CylSpaceCharge Limited Electron Emission

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        Calculate:   Current      Output Format        Notes

Definition:                           

Equation

Parameters

Diagram

Calculate Current in Cylindrical SC Limited Diode:        top

Parameter

Value

Units

Special Values

Inputs:

V (voltage)
l (length)  
rA (anode rad.)
rK (cathode rad.)
         

Outputs:

ISCL(current)

Z (impedance)

b (beta)

Output Format:                                                        top

Select Format: Scientific Engineering Fixed

 

Notes:                                                                       top

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  Raymond J. Allen