Used extensively in scientific and engineering applications, the Static Module computes magnetostatic and electrostatic fields. It uses the FEA method to solve Maxwell’s equations for the static case in a discretized model. For 3D magnetostatics, the algorithms used in the Static Module automatically treat volumes in the model which contain magnetic sources differently to volumes without sources. By using this powerful method, the module successfully avoids cancellation errors that may occur using alternative solution methods. As a result, the accuracy of the solution is often far higher than would be expected from a Finite Element Analysis. In this module users can specify magnetic material properties as linear, non-linear, isotropic, anisotropic, laminated or permanent magnet. In 3D, users are able to simulate coils/solenoids with extreme accuracy using Opera’s proprietary method which deploys the Biot-Savart integral to calculate magnetic fields from coils. Opera-3d includes a helpful library for easy definition of standard shapes, such as solenoids and racetracks, and also offers users the flexibility to create coils of any topology. Using the “lossy dielectric” option, users can simulate electric fields resulting from charging of low-conductivity dielectrics.

# Solutions

## Opera

Opera Simulation Software is a Finite Element Analysis software suite which allows users to perform simulations of electromagnetic (EM) and electromechanical systems in 2 and 3 dimensions. Opera complements the existing SIMULIA EM portfolio with its strength in low frequency simulation, which is extremely useful for the design of magnets, electric motors and other electrical machines.

The Dynamic Electromagnetic Module can be used to calculate time varying electromagnetic fields and eddy current flow in Electromagnetic devices and systems. This includes eddy currents induced by simple moving conductors, i.e. where the movement does not change the geometry (e.g. rotating disk or infinite pipe of constant cross-section).

There are three different types of dynamic solution available, each having a different form of time variation:

- Harmonic calculates steady-state ac currents where all fields and potentials are oscillating at the same frequency
- Transient calculates transient eddy currents induced by the fields of driving currents, boundary conditions and external fields which change in time in a predetermined way
- Fixed Velocity calculates eddy currents induced by motion which does not change the geometry of the model. The source fields and driving conditions are all time invariant

The Electromagnetic Motional Module computes time varying fields and eddy currents in devices with rotating or linear movement causing re-meshing during solution. Parts of the geometry, and hence the finite element mesh, are allowed to move independently at speeds controlled by the user or calculated as the analysis proceeds. The analysis is a transient analysis, with eddy currents being induced in conducting media both through the effects of the moving magnetic fields, and through the time variation of the model sources.

This module has been designed to include dynamic modeling of all types of electrical machines, for example, including permanent magnet (PM), induction, switched reluctance, synchronous and synchronous reluctance. It can be used to investigate commutation effects, transient responses as well as steady state performance, and unbalanced local effects.

Eddy current losses in all materials, including permanent magnets can also be calculated. Calculations can include the electrical drive under normal and fault conditions and a dynamic mechanical load. At each time-step, the module calculates the electromagnetic force on the moving parts (rotation or translation) and applies an incremental movement followed by recalculation of the electromagnetic fields.

Quenching of superconducting magnets can be analyzed using this module. The Opera quench module utilizes the temperature rise of a superconducting magnet during a quench, including the transition to being resistive as the quench propagates through the magnet. The heat that triggers a quench event can be from a variety of sources. In a DC system typically it will be due to a failure with the cryogenic system, ramping the system too quickly or in test situations can be introduced deliberately. In simulation we can include this heat as a surface or volume property or through rate dependent, ohmic or hysteresis losses in materials due to current flowing or fields in them. In this instance we have significant anisotropy in the material properties as thermal conductivity is dominant along the winding direction, requiring specific modelling techniques for efficiency and accuracy.

The quench module uses advanced FE techniques to model the highly non-linear transient behavior of a magnet during a quench. Using an algorithm which couples the electromagnetic solution to the thermal and circuit solutions (to determine the currents in the coils), the full quenching process can be analyzed.

The Thermal Analysis Module computes the steady state or transient temperature, heat-flux, and thermal-gradient fields due to electromagnetic heating or external heat sources. Thermal properties, such as the conductivity tensor or specific heat, and heat source density can be specified as a function of position, and can be temperature dependent (leading to a non-linear analysis).

The thermal module may be used in stand-alone mode with the user defining the distribution of heat input, or it can be used in a multi-physics simulation with other Opera solution modules providing the distribution of heat. It is possible to include multiple heat sources (for example eddy current heating and iron losses in a motor) in a single calculation. The thermal module will calculate the temperature distribution in the model, which may modify the electromagnetic solution (if material properties are temperature dependent). Stress induced by thermal expansion can be analyzed using the Stress Analysis Module. The deformation caused can be used in subsequent thermal and electromagnetic simulations.

The Stress solver can solve for linear static stresses in 2 or 3 dimensions. Results include deformations, strains and stresses. In 3 dimensions the stress solver can also be used to calculate the natural modes of the structure ie. the eigenvalues and eigenvectors.

The Charged Particle Module calculates the interaction of charged particles in electrostatic and magnetostatic fields. It uses the Finite Element method to solve Maxwell’s equations for the steady-state case in a discretized model, and provides a self-consistent solution including the effects of space-charge, self-magnetic fields and relativistic motion.

A comprehensive set of emitter models is provided, including thermionic and field effect emission from surfaces, secondary emission from surfaces and within volumes (used to model gas ionization), and models for unmagnetized and magnetized plasmas. It is possible to include multiple species of charged particles, each having user defined charge and mass.

The Charged Particle module can be used in a multiphysics analysis, for example, whereby the particle beam generates heat.