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Package
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Trak Charged Particle Toolkit
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Input files
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MagneticLens.MIN, MagneticLens.PIN, MagneticLens.TIN, MagneticLensSat.PIN, softiron.dat
Download EBeamFocus.zip
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Description
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The goal was to model a design for the final focus lens of a high-current radiographic accelerator to determine limits on focal spot size set by spherical aberration. The top figure shows the cylindrically symmetric geometry of the solenoid lens, a 240-turn coil surrounded by a soft iron flux return yoke. The parallel input electron beam had kinetic energy 18.0 MeV, current 2.0 kA, and a radius of 1.25 inches with an envelope approximately parallel to the axis. The study included the following tasks:
- Use Permag to determine a linear solution with 1.0 A drive current with a fixed value of magnetic permeability in the yoke (MuR = 3000).
- Use the field solution to track electron trajectories through the lens over the input radius range. Adjust the magnetic field multiplication factor in the Trak input file to achieve the best focus at a distance of 14.0" from the magnet center. The process gives the approximate magnet input current.
- Find the minimum focal spot size.
- At the operating current level, do a PerMag calculation that includes the saturation properties of the yoke. 1) Determine whether saturation is a concern. 2) Compare the field profiles along the axis to ensure that the linear model was sufficient to determine the electron trajectories.
- Compare the limits set by the lens aberration to those set by space charge and emittance.
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Results
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The best focus was achieved with a magnetic multiplication factor of 428.9, corresponding to an input current of 428.9 A to the 240-turn coil. At this value, the beam envelope radius was less than 0.012". For comparison, the calculated space-charge-limited spot size was negligibly small while the calculated focal point radius based on the measured beam emittance was about 0.014". The conclusion was that spherical aberration was not a concern. The second field calculation was performed with a non-linear material model and a total coil current of (240.0)(428.9) = 102,936 A. The relative magnetic permeabilty had a large value over the yoke volume except for small areas near the inner radius. The calculated peak field differed by only 0.07% from the linear calculation.
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Comments
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The example illustrates the treatment of ferromagnetic mateials in PerMag and field scaling in the Track mode of Trak.
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