Solutions to Final Exam
1. ~ 80% speed of light
d = 0.07 nm
M = 188
z'o- z' = 3.5 x 10-6 mm
approximately 1000 e
2.
pincushion distortion
Chromatic aberration can occur due to instabilities in the acceleration potential.
Distortion aberration can be influenced by apertures.
3. A and B are the beginning and end of the lens field.
The plot shows a larger area above the x-axis. The integral
and therefore f2 are positive.
Positive f2 means the lens is focusing.
For VA< VB f2 is positive
For protons and VA>VB f2 is positive.
4. In region 3 the current is exponential in T.
In region 2 the current is limited by the amount of charge that the anode can extract from the reservoir at the cathode.
… the current is not T-dependent
… is space-charge limited.
In region (1) the current depends on the barrier height between anode and cathode.
… is strongly T-dependent.
…depends on the cathode material through the workfunction.
Field emission typically occurs
when the field is > 106 V/cm
when the barrier width approaches 50 Angstrom
5. f2 = 262 mm
The smallest value would be 32 mm at q = p/2.