|
Package
|
Trak Charged Particle Toolkit
|
|
Input files
|
BeamExpandTrak.DST, BeamExpandTrak.MIN, BeamExpandTrak.EIN, BeamExpandTrak.TIN
Download ExpandBeamTrak.zip
|
|
Description
|
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 Trak parameters to achieve good convergence.
|
|
Results
|
The lower figure shows properties of the beam displayed in the distribution mode of Trak at the exit position. The f(r,r') plot shows an ordered expansion with final envelope radius R = 14.3 mm and final envelope angle R' = 5.26 deg = 0.0918 radians. The reference Charged Particle Beams (Sect. 5.4) discussion the theory of expansion of a uniform current-density beam. The model parameters are Chi = 14.3/2.0 = 7.15, F(Chi) = 6.52, 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)) = 0.095 rad and the predicted transit distance is L = (Ri/sqrt(2*K))*F(Chi) = 193.0 mm. Both values are close to the code results.
|
|
Comments
|
The text Charged Particle Beams is available for download at https://www.fieldp.com/cpb.html. The example beamexpandomni.html shows the same calculation in 3D with OmniTrak.
|
