Charged Particle Tracing
The Charged Particle Tracing Interface is designed to model the motion of electrons, individual ions, or small ion clusters in electric and magnetic fields. Because the model particles are generally on the atomic or molecular scale, extrinsic properties like particle mass and charge number are specified, but material properties like density or specific heat are not well defined. For larger particles where these intrinsic material properties are defined, consider using The Particle Tracing for Fluid Flow Interface (the particles might still be charged, and can still be subjected to electric and magnetic forces, despite the Particle Tracing for Fluid Flow interface not having “charged” in its name).
Although this physics interface is called “Charged Particle Tracing” it also has some applications involving neutral species because of its built-in capability to model intermolecular collisions in low-pressure environments.
Electric and Magnetic Forces
Any number of Electric Force and Magnetic Force nodes can be added to the model in order to exert electric and magnetic forces, respectively, on the model particles. If multiple particle species are included, the charge of each species is queried separately, so that positive and negative ions (for example) can be driven in opposite directions by an electric field within the same model.
The electric force can be defined directly or by taking the gradient of an electric potential. Any electric or magnetic force can be stationary, transient, or periodic; the periodic forces are most often sinusoidal in time but can also be modulated by another user-defined function. If the electric or magnetic field is solved for in the frequency domain, the frequency of oscillations can be taken directly from the previous study.
Collision Modeling
While some particle phenomena occur in extremely low-pressure environments such as vacuum chambers or outer space, there are also many application areas where the collisions between the model particles and the molecules of the surrounding gas must be taken into account. The Charged Particle Tracing interface includes built-in features to model the collisions between model particles and the surrounding gas via a Monte Carlo approach. At each time step taken by the solver, the probability of each model particle colliding with a gas molecule is computed, based on the particle velocity, density of the gas, and collision cross section data. The dedicated Collisions node supports a variety of reaction types, such as Elastic collisions and Resonant Charge Exchange reactions. Some of these reaction types can cause additional model particles to be created during a simulation, a process called secondary emission.
Space Charge Effects
A computationally efficient way to approach charged particle tracing modeling is to first solve for any external electric or magnetic fields, using for example the Electrostatics interface or the Magnetic Fields interface, and then use these fields to exert electric and magnetic forces on the ions or electrons with the Charged Particle Tracing interface. Because the external fields affect the particles, but the particles do not perturb the fields when they are modeled in this way, this approach is called a unidirectional coupling.
In a unidirectionally coupled model, the external fields can be solved for using a Stationary, Frequency Domain, or Time Dependent study. The particle trajectories are then solved for in a separate Time Dependent study step. The fact that the particle trajectories are computed in their own study step allows efficient and computationally inexpensive iterative solvers to be used.
If the number density of the charged particles is sufficiently large, the particles may begin to cause significant perturbations in the external fields. There is no specific magnitude of the number density at which the space charge effects become significant; rather, as a general rule they should be included if their contributions to the external electric or magnetic fields is of a comparable order of magnitude to the sources or boundary conditions included in the other physics, such as surfaces maintained at specified potentials or external current sources. The bidirectional coupling between particles and fields can be included in the model by using The Particle–Field Interaction, Nonrelativistic Interface, which automatically adds the dedicated Electric Particle Field Interaction Multiphysics node to account for space charge effects.
If, in addition, the particles move at relativistic speeds, the current density due to particle motion may become significant. The Particle–Field Interaction, Relativistic Interface automatically adds the Electric Particle Field Interaction and Magnetic Particle–Field Interaction Multiphysics nodes to account for the space charge density and current density of particles, respectively. Magnetic particle-field interactions are usually negligibly small compared to electric particle-field interactions at nonrelativistic speeds.
Electron Beam Divergence Due to Self-Potential: Application Library path Particle_Tracing_Module/Charged_Particle_Tracing/electron_beam_divergence
The computational requirements for models that include particle-field interactions increase significantly over those that neglect them. If the fields and particle trajectories are directly coupled to each other, both must be computed in the same Time Dependent study, and a fairly small time step must be taken by the solver to account for the constantly changing electric potential. In addition, the space charge density and current density are computed using variables that are constant over each mesh element, so it may be necessary to refine the mesh or increase the number of model particles to more accurately model particle-field interactions.
If the fields are stationary, as often occurs when beams of particles are released at constant current, it is possible to significantly reduce the computational cost of the model by using a Stationary solver to compute the fields and a Time-Dependent solver to compute the particle trajectories. It is also possible to create a solver loop that alternates between the Stationary and Time-Dependent solvers so that a bidirectional coupling between the trajectories and fields can be established; a dedicated Bidirectionally Coupled Particle Tracing study step is available for setting up such a solver loop. The process of combining these solvers is described in the section Study Setup.
Coulomb Forces
If the density of charged particles is extremely high then it can be necessary to include the Coulomb force that acts between the particles. This is done by adding a Particle-Particle Interaction node to the model. When particle-particle interactions are included in a model the computational requirements increase and scale as the number of particles squared. In such models, it is often best to start with a small number of particles, run the study, and then assess whether or not the effect is significant.
Coulomb forces and bidirectionally coupled particle-field interactions usually should not be included together in the same model because this causes the force exerted by each charged particle on other charged particles to be double-counted, once directly and once via the electric field defined in the modeling domain.
Generally the bidirectionally coupled particle-field interaction approach is better when the number of model particles in the model is larger, or when there is a continuous beam of charged particles traversing the simulation domain. The Particle-Particle Interaction is more accurate when the model contains only a handful of charged particles.