# Magnetic lens

1. May 2, 2010

### jam12

Hello,
I wanted to ask, is it possible for a magnetic lens to have many focal points, when the magnetic field of the lens is sufficiently large? if so what is the reason for this? how does this give better resolution of images compared to a simple optical lens.
I know for a normal optical lens that there is only one point where electromagnetic waves are focused to, thus giving a single focal point.

2. May 2, 2010

### Rajini

Hi,
Normal optic lens (made of glass- used for e.g., palm reading etc) are good for focusing light (not x-ray or electron beam).
But magnetic lens, which are made of solenoid (wires wounding and no glass), are in general used for focusing matter, for e.g., electron beam. In a transmission electron microscopy one uses magnetic field to focus (magnetic lens) electron beam onto sample/specimen. But what is the use of having more focal points..? But you can control the focal length by varying the magnetic field..Electrons spiral when travels in a magnetic field (Lorentz force)
hope this helps.

3. May 3, 2010

### jam12

Thanks, but im still unsure why a magnetic lens can have more than one focal point when the magnetic field of it is increased.

4. May 3, 2010

### Rajini

Focus point means all rays are focused to one point. Electron beams are focused to a point using magnetic field. Now if you want to have another focal point you tune the magnetic field. So the electron passing through the magnetic field can be focused to a different point. So one can say by this you have different focal point.
Point to note is electron can be tuned using magnetic field. And this magnetic field is magnetic lens.

5. May 3, 2010

### jam12

yes i understand that you can tune the magnetic lens to get a focal point required, but what im saying is that at any one time, is it possible to have more than one focal point?.

With out going into too much detail, I have a graph (for a high magnetic field in the lens) where i can see that it crosses the x axis more than once, ie it curves up and down ( a bit like a sin wave) but crossing the axis 4 times, doesn't this suggest more than one focal point?
For low magnetic fields, i have only one intersection suggesting that their is only one focal point for the lens.

6. May 3, 2010

### Rajini

I really don't know exactly about what you are telling.
Could you upload the graph ?
It could also be some sort of aberration?

7. May 4, 2010

### Bob S

If charged particles of a fixed momentum are emitted from a source on the z-axis of a solenoid with a constant magnetic field Bz, the particles will have both a longitudinal momentum along the z-axis, and a relatively small radial momentum component. The particles with the radial momentum component will undergo circular motion in the r-theta plane, and periodically return to the z axis. Because the motion in the r-theta plane is circular, and the period is independent of the radius of gyration, all the particles will return to the solenoid axis at the same point. The gyration frequency is

f = eB/(2πm) Hz where e and m are the charge and mass of the particles.

If the solenoid is sufficiently long, the particles will periodically re-focus at successive points at equal distances along the axis of the solenoid.

To understand this in detail. download Humphries' free book on the Principles of Charged Particle Acceleration at

http://www.fieldp.com/cpa.html

Review Sections 3.6 (book page 40) and 3.7 (book page 43) on motions of charged particles in cylindrical coordinates in magnetic fields.

Bob S