Use one 10kV toroidal sweep plate as a beam detector to monitor the primary ion beam signal during sweeping one top 4kV toroidal sweep plate. (One dimention calculations)

1. Assume the current distribution in the beam follows Gaussian distribution with the current density be expressed as I = Io * exp(-x²/(w/2)²). Where, Io - maximum density, x - direction perpendicular to the beam axis, w - is the 'e' folding beam size.

Of course the above model can be modified to approximate the real world. I don't think it will change the conclusion drastically.

2. Let's 1st look at what we can get when we try to sweep one T4 toroidal plate. Notice that the T4 plate can not be driven beyond +/- 4kV. (Of course in the calculations, we can put in any voltages we like)

3. Sweep T4 plate at 10kV peak to peak. (Of course in practice, only 8kV is available)

We can distinguish two peaks if our assumption is right. And two peaks appear if over sweep happens. If the beam size bigger than 10mm, two peaks tend to overlap.

4. Sweep T4 plate at 8kV peak to peak. (This is the maximum value we can have)

We can still distinguish two peaks if the assumption is right.

5. Sweep T4 plate at 6kV peak to peak.

We can only see one peak right now. We can imagine that as the sweep voltage decreases, the signal will decrease too. We can this from plots below.

6. Sweep T4 plate at 5kV peak to peak

7. Sweep T4 plate at 4kV peak to peak.

It seems the sweep voltage is too weak to steer the beam onto the T10 plate. This may not be true if the beam width becomes large. See the plot below

8. Sweep T4 plate 4kV peak to peak, with beam width=20mm

We can see that the signal appears again if the beam is fat enough. Then, what happens if the ion beam size can be reduced to, let's say w=2mm?

9. Sweep T4 plate at 8kV peak to peak, with beam width=2mm

The peak is flat! This is the indication that the beam is well focused.

Make sure that this flat top is not caused by the saturation of the I/V convertor used to measure the current.

10. Sweep T4 plate at 7kV peak to peak, with beam width=2mm