| Assumes no initial electron
velocity. |
| Assumes no ions (ions generally
increase electron current 100% (halve impedance), but are a small fraction
of total current) |
| Length is generally cathode length
plus twice the AK gap to account for spreading of the electron source. |
| Can also be expressed: |
 |
where, I is in kA, l and rA in
cm, and V in Volts. (note: mc2/e=0.511MV) |
| The first 14 power series
coefficients are as follows: |
|
0 |
0.0 |
|
1 |
-0.40 |
|
2 |
+0.09166667 |
|
3 |
-0.01424242 |
|
4 |
+0.001679275 |
|
5 |
-0.0001612219 |
|
6 |
+0.00001293486 |
|
7 |
-8.87693E-7 |
|
8 |
+5.46192E-8 |
|
9 |
-2.94843E-9 |
|
10 |
+1.36026E-10 |
|
11 |
-7.1101E-12 |
|
12 |
+2.6644E-13 |
|
13 |
+1.2526E-15 |
| (from Currents Limited by Space
Charge Between Coaxial Cylinders by Irving Langmuir and Katharine B.
Blodgett, Physical Review II Vol.22, October 1923) |
Copyright © 2000-2021 Raymond J. Allen
|
