electron beam through solenoid coil

Hi,

How does a solenoid act to focus a beam of electrons that are passed axially through the coil?

cheers, Jamie

Reply to
Jamie M
Loading thread data ...

You got me interested.....I stumbled on this:

formatting link

Reply to
Dennis

Hi Jamie,

Your question made me curious about this effect that seems pretty non-intuitive given what we know about the magnetic field inside a solenoid and the Lorentz force, etc. A lot of stuff seems to be behind paywalls but I did find this reference on Google Books that seems to be relevant:

formatting link

The interaction between the magnetic field and the space charge electric field generated by the beam is apparently pretty interesting. You'll have to know some electromagnetic physics to follow it, but the math doesn't look too bad.

Reply to
bitrex

I don't think it's a very good explanation, because AFAIK if the beam were an "ideal" infinitely narrow stream of electrons no lensing would occur, the particles would just spiral around and around. The effect can't be explained solely by the Lorentz force. A "simple" analysis is supposedly offered here:

formatting link

...but unless you're a subscriber you'll have to pay $30 for it.

Reply to
bitrex

formatting link

Not taking the space charge of the beam into account, at the bottom of page 91 it says the solenoid lensing effect has to do with the transition from zero field to constant field and fringing effects.

Reply to
bitrex

Well, assume the electron beam begins roughly on axis of the solenoid and well outside the solenoid so the magnetic field is low compared to the field at the center of the coil. Picture the lines of magnetic field close to the axis - at the center of the coil they are lines parallel to the axis but as they leave the coil they slowly diverge. If the transverse energy of the electron beam is "low" so that the cyclotron orbit diameter of an electron about a particular line of magnetic field is small compared to the diameter of the solenoid, the electron will spiral about that line of force and follow it into the solenoid. Since the lines of force converge as they enter the solenoid the electron beam is condensed, by the ratio of the magnetic field at the electron beam source to the full field at the center of the solenoid. The cyclotron orbit diameter is also reduced by the field ratio. The system is symmetrical so the beam expands as it leaves the solenoid, regaining its initial diameter as the field falls to the initial value. This is a simple qualitative picture, of course. Because the magnetic field lines are not exactly parallel a small retarding force is generated. The greater the magnetic field gradient and the greater the transverse energy of the beam the greater this force, so if you have a low enough energy along the solenoid axis and a large enough transverse energy and field gradient the electron will be reflected back out of the solenoid - this is a "magnetic mirror". Conversely, a beam with high energy along the axis, centered on the solenoid, with very low transverse energy, will penetrate the solenoid with virtually no loss (so every magnetic mirror leaks a little right on axis).

On one model of Nicolet (then Waters, Extrel, Finnigan) Fourier transform mass spectrometer the filament was located outside the main field and on axis. The filament was a strip of rhenium ribbon 0.03" wide by about 0.3" long, in a field of about 3/7 tesla. There was a small, 2 mm orifice at the center of the field at 3 tesla, and it was quite easy to align the filament so the entire beam passed through this hole with no loss, with beams of 5-50 uA at 70 eV. Actually, so long as the filament was within a disc of about

0.5" diameter the beam would clear the hole. If the beam were compressed by the field ratio it would be about 0.042" x 0.004" (about 1 mm x 0.1 mm), half the size of the hole. In one apparatus I built the filament was moved another two or three feet further away, and since the total range of electron filament adjustment I had was about 1" I was actually unable to misalign it enough to make the beam hit the edge of the hole. At 70 eV and these currents the space charge of the electron beam is basically negligible so each electron follows its own path with no interaction with other electrons. At lower energies and higher currents the space charge acts to spread the beam laterally, especially in the low magnetic field portion of the electron trajectory, and to increase the distribution of the energy along the axis. This smearing all acts to make the magnetic mirror more efficient, and at low enough energy the beam doesn't penetrate at all. Experimentally I once moved a filament from full field out to about 1/8 of full field and measured the maximum current collected on a solid plate behind that orifice hole, and on the orifice plate, at constant filament power as the extraction voltage was varied. The higher the magnetic field at the filament the higher the space charge limited current that can be extracted from the gun, while the lower the field the more the beam will be compressed as it traverses the solenoid so the greater the current that will pass through the 2 mm orifice. At 70 eV it really didn't matter so far as current goes but the alignment was much less critical at the lower field, so the Nicolet position worked very well. Down at about 7 eV the best position was about 10" from the orifice plate, where the field was estimated (from memory here) at about 90% of full field. Space charge in the gun was clearly dominating but a little magnetic compression could still be achieved. Going all the way down to 1 or 2 eV the closer to full field the better, in terms of current through the orifice. At this low energy space charge between the filament and the extraction grid was all-important. Anyway, just thought you might find some old experiments interesting :-).

----- Regards, Carl Ijames "Jamie M" wrote in message news:jhf76n$r8u$ snipped-for-privacy@speranza.aioe.org...

Hi,

How does a solenoid act to focus a beam of electrons that are passed axially through the coil?

cheers, Jamie

Reply to
Carl Ijames

Apparently, not too nicely. If the electron beam started "parallel" giving a specified spot size, the coil AFAIK would be of no help or hindrance because there is no divergence. The beam would slowly defocus due to mutual repulsion. SLAC and others use a combination of quadrupole magnets and drift spaces to give a focus at one point along the drift space afterwards.

Reply to
Robert Baer

A cheaper alternative with raytraces of the paths taken is at:

formatting link

It also discusses some of the design heuristics on that site without giving away any trade secrets.

The thing you have to remember is that no solenoidal coil of finite length is anything like the idealised model of university physics. The details of the fringe fields and the shapes of the exterior facing pole pieces are important to get the things to behave exactly as required.

--
Regards,
Martin Brown
Reply to
Martin Brown

On a sunny day (Tue, 14 Feb 2012 19:01:38 -0800) it happened Jamie M wrote in :

That is the focus setup in the old vidicon system. The electrons start spiraling in ever smaller circles, and if the field strength is just right the focal point of the spiral is at the target. This is because electrons like to move sideways in a magnetic field, ever going sideways creates a spiral in your beam.

In the old vidicon deflection system the deflection coils were located inside a bigger focus coil. Changing the focus current (in the big coil) would also rotate the picture..

Reply to
Jan Panteltje

Don't know. The lenses in an electron microscope were lumps of high purity soft iron (nickel plated to stop them rusting) that concentrated the magnetic field generated by the solenoid inside that

- carefully shaped - lump of soft iron

formatting link

The lens shape shown has little to do with reality. This reference shows a schematic approximation (on page 10) which comes a little closer to reality

formatting link

The Mulvey lens was an interesting variant, but with conventional conductors it gets too hot to be practical for sustained use

formatting link
lvey%20lens&f=3Dfalse

Someone should have built one with a high-temperature super-conducting winding by now, but if they have I've not heard of it.

-- Bill Sloman, Nijmegen

-- Bill Sloman, Nijmegen

Reply to
Bill Sloman

Hi,

Thanks for all the replies! That is a lot of interesting information, the only reason I can see why the solenoid coil will act asymmetrically (different electron beam angles on the input and output of the coil) is perhaps because of the inherent charge of the electron causing "space charge" gradients? That picture on page10:

formatting link

of the electron beam focus being proportional to solenoid current shows the asymmetry of the input and output of the solenoid. Is that diagram correct so that you can focus a beam to a position beyond the solenoid?

cheers, Jamie

Reply to
Jamie M

formatting link

Hi,

Also apparently if the electron is considered as an electromagnetic wave, then using maxwell's equations gives the correct results:

formatting link

"As electrons can exhibit non-particle (wave-like) effects such as diffraction, a full analysis of electron paths can be obtained by solving Maxwell's equation?however in many situations, the particle interpretation may provide a sufficient approximation with great reduction in complexity."

cheers, Jamie

Reply to
Jamie M

You know, it's strange how this thread comes in as I am also working on a magnetic project that involves some research similar to what is being discussed here.

Blowing off the dust from old notes and references that hasn't see the light of day in years, along with new material adding to it. :)

Jamie

Reply to
Jamie

The focal point of an electron beam emerging from the final lens of an normal scanning electron microscope is below the lens - usually a centimetre or so below the lens - well away from the peak of the magnetic field doing the focusing.

The Mulvey lens is an immersion lens and doesn't work this way, but despite it's charms it isn't all that practical.

-- Bill Sloman, Nijmegen

Reply to
Bill Sloman

ElectronDepot website is not affiliated with any of the manufacturers or service providers discussed here. All logos and trade names are the property of their respective owners.