Chapter 2. SIMION Basics (SIMION® 8.0 User Manual)

The movement of a particle (its acceleration) is defined by the force on it, as given by Newton's Second Law:

This force applied over a distance of movement is work (consuming energy):

The forces between charged particles are given by Coulomb's Law:

The electric field is the force per charge or (in terms of work) the change in work per charge (i.e. voltage) over distance:

Conversely, we may think of the electric field as the cause of the force on a charged particle:

Putting this together, the acceleration on a particle (or it's trajectory) is determined by the electric field as such:

A magnetic field will also apply a force on a particle, but only if the particle is moving (non-zero velocity):

Magnetic force is always normal to both the B magnetic field vector and the U velocity component normal to the B magnetic field vector (following the right hand rule):

A simpler equation results from using only the vector velocity component normal to the magnetic field:

Putting this together, the acceleration of a particle (or it's trajectory) is determined by the magnetic field as such:

Note: Static magnetic fields change an ion's direction of motion but not its speed (kinetic energy).

Refraction (bending of ion trajectories) results from electrostatic and/or magnetic forces normal (at 90 degrees) to the ion's velocity. We can determine the radius of this refraction.

The electrostatic radius of refraction is

The magnetic radius of refraction is

Interpretations of Radius of Refraction

There are significant differences between light and ion optics:

The electrostatic or magnetic field potential (e.g. Volts or Mags - SIMION's magnetic potentials) at any point within an electrostatic or static magnetic lens can be found by solving the Laplace equation with the electrodes (or poles) acting as boundary conditions. The Laplace equation assumes that there are no space charge effects and boundary conditions are sufficiently constrained.^[1]

The Laplace Equation

The Laplace equation constrains all electrostatic and static magnetic potential fields to conform to a zero charge volume density assumption (no space charge). This is the equation that SIMION uses for computing electrostatic and static magnetic potential fields.

Poisson's Equation Allows Space Charge

Poisson's equation allows a non-zero charge volume density (space charge). When the density of ions becomes great enough (high beam currents) they will (by their presence) significantly distort the electrostatic potential fields. In these conditions, Poisson's equation should be used (instead of Laplace's) to estimate potential fields. SIMION does not support Poisson solutions to field equations. It does however employ charge repulsion methods that can estimate certain types of space charge and particle repulsion effects.

The Nature of Solutions to the Laplace Equation

The Laplace equation really defines the electrostatic or static magnetic potential of any point in space in terms of the potentials of surrounding points. For example, in a 2-dimensional electrostatic field represented by a very fine mesh of points the Laplace equation is satisfied (to a good approximation) when the electrostatic potential of any point is estimated as the average of its four nearest neighbor points:

Physical models (as opposed to numerical models) have historically been used to solve many Laplace equation problems. These models have the advantage of giving physical insight into problems that can be difficult to understand.

Potential arrays are dimensioned by the number of points in each dimension (x, y, and z). Therefore an array of nx = 51 would have 51 points in the positive x direction. All arrays have their lower left corner at the origin (xmin = ymin = zmin = 0). Thus if nx equals 51, xmin equals 0 and xmax equals 50 (a width in x of 50 grid units).

All 2D arrays have nz = 1 (zmin = zmax = 0). Thus 2D arrays are always located on the z = 0 xy-plane.

Figure 2.4. 2D potential array with (1) cylindrical symmetry generating a volume of revolution around the x-axis, (2) planar symmetry generating a planar symmetrical volume, (3) cylindrical symmetry plus x mirroring, (4) planar symmetry plus x and y mirroring.

Arrays can use a lot of memory. A 100x by 100y by 100z 3D potential array requires one million points. Each point requires 10 bytes of RAM. Thus 10 megabytes of RAM are required for each million array points.

Two potential array symmetries are supported: Planar (2D and 3D arrays) and cylindrical (2D arrays only). When SIMION refines (solves the Laplace equation) or projects an array instance (3D image) of an array into its ion optics workbench volume, it uses the array's symmetry. If the 2D array has a cylindrical symmetry it will be projected to create a volume of revolution about its x-axis. Figure 2.4 (top-left) shows an isometric 3D view of the array in Figure 2.3 assuming it has cylindrical symmetry. Note: The cylindrical 2D array is visualized as if it were 3D planar to take advantage of fast planar visualization methods. However, apertures are really round (despite how they appear) and the cylindrical symmetry is fully retained for ion trajectory calculations.

In contrast, Figure 2.4 (top-right) shows an isometric 3D view of the array in Figure 2.3 assuming it has 2D planar symmetry. Note that 2D planar symmetry assumes that the array itself is only one layer of an infinite number of layers in z (for refining purposes). When SIMION projects a 2D planar array as an array instance within the workbench volume it assumes a z depth of +/- ny (grid units). You may edit the array instance definition to increase this z depth. This option allows a 2D planar array to be used to represent the interior (symmetrical) portions of objects like quadrupole rods (saves array space).

Many electrode designs have a natural mirrored symmetry. Designs that mirror in y have a mirror image of the electrode/poles in the negative y. SIMION supports three mirroring symmetries: x, y, and z. Mirroring allows you to use a smaller array to model a larger area (or volume) when conditions permit. For example: A 3D planar array can be mirrored in x, y, and/or z. If the design symmetries permit, this would allow the modeling of a 3D volume with one eighth the number of points required if no mirroring were utilized. SIMION takes mirroring into account when refining arrays and projecting their instances into the workbench volume.

X mirroring is allowed for all 2D and 3D arrays. Y mirroring is required of 2D cylindrical and allowed in 2D and 3D planar arrays. Z mirroring is only allowed in 3D planar arrays.

Figure 2.4 (bottom) shows mirroring enabled on both the cylindrical (bottom-left) and planar (bottom-right) geometries discussed previously.

SIMION uses the same finite difference methods for refining either electrostatic or magnetic potential arrays. However, the definitions for potentials and gradients used are different and it is important that you understand these differences.

Potentials and Gradients in Electrostatic Arrays

Potentials in electrostatic arrays are always in volts. SIMION uses the refined array potentials to determine field gradients (voltage gradients). Electrostatic field gradients are always in volts/mm. When an array instance of a potential array is projected into the workbench volume, it is scaled by a user specified number of millimeters per grid unit (or defaulted to 1 mm/grid unit). So although electrostatic gradients start out as volts/grid unit they are divided by the instance scaling factor to obtain volts/mm:

Thus array instance scaling can have a dramatic impact on electrostatic gradients and therefore ion accelerations.

Potentials and Gradients in Magnetic Arrays

SIMION is not a magnetic circuit program. You have to supply the magnetic potentials for it to refine. Unlike electrostatics, in magnetics we normally think of and measure gradients or more precisely flux (gauss) as opposed to potentials. This presents a problem because SIMION needs scalar magnetic potentials to refine.

In order to deal with this dilemma SIMION defines magnetic potentials in Mags. Mags are defined to be gauss times grid units. Thus the gradient of magnetic potential is simply gauss. Note: Mags are gauss times grid units instead of gauss times millimeters. If Mags were gauss times millimeters then instance scaling would confound us further. With this approach, magnetic fields remain the same whether the array is scaled to be a certain size or 10 times as large in the workbench volume. Thus instance scaling has no impact on the magnetic fields (flux in gauss) produced by magnetic potential arrays.

SIMION also makes use of a magnetic scaling factor ng as a property of magnetic potential arrays. The ng scaling factor has been provided to further simplify your life. It would often be very nice for Mags to be directly related to gauss. Let's say we have a simple two pole magnet. We would like to set one pole to 1000 Mags and the other to Zero Mags and have the field in between be approximately 1000 gauss. If the two poles are separated by let's say a 60 grid unit pole gap we would specify the value of 60 for ng to automatically scale the Mags potentials roughly into gauss.

Note: The B field vector always points from greater magnetic potential (e.g. 1000 Mags) toward lesser magnetic potential (e.g. 0 Mags).

Beware! Magnetic potentials are not as simple as electrostatic potentials, and some magnetic fields cannot be expressed as scalar potentials but rather as vectors. While we can safely assume that all points of an electrode have the same electrostatic potential (e.g. volts), it is dangerous to assume that the same is generally true for magnetic poles. Magnetic poles do not as a rule have totally uniform magnetic potentials across their surfaces (permeability not being infinite). Thus you must allow for this fact if the effects could be significant enough to impact your results. Remember: User beware. ^[2]

User defined potential arrays come in two classes the basic potential array (.PA file extension) and the fast adjust definition array (.PA# file extension).

The basic potential array has its electrode/pole potentials defined as described above. These arrays are then processed by the Refine function to solve for the non-electrode and non-pole potentials. The basic array is always saved with a .PA file extension. An array's file extension is important because SIMION assumes that all arrays with a .PA file extension are basic potential arrays for refining, adjusting, and viewing purposes.

The fast adjust definition array is much like the basic potential array except the electrode potentials are not explicitly defined but rather are indices to potentials that are defined later (after refining). Here, the Laplace equation is solved independently for each electrode. Using the additive property of the Laplace equation, these independent solution can then be linearly combined for any desired combination of electrode potentials. In this way, you may adjust the potentials on the electrodes quickly--hence the name fast adjust--without the relatively slow step of re-refining. This even makes practical things like simulations of quadrupole rod oscillations in the megahertz range. All fast adjust definition arrays must be explicitly saved with a .PA# file extension so that SIMION will recognize and process them properly.

We often need to change the electrode/pole potentials of an already refined array to tune a lens or adjust a magnet's field. SIMION supports three different strategies:

SIMION maintains a working copy of each active potential array (up to 200) in memory (RAM). When you change something in a potential array you are only changing the in-memory copy. Likewise when you fly ions through instances of potential arrays in the workbench you are using the in-memory copies of the potential arrays.

User defined potential arrays are normally saved as .PA or .PA# (extension) files in your project directory. When you create a new potential array only the in-memory copy is created. It is your responsibility to save any new or changed potential arrays to your project directory as required. Saving potential arrays preserves your work between sessions.

The Adjust Preferences button allows you to adjust various SIMION and GUI characteristics. Clicking the Adjust Preferences button brings up a screen that allows you to change colors, sounds, and other options. If you haven't explored Adjust Preferences, do it now. Descriptions of all options can be found in the GUI discussion in Appendix C.

The Main Menu Screen (Figure 2.5) contains a window with a list of each currently allocated PA memory region and the name of the potential arrays in each (long file names are supported - however a long file name may be displayed truncated to fit the width). One of these will be selected as the currently active potential array. This is the array that will be acted upon by functions like: Load, Save, Modify, Refine, Fast Adjust, etc.

A particular potential array is selected by clicking (depressing) its button.

The last button in the list is always marked empty PA. This empty PA is available for allocating memory for a new potential array. Up to 200 potential arrays can be loaded in RAM at one time.

The Main Menu screen has a Remove All PAs From RAM button. This button is used to remove all working copies of PAs from RAM. Its primary function is to restore a clean slate when you are about to start a new project or the clutter of PAs has become unmanageable.

The first step in starting any new SIMION project is to create a project directory to hold all the files you'll create. Remember, SIMION expects that all project files reside in the same directory. You ignore this rule at your peril!

Let's create a new directory called basic that is directly below the c:\Program Files\SIMION-8.0\mystuff directory (or anywhere else you may like). On convenient way to this is shown (Figure 2.6):

Figure 2.6.  Steps in creating a new project folder.

Figure 2.7.  Creating a new potential array.

The next step is to create a new potential array in memory (Chapter 4). Use the following steps for this example (Figure 2.7):

For this exercise, we are going to make a fast adjust definition array (.PA#) of a simple three element lens. It is a useful example because fast adjustable arrays are the most commonly created array type. The choice of a simple three element lens provides something to play with that will give you insight into how electrostatic ion optics really work.

Let's Do It!

Click the Modify button on the Main Menu Screen to access the Modify function. You should now be looking at the Modify Screen (Figure 2.8). Each electrode is defined by setting its point type (e.g. electrode) and voltage, marking its area of points, and then clicking the Replace button to replace the marked points with the defined values. The followings steps should be used:

Figure 2.8.  The steps in creating electrodes in the Modify function.

1. For electrode number one, make sure Electrode point type is selected and set the Potential panel to 1.0 volt.

2. Check to see that the Box (box) button is depressed. It selects box area marking.

3. Now move your cursor to the upper left corner point of the array. Hold down the left mouse button, and drag the cursor (keeping the left mouse button depressed) to the bottom of the array one point to the right (to mark an area two points thick). Now release the left mouse button and the area is marked. If you make a mistake marking, just re-enter the correct mark.

4. Click the Replace button and click the YES button to replace the points in the marked area with 1 volt electrode points. If the wrong points are marked, you can erase them by changing the point definition to Non-Electrode of 0.0 volts, marking the error's area, and doing Replace to replace the marked points with non-electrode 0.0 volt points.

5. Change the Potential panel to 2.0 volts and insert electrode number two (as in Figure 2.8) in the same manner as electrode one.

6. Change the Potential panel to 3.0 volts and insert electrode number three on the right edge (as in Figure 2.8) in the same manner as electrode one.

7. When you're done creating the electrode definitions, click the OK button to exit Modify and keep the array changes (in-memory copy).

At this point the only copy of this array is the in-memory copy. SIMION has assigned it a temporary name of NONAME01.PA and has a asterick (*) after it to indicate that it is not saved (and possibly also an exclamation (!) symbol to indicate unrefined). We next need to save this file as test.pa# in the basic directory. The .PA# file extension tells SIMION that this is a fast adjust definition file (important). Use the following steps to save the array (Figure 2.9):

Figure 2.9.  Steps to save potential array as text.pa# in the basic project folder.

The next task is to refine the potential array (solve for the electrostatic fields). When you refine a .PA# potential array SIMION doesn't actually refine the .PA# array itself. It uses the .PA# array as a definition for the collection of arrays (one per each adjustable electrode plus one for the combined solution) that Refine actually creates, refines, and saves in the current directory (basic). Use the follow steps to refine the array (Figure 2.10):

Figure 2.10.  How to refine a .PA# file.

SIMION will scan the array, determine the number of adjustable electrodes, create each of the four required arrays (.PA0, .PA1, .PA2, .PA3), refine each array and save them in the basic directory.

When all this is completed, you will be returned to the Main Menu Screen. You can verify that these four fast adjust support files have been created by clicking on the Browse Files button to look at the contents of basic (Figure 2.11).

Figure 2.11.  View of the files created by the Refine.

The .PA1, .PA2, and .PA3 files contain the respective solutions for each of the adjustable electrodes. If there had been one or more non-zero non-fast adjustable electrode points (e.g. one with a non-integer voltage such as 5.6 volts), SIMION would have automatically created a .PA_ fast scaling solution file as well for those voltages. The .PA0 file is the final solution array you will fast adjust and fly ions through.

In the Browse Files dialog box, click the Cancel button or hit the Esc key to return to the Main Menu Screen.

The actual fast adjust file is the TEST.PA0 file (the fast adjust definition file was the TEST.PA# file). This file contains the final solution, accounting for all electrodes adjusted to their final voltages (in this case, the final voltages will actually be 1000V, 1000V, and 0V, not 1V, 2V, and 3V).

Initially, all adjustable electrode voltages are set to zero in the .PA0 file.

The TEST.PA0 file is the file we must actually fast adjust. We could load it in place of the TEST.PA# file by clicking the Load button and selecting the TEST.PA0 file button to load the file. However, the Fast Adjust function will do this automatically anyway. When clicking the Fast Adjust button (assuming that the TEST.PA# file is currently selected), SIMION looks at the file, sees it is a .PA# file, and automatically loads the .PA0 file in its place. SIMION then allows you to fast adjust it (Figure 2.12).

We want to set electrode number one to 1,000 volts, electrode number two to 1,000 volts, and electrode number three to 0 volts (its current value). Use the following steps:

Figure 2.12.  Steps to fast adjust potential array.

Note: SIMION fast adjusts the in-memory copy of the .PA0 file. If you want to retain these values between sessions you should save the updated in-memory copy back to disk. For example: Click the Save button, hit the Enter key (to save), click YES to replace.

To view the TEST.PA0 potential array, make sure its selected in the potential array list on the main screen and click the View/Load Workbench button. Your screen should look like Figure 2.13.

You can click the ZY, XZ, and 3D Iso buttons to see other standard views. Adjust the Display Quality panel from 0 (lowest quality) to 9 (highest quality) in 3D Iso view to see what it does. Also use the Orientation Sphere object to change views (point the cursor to it and drag the sphere about with either mouse button depressed). There are twelve 2D and eight 3D standard views. See if you can use the Orientation Sphere to see them. When you're through exploring, click the XY button to return to your starting view.

Figure 2.13.  Using the View screen to visualize the potential array in a 2D XY view. Main functions are labeled.

Figure 2.14 shows a potential energy view of the potential array. To duplicate this view, click the XY button (or make sure it is depressed) and then click the PE/Contours tab and press down the PE View button to switch to a potential energy view. The PE view is also affected by the Display Quality and Orientation Sphere controls.

Figure 2.14.  Potential energy view of potential array using the PE View function.

The next task is to define some particles to fly (Figure 2.15).

Figure 2.15.  Defining initial conditions of ions to fly.

Click the Fly'm button to fly the defined ions. Your screen should be something like Figure 2.16 if you're still in a PE View.

Figure 2.16.  Particle trajectories flown while displaying potential energy view.

You can fly the ions together by selecting the Grouped check box before you click Fly'm. Further, you can keep the ions flying by selecting the Rerun check box too. It gives a movie effect (click Fly'm again or hit the Esc key to stop). Trajectory computations will speed up if you change the Trajectory Computational Quality panel from 3 (its default) to 0 (for a simple simulation like this, SIMION may calculate these too quickly already to notice a difference). There are all sorts of things to learn and try for yourself!

SIMION allows you to fast adjust electrodes from within the View function. To accomplish, click the PAs tab, select the test.pa0 in the PA Instances list (it is already selected since there is only one to select in this example), and click the Fast Adjust button.

Figure 2.17.  Particle trajectories flown while displaying potential energy view.

For this example adjust the voltage of electrode number two to zero volts and fast adjust it. Now click the Fly'm button. Notice the shape of the potential energy surface has changed dramatically. The ions diverge rather than focus (Figure 2.17).

Let's assume we want to adjust the voltages so that the ions just focus when they hit electrode number three. The first step is to enable the Rerun and Grouped check boxes (on the Particles tab). Now click the Fly'm button. Notice that the ions keep flying like in a movie. Under the PAs tab click the Fast Adjust (Voltages) button to enter the Fast Adjust screen. Change electrode number two to 900 volts and Fast Adjust. Check the focus. If it's not quite right click the Fast Adjust button and try again. This is known as interactive tuning.

It is important that you save your work. This allows you to quickly resume your efforts in a subsequent SIMION session. The following material shows you how to save your .IOB file (ion optics workbench definition file) as well as saving an auto-loading .FLY2 (ion group definition file).

Let's pretend that this is a new SIMION session and that we want to reload that landmark simulation that we performed above. Click the Quit button and YES button to exit from View back to the Main Menu Screen. Now click the Remove All PAs From RAM button and YES to return all of PA memory to the available memory heap. SIMION now has no files loaded.

Click the View/Load Workbench button. SIMION doesn't have a potential array to view (the Empty PA is selected in the list of potential arrays), so it automatically opens the file selection dialog box and prompts you to select an .IOB file. Select the test.iob file (saved above). SIMION will load the .IOB file and all the potential arrays it references.

SIMION will now check for auto-loading files. In this case it will find a file called test.fly2 (assuming you said Yes to saving an auto-loading ion definition file when the test.iob> was saved). This file will be automatically loaded. SIMION also can save and auto-load other files. These include .ION (ion by ion definitions), .REC (data recording), and .KEPT_TRAJ (kept ion trajectory files). These features are discussed in Chapter 7.