Example of Trajectory Analysis ≫

ELF/BEAM is a charged particle trajectory analysis software.
It calculates trajectories of charged particles in electromagnetic fields calculated by ELF/MAGIC or ELFIN.

## ELF/BEAM Charged Particle Trajectory Analysis

The electric and magnetic fields on the trajectory of a charged particle are calculated directly from the source, so there is no need to create a spatial mesh.

The FEM calculates the spatial electric and magnetic fields from the potential of the spatial mesh, which is less accurate, but ELF/BEAM calculates the electric and magnetic fields directly from the source, which is not less accurate.

The calculation of the electric and magnetic fields created by the source is based on the analytical integral formula.
Therefore, the electric and magnetic fields are highly accurate until near the elements.

High-precision charged particle trajectory analysis can be performed using high-precision electric and magnetic fields.
Sputtering, cathode-ray tube analysis, etc. can be analyzed with high accuracy.

Trajectories of charged particles in magnetic fields can be calculated. (ELF/MAGIC + ELF/BEAM)
Trajectories of charged particles in electric fields can be calculated. (ELFIN + ELF/BEAM)
Trajectories of charged particles in electric and magnetic fields can be calculated. (ELF/MAGIC + ELFIN + ELF/BEAM)

You can choose between the Euler method, the fourth-order Runge-Kutta method, and ELF's original method.
ELF's original method has many improvements to achieve high accuracy in small computation time.
ELF's original method is the fastest for the same accuracy.

Uses the formula for longitudinal and transverse masses.
Calculations can be made with high accuracy until close to the speed of light.

Coulomb interaction between charged particles can be taken into account.
The trajectory of a charged particle is calculated by placing a line charge on the trajectory of the flying charged particle and repeating the calculation, taking into account the electric field created by the line charge.

The output is the position, velocity, and acceleration of the charged particles.

## acceleration

The ELF series is highly vectorized and parallelized.
As a result, when computed on multiple cores, it is faster in almost every part of the system.

## Applications

・Electron Microscope
・Electron Gun
・Accelerators
・Sputtering
・Flat Cathode Ray Tubes

ELF/BEAM is also used in many other areas.

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