What Determines the Focal Length of an Einzel Lens in TOF Mass Spectrometry?

[kiwi83]

Hi,

Im working on a project in designing a (TOF) mass spectrometer and want to include an einzel lens in order to help focus the ion beam onto the detector.

I know the basics behind the operation of the lens, but am struggling to find any equations for the focal length of an einzel lens.

Obviously, it will be determined by the potential applied and the velocity of the ions in the beam, but I know that simply using standard equations will not work.

Does anyone out there know what I am looking for?

Thanks,

kiwi

 

[krab]

Hi,

Im working on a project in designing a (TOF) mass spectrometer and want to include an einzel lens in order to help focus the ion beam onto the detector.

I know the basics behind the operation of the lens, but am struggling to find any equations for the focal length of an einzel lens.

That's because no closed-form expression exists; the equations of motion have no analytical solution. Some figures exist, look for example at http://www.mit.edu/afs/athena/course/22/22.09/ClassHandouts/Charged Particle Accel/CHAP06.PDF

Obviously, it will be determined by the potential applied and the velocity of the ions in the beam, but I know that simply using standard equations will not work.
kiwi

That's the easy part. The dependence is only on the ratio of electrode potential to beam potential (beam potential being particle energy / particle charge), so once you have optics as a function of electrode potential for one beam energy, you have it for all.