron emission required, and the discharge transitions to a different mode, probably an"anomalous glow discharge” 16.522,S Propulsion Lecture 11-12 Prof. Manuel mar Page 5 of 18or, rearranging, Tc − Te Te − Tw = 1+ 1 + 4λ I * 2 I * (13) which shows how Tc eventually increases linearly with I * , but its variation is faster ≈ I * ( ) at low current. The field itself follows from (4). Define a non-dimensional field E* = E Eref ; Eref = 2 2kc a 1 R (14) and then E* = 1 ra = 1+ 1 + 4λ I * 2 (15) which indicates a decreasing field (and voltage) as the current increases. These results are summarized in Fig. 2, calculated with λ =1/ 4. The negative slope of the line E* = f I * ( ) is typical of arc discharges, and creates some difficulties in their operation. We note first that the increase of E* as I* decreases does not continue indefinitely; below some current level, the thermal power input to the electrodes (particularly the cathode) is insufficient to sustain the electron emission required, and the discharge transitions to a different mode, probably an “anomalous glow discharge”. 16.522, Space Propulsion Lecture 11-12 Prof. Manuel Martinez-Sanchez Page 5 of 18