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Input files
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BeamExpandOmni.DST, BeamExpandOmni.MIN, BeamExpandOmni.HIN, BeamExpandOmni.OIN
Download BeamExpandOmni.zip
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Description
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The example models the expansion of an ion beam in a vacuum space resulting from space-charge forces. This is a sensitive test of code accuracy because the acting forces are generated solely by the self-consistent beam distribution. The parallel input beam of He++ ions has radius 2.0 mm, energy 80 keV and current 20.0 mA. The example illustrates creation of a specified beam distribution with GenDist and choice of OmniTrak parameters to achieve good convergence.
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Results
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The top figure shows properties of the exit beam distribution displayed in GenDist. The f(x,y) plot shows an ordered expansion with final envelope radius R = 13.9 mm. The phase-space plot f(x,x') indicates a final envelope angle of R' = 0.09 radians = 5.16 deg. The reference Charged Particle Beams (Sect. 5.4) discussion the theory of expansion of a uniform current-density beam. The model parameters are Chi = 13.9/2.0 = 6.95, F(Chi) = 6.39, ion velocity vi = 1.96E6 m/s and beam current Ib = 20.0E-3. The generalized perveance is K = (Z*e*Ib)/(2*pi*Epsi0*mi*vi^3) = 2.29E-3. The predicted envelope angle is R' = sqrt(2*K*ln(Chi)) = 0.094 rad and the predicted transit distance is L = (Ri/sqrt(2*K))*F(Chi) = 189.0 mm. Both values are close to the code results.
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Comments
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The text Charged Particle Beams is available for download at https://www.fieldp.com/cpb.html. The example beamexpandtrak.html shows the same calculation in 2D with Trak.
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