How to stabilize magnetic fields in/around electron microscope? Let us assume we have a very strong electron microscope. One that would need multiple electro-static and electro-magnetic lenses.
The electrostatic lens is used to accelerate the electrons to a desired energy.
The electro-magnetic lens is used to change the path of the beam.
Now I'd assume that especially the electro-magnetic lenses, created by running high currents through a coil, can create significant magnetic fields. 
On one hand I'd expect that:


*

*These magnetic fields interact with each other if we have more than 1 electro-magnetic lens.

*That the magnetic fields generated could cause problems outside of the E-microscope machine, like pulling metal objects towards it. Just like the MRIs in hospitals. 


But neither seems to be the case. Why?
When I was there, I asked about that but got only a very short answer:
'We use Helmholtz coils to stabilize the magnetic field'
What exactly does that mean? Can anyone help?
 A: Your question suggests that there is some external source of magnetic fields (this can be any high-power instrument in the lab, a tram on the street etc.), and you want to reduce its harmful influence on the electron beam in your microscope. This is often the case indeed, an accelerating tram pulls rouhly 1000 A from the overhead lines and the magnetic field can deflect the e-beam by fractions of a micrometer, making a high-resolution SEM image wobbly. In such situations, big Helmholtz coils are built around the whole SEM, with a sensitive magnetometer and feedback electronics that compensates the external field. 
You are however asking about the interference of multiple magnetic coils within the SEM. First of all, the magnetic field of the coils should be linear and additive with respect to the individual fields of each coil. Second, the coils are enclosed in their own magnetic "cores" (or, shieldings) that guide the magnetic field into a well-defined volume within the e-beam column. So there is negligible overlap of individual coils' field anyway. You can see these "cores" in any cross-section diagram of a SEM online.
As a closing note, there are no "electric lenses" in a common SEM nowadays (excepting the Wehnelt cathode assembly on the top). There is "acceleration voltage" around the cathode, but this is not called a "lens". The rest of beam shaping is done with magnetic lenses.
