bem-comsol

bem-comsol is a python package that can simulate electrostatics for ion traps using boundary element method provided by COMSOL Multiphysics. It also provides a tool to analyze 1D electric potential and find the eigenmodes.

The diagram above shows how the program works. The program requires you to create the basic modeling workflow in COMSOL and save it as an mph file. Then, execute the Python code, and the program will automatically use the control voltage method to sequentially set electrode voltages and export spatial potential data as CSV file.

Then, you can run the mode solver to analyze and solve the one-dimensional axial potential, or you can use the data exported by the program for post-processing on your own.

Installation

Use pip to install bemcomsol

pip install git+https://github.com/fengxiaot/bem-comsol.git

import the package

from bemcomsol.simulation import simulate,load
from bemcomsol.mode1d import eqposition,eqposition_analytic,eqposition_sym,mode1d,mode1d_analytic

Build an model in COMSOL

You should create the basic modeling workflow in COMSOL and save it as an mph file. If you are an expert in COMSOL, you only need to view the [Define Parameters](#Define Parameters) and [Export Data](#Export Data) section.

Create mph File

Use Model Wizard to create a 2D/3D model and add Electrostatics, Boundary Elements (esbe) module, then choose Stationary study.

Import Geometry

For simple electrode shapes and preliminary validation of principles, the geometric design can be accomplished within COMSOL. For complex electrode shapes or mature designs, COMSOL also supports importing geometries from external sources. Below, we will show the method of importing geometries from external sources using model/SimpleTrap.stl as an example.

1. In the menu bar, select Geometry -> Import
2. For the Sourse, select Mesh or 3D Printing file , then find model/SimpleTrap.stl , click the import button
3. In Geometry , set length unit to $\mu \mathrm{m}$, click Build All button.

Set Materials

Though solving the model does NOT requires specification of materials of electrodes (since it uses BEM method), COMSOL still asks you to specify them. Otherwise, an error message will occur.

1. In the menu bar, select Materials -> Add Material from Library , then search for Copper.
2. Under Copper, for Geometric entity level , select Domain , for Selections, select All domains .
3. In the menu bar, add Perfect Vacuum from library again.
4. Under Perfect Vacuum, for Geometric entity level , select Domain , for Selections, select All voids .

Define Parameters

This is the most important step. Under Global Definitions -> Parameters , create some parameters for the DC voltage, following the rules below:

• Name should have a prefix 'DC'.
• Expression can be any value. Python code will sequentially set them to 1[V] .
• The number of parameters should be the same as the number of electrodes you want to apply control voltage method. You don't need to create a parameter for grounding electrodes or those having a constant voltage.

Create Boundary Selections

This step is not a must but will bring a lot of benefits.

1. In the menu bar, select Definitions -> Explicit , label it with your preferred name
2. In Input Entities , set Geometric entity level to Domain , then click on one of the electrodes on the right
3. In Output Entities , select Adjacent boundaries
4. Repeat the steps for each electrodes

Set Boundary Conditions

Now let us define the problem.

1. Click Electrostatics, Boundary Elements (esbe), under Infinity condition, select Asymptotic value at infinity and set $V_\infty = 0$
2. In the menu bar, click Physics -> Boundaries -> Electric Potential
3. Under Boundary Selection, choose the selection of exterior boundaries of one of the electrodes you have just defined in the [previous subsection](#Create Boundary Selections). Under Electric Potential, set $V_0 = \mathrm{DC}i$, the name of parameters you defined just now.

4. Repeat the steps for each electrodes

Mesh and Study

In Mesh , you can change the element size of BEM method, you can also build user-controlled mesh or refine certain area. We are going to use the default settings here. Just click Build All.

In Study , you can define the details of iterator. We are going to use the default settings here. Just click Compute.

Export Data

In Results -> Datasets , you can see two nodes: Study/Solution and Grid 3D. The first node stores the surface electric field of the electrode, while the second node stores the electric field in the external space. In most cases, we only care about the latter.

1. In Results -> Datasets -> Grid 3D , define the external space you are interested.

   • Under Parameter bounds, you can set the boundary of the box.
   • Under Resolution, you can define the number of data points to be sampled in each direction. The default value 30 is usually too low.

   You can click the Plot button any time to check your definition of box boundaries.

2. (optional) If you are interested in electric potential on a specific plane or line, you need to define a Cut Plane or Cut Line 3D. For example, we only want to know the electric potential on $x$ axis: $y=0, z=3, x \in [-200,200]$ (unit: um), do the following steps:

   • In Results -> Datasets -> Cut Line 3D , create a Cut Line 3D.
   • Under dataset, select Grid 3D . NOT study/solution !!!
   • Under line data, define the cut line.

   You can click the Plot button any time to check your definition of line boundaries.

3. (optional) Create a plot group to quick view the potential distribution. Dataset should always be Cut Line 3D or Cut Plane, NOT study/solution!

4. In Results -> Export -> Data, define the dataset you want to export.

   • Under dataset, select Cut Line 3D or Cut Plane or Grid 3D.
   • Under expressions, you can type in esbe.V (electric potential), esbe.Ex/esbe.Ey/esbe.Ez/esbe.normE (electric field).
   • Under output, you can set the filename (such as output.csv, must in CSV format). The Python program will automatically change it later.
   • Under advanced, check the box for Sort .

Now export data and check if it functions properly! If so, save the workflow as an mph file.

Python