MICHELLE* is a general purpose two-dimensional (2-D) and three-dimensional (3-D) charged particle beam optics code.

MICHELLE has models for both equilibrium flow particle trajectories and initial-value time-dependent beam trajectories. It self-consistently computes the emission and transport of charged particles in the presence of electrostatic and magnetostatic fields. The charged particles contribute to the static fields, and the static fields act on the charged particles.

The equilibrium flow particle model is also known as a steady-state static PIC code or a gun code. The time-dependent model is an electrostatic time-domain particle-in-cell (PIC) code.


Engineers and scientists use MICHELLE to analyze and design a wide variety of electron and ion sources, accelerator beamline components, and vacuum electron device components. The code is used in industry, national laboratories, and academic research institutions.

MICHELLE can model devices that range from simple 2-D axisymmetric devices to very complicated 3-D devices, including those with fine geometric features on disparate spatial scales. The following are some examples of devices MICHELLE can model.

Beam Formation

  • Electron sources: pierce diodes, axisymmetric diodes, annular beam diodes like magnetron injection guns (MIGs), multiple beam guns, sheet beam guns, and gridded guns.
  • Ion sources: volumetric ion sources, ion thrusters.

Beam transport and focusing systems

  • Accelerator component beam transport using magnetic field focusing or electrostatic focusing, electron and ion beam lithography (single beam and multiple beams), beam control for large-scale electron beam materials processing.

Beam Collection

  • Beam dumps, depressed collectors, multistage depressed collectors.


MICHELLE was developed to be an architecture that hosts multiple Electromagnetic and Electrostatic field solvers with Particle tracking capability for both Time-Dependent and Steady-State. It is based on a Finite-Element Particle-In-Cell formulation employing a conformal mesh to resolve very complex geometries with fine features.

The finite-element field solver computes the electrostatic and magnetostatic potentials, the latter a full vector potential in 3-D. The field solver works efficiently with both multiblock structured grids and unstructured grids. Coupled with fast, robust, reliable and accurate particle trackers for both mesh types, and a complete set of emission algorithms, this mesh flexibility allows MICHELLE to model very complicated devices for the most demanding design and analysis applications.

Currently at Version 4, the MICHELLE code supports the following features:

  • Computes the self-consistent emission and transport of charged particle streams (rays) in self and external fields, both electric and magnetic.
  • Has a variety of emission models including space-charge-limited, temperature-limited and field-emission, an extensive facility for secondary emission, volumetric ion source model, and a charge exchange model.
  • Java-based graphical user interface for preparing runs, and a Windows postprocessor for viewing results. The preprocessor interfaces with the powerful ICEM-CFD mesh generator suite.


MICHELLE has the following benefits:

Can employ a multiblock structured grid, an unstructured grid, or both in a multiblock hybrid mesh that best takes advantage of both grid types.

  • This allows MICHELLE to model very complicated geometries and resolve very strong field gradients as necessary. The conformal mesh capability and grid types supported allow disparate feature scales to be captured in the analysis.

Supports linear and quadratic element shapes and basis functions: triangles and quads in 2-D; tetrahedral, hexahedra, prisms and pyramids in 3-D.

  • The different element shapes allow the user to improve the accuracy of a simulation by choosing the optimum mesh topology for the geometry and physics desired.

Has two mesh-adaptive particle pushers: a fast Boris-type pusher for structured grids and a unique accurate, reliable pusher for unstructured.

  • The option of different particle pushers allows the user to choose between speed and accuracy.

Integrated into the sophisticated ANALYST EM design environment and included adaptive mesh refinement and global design optimization.

  • Although MICHELLE can run in the Voyager User Environment, it is also available in the ANALYST electromagnetic code user environment, by Simulation Technology & Applied Research (STAR Inc). The ANALYST environment is a powerful design environment that includes CAD, Meshing with Adaptive Mesh Refinement, global parametric optimization available to MICHELLE. It also hosts STAR's parallel finite-element electromagnetic frequency domain codes in eigenvalue and driven-frequency models.

MICHELLE can be used to run complicated models with over 5 million tetrahedral elements and many tens of thousands of rays.

  • The robustness of the code to handle small to large mesh sizes in 2-D or 3-D geometries allows the designer to work rapidly to test different possibilities and gain intuition during the research and scoping stages of development. Subsequently, the designer can improve the mesh density as needed to validate the detailed or final designs.

Voyager Graphical User Interface

The MICHELLE code can be run as a stand alone or through the Voyager Graphical User Interface (GUI). The Java-based Voyager environment provides an intuitive project-based approach to managing multiple models and cases under a project heading. The interface included a wizard-style problem setup for quick setup to solution. It support job queuing and run-time diagnostics and dialogue. It also includes translators for interfacing to third-party mesh generation software and magnetostatic codes.

Voyager Post Processor

The Voyager Post Processor is an advanced Windows-based application for interrogating the vast MICHELLE solution data. It allows the user to view the geometry, field solutions on the computational mesh, and particle tracks through the domain. It can combine any combination of the above, has many built-in pre-calculated engineering quantities, and includes an Python interface for users to access and process custom diagnostics and quantities.

* MICHELLE was developed in collaboration with LANL, NRL and US Vacuum Electronics Industry mainly with Office of Naval Research funding through the Naval Research Laboratory and with Leidos Internal Research and Development funding.