This disk contains files corresponding to the three topics above, each having its own directory (folder). Load the three folders as sub-folders under your Sim6demo folder. Start SIMION within Sim6demo, select VIEW and then select the desired sub-folder and load in the .IOB file.
Most of these folders have the following files:
.PA* - Potential Array files - These files were generated using the full
SIMION program and represent various electrode and pole piece geometries, surrounded
by mesh points in which the finite difference equations have already been solved
by iteration. These arrays can be seen by using the MODIFY button after loading
an array or an IOB file. The mesh spacing is in terms of gu (graphical units).
A large number of .PA* files are generated, one for each electrode, so that
by superposition, you can adjust potentials on any electrode in the array and
get the resulting potential array without reiterating the finite difference
mesh for each change in electrode voltage.
Because you do not have the ability to refine or iterate the array to solve
for the potentials, you cannot create your own .PA files.
.IOB - Ion Optical Bench files - These files set up the entire optical
bench, and connect with the associated .PA files as required. A particular IOB
setup will set the scaling (mm/gu) between the real world and the potential
array points, the orientation of the PA within the optical bench and the relative
positions of other PAs within the bench. You can change the scaling and orientation
of the potential arrays and save the result as a new .IOB file.
.FLY- Trajectory Initial Conditions - These files are loaded by the LOAD
.FLY button within the DEFINE screen for trajectories, under the NORMAL tab
in the VIEW screen. You can create your own .FLY files and save them.
.REC - Trajectory Recording Files - These files define what, when and
in what format to record trajectory parameters, such as position, velocity and
direction angles. You can create your own definitions and save them by using
the RECORD-DEFINE buttons within the screen for trajectory initial conditions.
.CON - Contour Files - These files contain preset values for equipotential
line and gradient contours. You can create your own files and save them.
Appendix D of the Docs folder describes all of the files available in SIMION. We will be using only the above subset.
Click on the VIEW button to scan the drive for directories, then select the
folder INDEX. Click on the file INDEX.IOB to change its font from black to red,
then click on the USE button at the top of the screen. You have now loaded in
the INDEX example and its associated potential arrays. Increase the resolution
of the screen drawing by changing the number under the WB VIEW tab. Its default
is 3. Increase it to 6 to see the transparent mesh electrodes that bound the
two potential regions.
This is a space which has two regions with uniform potentials, separated by
a vertical boundary of only one gu (mesh unit) within which an electric field
exists which gives particles passing the boundary an impulse in the horizontal
direction only. This demonstrates the particle optics analog to light optical
index of refraction. The example trajectories within the .FLY file show the
effect of refraction at this interface.
Problems:
T1) Calculate the expected deviation of the 45 degree trajectory in the example,
based on the refractive index of the electrostatic fields. Does it agree with
the computer program value?
T2) Select a particular trajectory, not horizontal, and reverse its path by
starting it from the image recording plane position with an angle and initial
KE to cause it to retrace its path from image back to object space. Does it
return to its origin in object space? Should it?
There is one magnetic field example and two electrostatic examples within this folder. Load the magnetic example MAG1.IOB. Take a look at the geometry using the 3D ISO button under the WB VIEW tab. It consists of two pole pieces. For running trajectories and seeing them, click on the YZ button. SIMION solves for a magnetic scalar potential and then determines the field from the gradient of this potential. Load the MDEF1.FLY and the MAG2.REC file. Take a look at the initial and final KEs of the trajectories. They are equal since the force is at all times perpendicular to the incremental distance traveled and therefore doesn't do any work on the particle.
Problems:
T3) Calculate the value of Br (Field-radius product) for the electrons in the
example. Reduce the field from 40 Gauss to 20 Gauss by clicking on the PAs tab
and the FAST ADJUST button. Now load the .REC file MAG1 to record the trajectory
endpoints in this case. Calculate the deflection angle expected for any trajectory
by the analytic formula. Now measure and record the angle calculated in SIMION
(you will have to modify the RECORD-DEFINE parameters - be careful of the angle
definitions, see the last page of this handout). Why is there a discrepancy
between SIMION and the calc? T4) Select a particular trajectory, record the
endpoint direction angle and KE and then reverse it by loading the KE and an
angle 180 deg. from the endpoint angle. Does this field show time reversal symmetry?
Load the ELEC1.IOB to see a case of two electrostatic deflection plates in
space with no surrounding structure. DEFINE trajectories using the LOAD .FLY
button to load Edef.fly. When you run these trajectories, you will see that
some of them hit the plates. To reduce the deflection voltages, click on PAs
tab, Fast Adjust, to reset the plate voltages to +600 and =600V.
You now see a set of trajectories passing through the plates and continuing
on out of the potential array space into the workbench space where there are
no longer any fields acting on them. Set up an endpoint recording by again using
the trajectory DEFINE button, and at the bottom of the screen, click on RECORD
and DEFINE. Load the preset file ELEC2.REC by using the LOAD button, clicking
on ELEC2.REC and USE. Now run the trajectories, and note the recording at the
position of X=60mm. You can bring in the right side of the workbench space by
clicking on the Workbench tab and changing the Xmax value to, for example, 100mm.
The red dots show the trajectory recording positions. Change the trajectory
quality number (default 2) to 120 to increase the trajectory accuracy.
Notice that the electrons pick up some net KE as they pass through this deflector
model. To see what might be causing this, click on the Contour tab and set the
number to the right of Auto to 8, then click on Auto. You can now see that this
increase in KE is an artifact of the potential array. The restrictive boundaries
on the fringing fields won't permit realistic modeling of the fields, so that
as the trajectories pass out of the potential array they are left with about
13eV of excess energy.
To take a look at a more realistic, bounded deflection system, click on QUIT,
YES and then REMOVE ALL PAs from RAM. This clears out the potential array from
the case just seen. Now click VIEW, click ELEC2.IOB, click USE and YES to restore
potentials. You now have the plates as before but now zero volt plates bound
them on the entrance and exit areas. Since the entire structure is longer, reduce
the plate voltages to +300 and -300V to keep the trajectories from hitting the
plates.
Set the trajectory quality to 120 and run the trajectories (FLY'M).
Problem:
T5) You can see that the trajectories gain or lose KE on the order of 0.1eV
as they pass through this deflector. Why is this? Only one trajectory has the
same KE as it came in with. Is this an artifact of the program or real? Try
selecting one trajectory and reversing it. Does this field show time reversal
symmetry?
This folder contains a file for the hyperbolic lens, which was demonstrated in class and also shown by the gravitational model analog. You can load the files as before. To compare this model with the gravitational model you have seen, click on the PE View tab to see the potential energy 3D diagram, corresponding to the gravitational model. You can see the trajectories appear like the marbles in the gravitational model by clicking on the Normal tab, and then GROUPED and DOTS in the trajectory area. To stop trajectories from running use the ESC key on your keyboard.
This problem set is due on Tuesday.
These problems continue the development of the ideas in INDEX and DEFL.
T6) Note your solutions to problem T1. You should have both the computer
and the analytical solution to the angle of the trajectory which is incident
on the interface at 45 degrees.
Using the DEFINE screen, where you define the initial conditions of the electrons,
locate the initial mass of the particle, given, for electrons, as 5.485799030E-4
amu. Try increasing this mass by a factor of ten (5.485…E-3) and record the
resultant refraction angle for the incoming 45 degree trajectory. Try increasing
the mass again and record the angle again. At what mass does the angle stop
changing?
T7) As you increase the particle's mass, the velocity slows for a constant Kinetic Energy. The theory of relativity predicts, and measurements support, the idea that the mass of a particle increases with increasing velocity, according to the following:
Where m0 = 0.911E-30 kg = the rest mass of the electron and c = 3E8m/sec = the speed of light. What does the behavior of the angle in SIMION tell you about how SIMION calculates velocities based on Kinetic Energy? What angle would you expect to observe in an actual experiment, 62.1 degrees or 60.8 degrees?
Read the original problem T2 and its solution. Make sure you understand the idea of trajectory reversal in an electrostatic problem and why the trajectories should return to the starting point.
T8) Note your answers to problem T3. You should be able to compare the computer output with the calculated radius by the formula for r in Klemperer (Eq. 2.24).
To explore this problem further, increase the magnetic field to 100 Gauss by using the PAs tab, FAST ADJUST button. Reduce the beam KE to 10keV using the DEFINE screen for defining trajectory initial conditions. Also, increase the starting y value to -76mm to start the trajectories at the bottom edge of the magnetic field. Use the RECORD-DEFINE buttons to change the recording plane to y = -76mm.
A) Now run the trajectories and record the radius of the semicircle
created within the pole pieces in SIMION.
B) Calculate the expected radius of electron motion using the equation in Klemperer,
or listed in the solutions, only this time for the 10keV electrons.
T9) The above problem has eliminated the fringing field effects outside of the magnetic pole pieces. However, there is a fringing field effect between the pole pieces because the field towards the edges (y=+/- 76mm) is smaller than at the center, where it is exactly 100 Gauss.
Let's try to eliminate this additional fringe field by running the trajectories so that they are close to the center of the field where the field is exactly 100 Gauss. Move the starting point for the trajectories to z=30mm and y=0mm, and the recording plane to y=0mm. Run the trajectories. They should go around in a circle. You can stop the recording by the FLY'M button or QUIT.
A) Record the radius for these trajectories.
T10) In the above problem, we have eliminated almost all effects but there is still a slight error between the calculated electron radius and the SIMION radius. The only thing left is relativity.
As you increase the particle's mass, the velocity slows for a constant Kinetic Energy. The theory of relativity predicts, and measurements support, the idea that the mass of a particle increases with increasing velocity, according to the following:
In electron optics, this mass increase can be compensated for by using a 'relativistically-corrected accelerating voltage', Vr, where
A) Using Vr from this formula in place of V in the equation for the electron radius, calculate the relativistically-corrected electron radius.
B) What is the error (in percent) between this calculated radius and the SIMION radius in T4*-A?
A computer simulation of the Davisson-Calbick aperture lens
Installation of files
Insert the folder Davcal as a sub-directory into the folder Sim6demo. Start SIMION within the Sim6demo folder, select VIEW and wait for the program to scan the files in your computer. When the file tree is displayed, select the Davcal folder. In the right hand column, the file 1AP3.IOB will be displayed. Click on it once to select it, then click on the USE at the top of the screen. This will load the IOB (Ion Optical Bench) file and its associated potential array files as follows:
In order to see the potential array, if you are in the VIEW screen, click on QUIT, YES and then click on MODIFY. This brings up the potential array and you can see the grid points and the defined electrodes. Note that Cylindrical Symmetry is set, so that the Y=0 horizontal axis is the axis of the cylinder. You can use the slider at the bottom of the screen to move the view from one side of the array to the other. To leave this screen, click on the QUIT button at the top left. Select VIEW to return to the IOB view.
Ion Optical Bench 1AP3.IOB
The .IOB file sets the potential array into workbench coordinates of mm; sets scale to 0.025mm/gu; sets 0mm X to center of aperture thickness; sets 0mm Y to axis
You should now see something on the screen similar to the figure above, without the captions. If you can't see the transparent mesh on the right, click on the box with the number 3 under the WB VIEW tab and increase the number to 5 or 6. This increases the drawing resolution and may make very thin electrodes visible.
Click on the PAs (Potential Array) tab and click on Fast Adjust. This will allow you to adjust the potentials on V1, V2 and V3 electrodes. Leave V2 and V3 at zero volts and set V1 to -1000V.
After exiting the Fast adjust screen, you are back in the VIEW screen. Click on the Normal tab and under the Ions section, click on DEFINE. This screen allows you to define the initial conditions of the electron trajectories. First, set the units to mm by clicking on the upper right box to change from gu (grid units) to mm (relative to workbench origin). Next set the mass and charge to those of an electron by clicking on the USE ELECTRONS button. Set the First x to just to the left of the transparent grid, say -5.1mm. Set the first y to be on axis, first y = 0. Set the delta y for .025mm to launch successive trajectories. The total number of trajectories launched can be changed by selecting the N= 5 box and changing the number there. The initial KE of each electron is shown in the window toward the bottom of the screen. This KE is directed in the direction shown by the Azimuth and Elevation boxes.
A zero azimuth and elevation corresponds to a launch angle along the positive X-axis.
When you have finished defining these trajectories, you can click on OK at the top of the screen to return to the VIEW screen, with these initial conditions loaded. Now click on the FLY'M button to see the trajectories run.
The next step is to record the exact radial position and trajectory slope of the trajectories which pass through the transparent grid at x=+5.0mm. To do this, click on the DEFINE button again to bring up the screen where you have defined the electron initial conditions. At the bottom of this screen are two buttons, RECORD and DEFINE. Click on the RECORD button to activate the recording feature, then click on DEFINE to define what you what to record. In this screen you can turn on or off the items by clicking the buttons; insert numbers in the boxes to specify coordinates. You can record as many things as you like, but the essential items to record for the Davisson-Calbick aperture lens are the Y position and Elevation angle at the location X= 5mm, where the trajectories leave the lens. By clicking on the various boxes and inserting numbers, set up this screen to accomplish this task.
Now click on OK to get back to the initial conditions screen and click OK again to return to the VIEW screen. Run the trajectories by clicking FLY'M and notice the data which appears in the window. If this is not what you want, go back to the recording define window and change things. Return to the VIEW screen.
The trajectory quality box within the Ions area of the Normal tab allows you to improve the accuracy of the trajectory calculation. You can find the details of how calculations are performed within the manual (DOCS folder in SIM6DEMO) in appendix E and chapter 8 of the manual explains what the trajectory quality number means. Pull up chapter 8 and search for "quality control panel" in the text. For our purposes, a quality number of 120 should be sufficient to yield reasonably accurate results.
Problems:
T11) Calculate the Davisson-Calbick focal length
for the example in 1AP3 above with a voltages of V1=?1000V, V2=0 and V3=0, spacing=5mm and for an incoming electron KE of 0.1eV. Note that VB is the beam kinetic energy as the electrons pass through the aperture. E2 and E1 are the electric fields in the spaces downstream and upstream of the aperture, respectively.
T12) Use SIMION to calculate trajectories close to the axis and determine the back-projected virtual crossover position for the trajectory launched closest to the axis. What happens to the crossover as the incoming ray is launched further from the axis?
T13) What is the functional dependence between the off axis launch radius and the position of the virtual crossover? What is the extrapolated virtual crossover position for a launch at Y=0mm?
T14) Now, using the same geometry, set V1=+1000V, V2=0, V3=0. Set the initial KE of the electrons to 1200eV. Calculate the f for this condition by the Davisson-Calbick formula.
T15) The crossover is now real and you don't have to extrapolate backwards to find its position. In the RECORD, DEFINE area for recording the trajectory parameters, instead of selecting X=5mm, select instead a condition of Y=0mm for triggering the recording of the X position. Use SIMION to calculate trajectories close to the axis and determine the crossover position for the trajectory launched closest to the axis. Remember to set the trajectory quality to at least 120. What happens to the crossover as the incoming ray is launched further from the axis?
T16) What is the functional dependence between the off axis launch radius and the position of the crossover? What is the extrapolated crossover position for a launch at Y=0mm?
See the folder Lablens in the EO web site. There are simulation setups for both the upstairs (room 220) and the downstairs (room 35) benches. There is only one potential array (field.PA) since the dimensions of both lenses are the same.
Put the Lablens folder as a subfolder under SIM6 or SIM7. Start SIMION and click on VIEW. Depending on which room you were in, select either the EOlab220 or Eolab IOB file and click on OK to load it.
Associated with each of these setups are .fly files for trajectory launch conditions and .rec files for trajectory recording positions. Note that the end of the workbench (where the electron splat position is recorded) corresponds to the position of the screen and the .fly file contains the electron launch position.
Check these positions with your lab data to ensure that the simulation will be correct. Also check the voltage ratio, set by the PA tab, Fadj. Note that there is another recording plane after the crossover which you can change to correspond to the mesh locations.
Set the increments on the launch elevation angle to correspond to your particular upstream mesh, located at position a from the source. Set the trajectory quality to 120 and run a set of trajectories to correspond to the front mesh experiment. Record the splat positions and compare with your experimental data.
Now use the trajectory information to calculate the m and µ values.
You can directly get the f0 and g0 values from the trajectories. Record your numbers for these two parameters.
Complete the simulation by calculating Sf and Sg values.