Cathodes and Electron Beams

Electromagnetic simulation software that includes advanced space charge capabilities enables X-ray tube engineers to optimize important tube design features. The engineer can model variables responsible for:

• focal spot characteristics,
• backscattered electron heating,
• relaxed manufacturing tolerances, and
• reduced insulator charging.

Observing the influence of a geometry change can take as little as fifteen minutes, making it feasible to analyze the way in which a number of different parameters affect the beam, and permit rapid development of an optimized final design.

The software includes several physical models of emitters:

• thermally limited,
• Child's Law,
• Langmuir-Fry (with virtual cathode),
• Maxwellian initial velocity distribution.
• Fowler-Nordheim field emission model
• Schottky model field emission model

The electric field and equipotentials can be displayed, giving insight into the behavior of the device (for example, where high electric fields cause arcing or field emission). Beam trajectories, space charge, and beam plots may be displayed as well.

2D Space Charge Analysis

A simplified analysis of an X-ray tube can be performed using the two-dimensional software package Opera-2d/sp, taking into account the properties of dielectric materials and the influence of space charge on electron emission as well as focal spot shape and size.

• The focal spot is often required to exhibit little or no electron current outside of the main focal area. The detailed features of the focal spot can be observed with a trajectory intersection plotter showing, for example, the total current density in the beam.

• In order to minimize anode heating and insulator charging, backscattered electrons from the anode may be modeled and collector design can be optimized.

3D Space Charge Analysis

A three-dimensionally accurate analysis of an X-ray tube can be performed using Opera-3d/Scala. The 2D model geometry may be imported into the 3D Geometric Modeler for ease of model generation. IGES or SAT files may also be imported from CAD packages.

• 3D analysis of the X-ray tube evaluates both the space charge influence on the emission of the beam, as well as the broadening effects of space charge at the focal waist.
• 3D modeling with Scala allows the effects of small changes to the filament geometry and location to be predicted.

Combined Electric and Magnetic Field Space Charge Analysis

In order to evaluate the influence of magnetic fields on the electron beam, both the 2D and 3D software can be used in conjunction with the magnetostatic field analysis software packages, Opera-2d/st and Opera-3d/Tosca. Combined electric and magnetic field analysis performed in this way evaluates beams with the influence of the electric field, the magnetic field, and space charge all interacting simultaneously during the analysis.

2D or 3D Analysis?

In many cases a full 3D analysis is necessary to completely model X-ray tube cathode structures, filaments and focusing components. 3D modeling is also valuable for exploring the influence of manufacturing tolerances on production costs and yields. In most instances, the 2D modeling of cathodes can provide quick "what if" information which, when combined with a final 3D analysis, can save considerable time and expense in developing optimized X-ray tube systems.

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