Understanding Pulsed Beam Characteristics of Negative Ions

[elduderino]

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 $$t_1$$ nanoseconds.

What are the new beam characterisitcs?

Homework Equations

Normal Distribution:
$$f(x)= \frac{1}{\sqrt{2 \pi \sigma^2}} e^{-\frac{t^2}{2\sigma^2}}$$

The Attempt at a Solution

I would have said the new current profile would be, for an incident DC beam of beam current I0

$$I(t)=I_0\frac{1}{\sqrt{2 \pi \sigma^2}} e^{-\frac{t^2}{2\sigma^2}}$$

if the beam emerges from the chopper at t=0. Also, since the FWHM of the beam is given to be $$t_1$$ the standard deviation would be

$$\sigma=\frac{t_1}{2.354}$$

(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

$$I(0)=I_0 f(0) = 0.046 I_0$$ (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.

 

[mark726]

Hello,

Thank you for your post. It seems that you have correctly identified the new current profile for the pulsed beam. However, the peak current may not necessarily be the same as the initial beam current (I0) due to losses in the chopper and other factors. It is also possible that the beam energy (E) may change due to the pulsing. To fully understand the new beam characteristics, we would need more information about the chopper and its effects on the beam.

In general, when a beam is pulsed, the peak current will decrease and the pulse width will increase due to the normal distribution of the beam. The total charge of the beam should remain the same, however, as long as there are no losses.

I hope this helps clarify the situation. If you have any further questions, please let me know.