INTEGRATED’s LORENTZ™ suite of CAE programs provide sophisticated simulation and design tools customized for charged particle trajectory analysis in 2D/RS and 3D. The diverse applications of LORENTZ™ include studying the motion of particles in traps such as a Penning trap, or the paths of particles through optical components such as bending magnet and multiple focusing magnets, or the behavior of beams such as the dual grid ion gun.

LORENTZ™ is available in combination with INTEGRATED’s well-established electric and magnetic field solvers. These solvers have proven their reliability over decades of use in applications as diverse as motor design, antennas, and high voltage transmission lines. Depending on the accompanying field solvers, several varieties of LORENTZ™ programs are available for applications involving electric(E), magnetic(M) or combined field analysis (EM) in 2D and 3D known as LORENTZ-2E™, LORENTZ-2M™, LORENTZ-2EM™, LORENTZ-3E™, LORENTZ-3M™ and LORENTZ-3EM™. For the high frequency option, please choose LORENTZ-HF™.

INTEGRATED’s Parametric and batch utilities may be used to run automatic variations on the LORENTZ™ model for purposes such as design optimization or tolerance testing.

Learn about LORENTZ™ Solver Methods and our Specialized Beam Analysis Physics Options.

Thanks to the parallelization of our programs (included in our packages at no extra cost) the solution speed is certainly a major benefit for designers requiring beam analysis and particle trajectory software.


  • 2D/RS and 3D charged particle trajectory field solver for a diverse range of applications.
  • Optical (beam) axis in the 3D package to provide a convenient reference for analyzing a beam.
  • Quasi-transient mode that rebuilds the field at different times for arbitrary time dependencies, which is much faster than doing a full transient solution.
  • At no extra cost, our software packages include:
    • Choice of solvers: To ensure you have confidence in the solution and for independent verification, both BEM and FEM methods are included in the same software package to suit your specific application needs. Not every solver fits every application, no “one size fits all”.
    • Choice of optimization tools: Parametric Analysis for those who need fast and easy optimization with a short learning curve. API and Scripting give more power to advanced users. Both tools are available in the same package.
    • Built-in material libraries: Customize and create your own library for easy access to the materials you use.
    • Integration with MATLAB®: Users' MATLAB code can include function calls to the INTEGRATED API to build geometry, assign physical parameters, solve, and obtain results.
    • Parallelization: When used on 64-bit computers, this permits full utilization of the available RAM to dramatically increase speed of solution and post-processing.
  • Intuitive interface that can be easily customized according to user preferences (overall appearance, toolbars, solvers, backgrounds, defaults, etc.)

“After some online research for a 3D electric field and magnetic field calculator we landed on the LORENTZ 3EM™ program. The interface has been surprisingly intuitive and powerful. I specifically wanted the ability to control the program through an external coding program (mainly through MATLAB but my coworker uses Python which is also supported.). They have a full API command list, as well as examples, which was very helpful in getting started. Their customer service has also been very responsive in helping me understand some specifics or fixing small bugs or implementing UI improvements. Overall I have been very impressed with the program and it has suited our needs well. ”

“Have recently started using LORENTZ™, based on colleague’s strong recommendation, and found it to be immensely useful. Has a wide range of versatility and importing custom geometries works well. Also received training on the package from IES and can’t speak highly enough.”

LORENTZ™ has very friendly user interface and the flexibility to develop CAD-like models”

“The best feature of LORENTZ™ is the combination of field calculation and trajectories calculation with high accuracy. It is quite convenient to check the field setting and to obtain the trajectories immediately. The calculation precision is satisfying if you make the right setting.”

“Comparison of our real hardware measured data with LORENTZ™™ has correlated extremely well and helped us save significant time and money.”

LORENTZ™‘s ability to import any computational domain or structure from CAD makes it extremely useful.”

LORENTZ™ has many intuitive features and one of them is to successfully analyze trajectory transient conditions. As far as customer service and technical support is concerned, the staff at Integrated Engineering Software is quick to respond to issues and provide solutions to any software problems.”

“I have been using LORENTZ™ a long time now. I am very pleased with the BEM solver and trajectory analysis feature of LORENTZ™ software. The ability to solve in multiple current emission regimes is the most unique feature to allow us to create powerful solutions.”

LORENTZ™ is an indispensable tool for electric and magnetic field calculations. To the best of our knowledge, no other software includes the BEM solver with CAD import capability which is extremely important for our application.”

“I have been playing around with the API this weekend. It’s a very powerful and a super useful feature! Good work guys! So far I have been using Excel to interface with LORENTZ™ and it works like a charm with both 2EM & 3EM.”

“The LORENTZ™ software is particularly useful for its direct ray tracing capability with high accuracy. That is the most beneficial and value for our research, and that is why we keep on maintaining and using the software. We really appreciate the quick response rendered by IES with regard to software purchase and maintenance, as well as the technical assistance rendered. I would say Lorentz is a great product to aid electro-optical design, and its accuracy outperforms rival softwares in the electro-optical fields. Thank you very much!”