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.