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electron beam through solenoid coil

Started by Jamie M February 14, 2012
Hi,

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

cheers,
Jamie
"Jamie M" <jmorken@shaw.ca> wrote in message 
news:jhf76n$r8u$1@speranza.aioe.org...
> Hi, > > How does a solenoid act to focus a beam of electrons that are passed > axially through the coil? > > cheers, > Jamie
You got me interested.....I stumbled on this: http://www.ammrf.org.au/myscope/sem/practice/principles/lenses.php
On 2/14/2012 10:01 PM, Jamie M wrote:
> Hi, > > How does a solenoid act to focus a beam of electrons that are passed > axially through the coil? > > cheers, > Jamie
Hi Jamie, Your question made me curious about this effect that seems pretty non-intuitive given what we know about the magnetic field inside a solenoid and the Lorentz force, etc. A lot of stuff seems to be behind paywalls but I did find this reference on Google Books that seems to be relevant: http://books.google.com/books?id=pw4KalLZZ7gC&lpg=PA281&ots=sKJ8yOU-K8&dq=Busch%E2%80%99s%20theorem&pg=PA275#v=onepage&q=Busch%E2%80%99s%20theorem&f=false The interaction between the magnetic field and the space charge electric field generated by the beam is apparently pretty interesting. You'll have to know some electromagnetic physics to follow it, but the math doesn't look too bad.
On 2/14/2012 10:21 PM, Dennis wrote:
> "Jamie M"<jmorken@shaw.ca> wrote in message > news:jhf76n$r8u$1@speranza.aioe.org... >> Hi, >> >> How does a solenoid act to focus a beam of electrons that are passed >> axially through the coil? >> >> cheers, >> Jamie > > You got me interested.....I stumbled on this: > > http://www.ammrf.org.au/myscope/sem/practice/principles/lenses.php > >
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: http://ajp.aapt.org/resource/1/ajpias/v77/i8/p737_s1?isAuthorized=no ...but unless you're a subscriber you'll have to pay $30 for it.
On 2/14/2012 10:01 PM, Jamie M wrote:
> Hi, > > How does a solenoid act to focus a beam of electrons that are passed > axially through the coil? > > cheers, > Jamie
http://books.google.com/books?id=pw4KalLZZ7gC&lpg=PA281&ots=sKJ8yOU-K8&dq=Busch%E2%80%99s%20theorem&pg=PA91#v=onepage&q=Busch%E2%80%99s%20theorem&f=true 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.
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$1@speranza.aioe.org...

Hi,

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

cheers,
Jamie 


Jamie M wrote:
> Hi, > > How does a solenoid act to focus a beam of electrons that are passed > axially through the coil? > > cheers, > Jamie
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.
On 15/02/2012 03:49, bitrex wrote:
> On 2/14/2012 10:21 PM, Dennis wrote: >> "Jamie M"<jmorken@shaw.ca> wrote in message >> news:jhf76n$r8u$1@speranza.aioe.org... >>> Hi, >>> >>> How does a solenoid act to focus a beam of electrons that are passed >>> axially through the coil? >>> >>> cheers, >>> Jamie >> >> You got me interested.....I stumbled on this: >> >> http://www.ammrf.org.au/myscope/sem/practice/principles/lenses.php >> >> > > 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: > http://ajp.aapt.org/resource/1/ajpias/v77/i8/p737_s1?isAuthorized=no > > ...but unless you're a subscriber you'll have to pay $30 for it.
A cheaper alternative with raytraces of the paths taken is at: http://fieldp.com/myblog/2010/designing-solenoid-lenses-for-electron-beams/ It also discusses some of the design heuristics on that site without giving away any trade secrets. The thing you have to remember is that no solenoidal coil of finite length is anything like the idealised model of university physics. The details of the fringe fields and the shapes of the exterior facing pole pieces are important to get the things to behave exactly as required. -- Regards, Martin Brown
On a sunny day (Tue, 14 Feb 2012 19:01:38 -0800) it happened Jamie M
<jmorken@shaw.ca> wrote in <jhf76n$r8u$1@speranza.aioe.org>:

>Hi, > >How does a solenoid act to focus a beam of electrons that are passed >axially through the coil? > >cheers, >Jamie
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..
On Feb 15, 4:01=A0am, Jamie M <jmor...@shaw.ca> wrote:
> Hi, > > How does a solenoid act to focus a beam of electrons that are passed > axially through the coil?
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 http://www.microscopy.ethz.ch/lens.htm 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 http://web.utk.edu/~prack/MSE%20300/SEM.pdf The Mulvey lens was an interesting variant, but with conventional conductors it gets too hot to be practical for sustained use http://books.google.nl/books?id=3Do-IFp53_1-IC&pg=3DPA396&lpg=3DPA396&dq=3D= Mulvey+lens&source=3Dbl&ots=3DpUD4fhjDPi&sig=3D_mhpBU4kSwH2IWPqLAuucJlMbFI&= hl=3Den&sa=3DX&ei=3DqJY7T7KXJ8SN-waK2t2sBw&redir_esc=3Dy#v=3Donepage&q=3DMu= 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