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elduderino
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Homework Statement
Problematic Part of the problem:
Consider a negative ion beam of He- ions. The given beam characteristics are the beam energy (E) and the beam current (I0).
An electrostatic chopper is placed on the beam line, which pulses the DC beam with a pulse width of say [tex]t_1[/tex] nanoseconds.
What are the new beam characterisitcs?
Homework Equations
Normal Distribution:
[tex]
f(x)= \frac{1}{\sqrt{2 \pi \sigma^2}} e^{-\frac{t^2}{2\sigma^2}}
[/tex]
The Attempt at a Solution
I would have said the new current profile would be, for an incident DC beam of beam current I0
[tex]I(t)=I_0\frac{1}{\sqrt{2 \pi \sigma^2}} e^{-\frac{t^2}{2\sigma^2}}[/tex]
if the beam emerges from the chopper at t=0. Also, since the FWHM of the beam is given to be [tex]t_1[/tex] the standard deviation would be
[tex]\sigma=\frac{t_1}{2.354}[/tex]
(from http://en.wikipedia.org/wiki/Full_width_at_half_maximum)
This seems pretty straightforward, however, this appears to be wrong because according to this, the peak current has changed, and become .046 times its initial value
[tex]I(0)=I_0 f(0) = 0.046 I_0[/tex] (where f(x) is the normal distribution)can anyone tell me what I am doing wrong.
I think I am not understanding the pulsing phenomenon.
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