Electron Focusing Lens

For a Modulated X-ray Source

Simulating an Einzel Lens

To design a lens for the MXS, we ran many simulations of the system to observe how the electrons behaved as we adjusted different parameters of the lens. This was done in the charged particle modeling software SIMION (ver 8.0) with some modeling of electric field lines done in MATLAB. We'll look through the results to find the best configurations and then select one of those to produce as our final version.


There are a number of components of the MXS that need to be accurately recreated so that we can test various lens designs, the first of which is the electron beam. The beam is comprised of six smaller beams of electrons arranged in a spiral galaxy or flower pattern around a central spot. To do this, we approximated the six beams as filled circles with a diameter of 1mm spaced equally around a circle 2mm in diameter that intersected each beam's center. This created a beam that was 3mm accross at it's widest point, so that while the shape isn't exactly what the electron multiplier actually produces it encompassed the entire area that the actual beam covered. If our model lens could focus this slightly larger beam, the real lens should be able to focus the actual beam. Each simulation is also run with 600 electrons in the beam, which is a gross underestimate of the number of electrons in the actual beam but a necessary sacrifice in terms of computing capability. We plan to run a simulation on the final design with a more accurate number of electrons, but we do not have the time to do all of our testing with as many ions as the real beam would have.

The approximation of the beam of electrons.

The next component that needs to be accounted for in the model is the target. The combination of the slanted surface and high potential- the target is held at 10kV- create a large field that deflects the beam downwards as it approaches. With no lens in place this simply curves the beam onto the target, but when the lens is inserted into the system it causes the beam to not be able to focus on the target. We think this is because the target can more easily affect the electrons that are moving towards the focus from above, causing them to accelerate downwards. The electrons approaching the focus from below undergo a direction change as the target pulls them in. This phenomonon, that the 'upper' electrons can descend more quickly than the 'lower' electrons, results in the focus never being able to be right on the target. However, the more parallel the electrons are when exiting the lens, the smaller the spot size on the target will be. (This is because the electrons travelling in parallel removes the effect from some of them going downwards and others moving upwards.)

A visualization of the effect of the target on the beam of electrons.

The final component of the housing that needs to be modeled is the housing of the MXS. Components inside the MXS share a common ground, and the housing is used as a conductor to connect all of the grounds together. This is an efficient way of managing connections as it cuts down the number of feedthroughs required to get voltages inside the MXS, but at the same time it causes the housing to alter the electric field inside of it. The effect isn't terribly large but the zero potential of the housing reduces the distance between the 10kV and 0V level, which causes the rate at which the potential field changes levels to increase. This in turn causes the beam to deflect more sharply than if the housing was not present.

A cut-away view of the lens and target inside of the housing, modeled in SIMION.

The Lens

An Einzel lens is typically constructed of three electrodes with the outer two held at ground and the inner electrode held at some positive voltage. This will cause a focus in a stream of positive ions, with the focal length of the lens set by adjusting the middle plate's voltage. Since our ion beam is a beam of electrons, we will build a lens that has a negative potential on the middle electrode. We would like for the lens to be as small as possible so that the lens is not the limiting factor in making the MXS as small as possible. (Ideally we would build a lens that is smaller than the Electron Multiplier, which is currently the largest component inside the MXS.)

One idea suggested to us at our Preliminary Design Review was to alter the shape of the electrodes to try to counteract the effects of the irregular field created by the target; specifically by changing the third electrode's shape to mimic that of the target by adding a triangular slant to the end of the electrode. This increased the degree to which the beam bent, so we played with where we put the slant in the lens system. Eventually we began to play with adjusting the voltage on the third plate, and hit a 'sweet spot' when we held the third electrode at the same potential as the second electrode. This gave us the idea to remove the third electrode entirely and extend the second electrode through where the third was previously. With this configuration, we were able to achieve results better than anything we had done so far with all pieces of the MXS modeled.

We still plan on simulating three-element lenses as well as two-element lenses, but the two-element lens has significant advantages as far as construction of the physical lens is concerned. With a three-element lens, we would have to route a wire around the third lens element to be able to hold the middle electrode at the correct voltage. This isn't a problem with the two-element lens, as the electrode that has to be held at a voltage doesn't have any other electrode between itself and the part of the housing that we can put a feedthrough in.

Results for a 2 Electrode Configuration

In order to optomize the small spot size of the electron beam on the target, our team chose to vary the following parameters: voltage on the 2nd plate, inner electrode diameter, outer electrode diameter, length of the 2nd electrode,and the distance between electrodes. We did our testing on a standard lens with the following paramters (then varied the parameter we were interested in): an outer diameter of .245", first plate length of .30", second plate length of .69", space between electrodes of .07", initial kinetic energy of 100eV.

Varying the Inner Diameter

For the -100 to -50 voltage range, we found that smaller diameters achieved a smaller spot size radius to a point. Once the voltage became too low, electrons began colliding into the walls of the electrode, which causes the spot size to increase sharply. In order to ensure that our lens has the smallest spot size, assuming that we would optimally hold the lens within a -70 to -78 voltage range, we chose an inner diameter of .14".

Varying the Outer Diameter

For the -100 to -50 voltage range, we found that we achieved the same spot size results for our range of outer diameter values. Because we can choose any outer diameter within that range and achieve the same results, we decided to use an outer diameter of .43", because that fits best within our MACOR housing.

Varying the Length of the Second Electrode

For the -100 to -15 voltage range, we found that longer lengths of the 2nd electrode gave smaller spot sizes. We did not test any longer lengths of the second electrode becuase we do not want it to be too long and we want it to fit nicely within the flanges we were provided. Therefore, we chose a 2nd electrode length of 0.60".

Varying the Distance Between the Electrodes

For the -100 to -50 voltage range, we found that there was no clear trend to the spacing like the other parameters. The possible reason for this is that the spacing between the plates alters the focal length. So it's possible that 0.078" has a more optimal focal length for the current setup, and then the beam doesn't focus better again until the spacing between the lens reaches a higher point. We chose a distance of 0.11" between the plates, because we felt it would focus the beam the best with the other parameters we chose and because it fits well for the flange sizes we used.

Varying the Voltage on the 2nd Plate

For this simulation, we used the parameters that we chose as the best for this lens configuration, that we outlined above. As we vary the voltage on the 2nd plate, accross electron energies, the spot size radius remains consistant. After running our preliminary tests from 50-100V we decided to continue with an electron energy of 100eV to see if higher voltages would yield better results. Lo and behold, they did.

These are the voltage varying results for the -50 to -100 volt range for varying electron energies. We hope to test the MXS over this voltage range as well as the positive one pictured above to see if our simulation matches up with the test results. The optimal negative voltage appears to be around -74V.