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```charge injection boundary condition.
Figure 4-14 shows electric field, current density, and charge density on the emitter
surface. The 12 o'clock position corresponds to location of the minimum gap between
the emitter and the outer cylinder. All choices except case 4 for the charge injection
parameters allow variation of the solution along the emitter surface. The electric field
variation is the same for each case except that cases 3 and 4 drive the field strength
closer to E,,,. This is consistent with the fact that pref = 10-6 Cm- 3 corresponds to
the intersection with the E, line in figure 4-7a. Case 1 and 2 drive too much current
injection such that the field is driven below E,,. Since pref is the same for cases 3 and
4, the effect of Eref surmised previously is confirmed; the lower Eref drives higher
sensitivity to the normal electric field resulting in greater variation in emitted current
along the surface.
p[C/m3 ]
Current Density [A/m2
X,
0.4
0.4
0.09
0.3
10
1
9
0.3
0.2
8
0.2 -.
0.1
7
0.1
0
6
-0.1
0.09
0.08
0.06
0-
0.05
--0.1 -
0.04
-0.2
0.03
0.02
4
-0.2
3
-0.3
2
-0.3
-0.4
1
-0.4-
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.01
-0.4
0.4
(a) Charge density.
-0.3
-0.2
-0.1
0
0.1
0.2
03
04
(b) Current density.
Figure 4-13: Charge density and current density solution using charge injection
boundary condition, pref = 10-6 Cm- 3, Eref = 12.14 kV/cm, and q0 = 250 kV.
Figure 4-15 is constructed similarly to figure 4-14 except the charge injection parameters are held constant at pref = 10-6 Cm- 3 and Erej = 12.14kV/cm and the
applied voltage
#o
is varied from 150 kV to 250 kV. The solution parameters do ex-
hibit more variation along the boundary and due to the lower choice of Eref. Some
instability is evident with ripples on the boundary and in the domain shown in figure
4-13. While increasing
#o
does drive up the emitted current, the effect is not lin-
60
```
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