Solenoid, Geometric Aberration

The first test case of geometric abberations will look at a beam passing through a single turn solenoid with the following input file.
TestCase_SingleTurnSolenoid_GA.rtf

The emittance component graph follows.
R001DVR1EC.pdf

The graph correctly shows that all emittance growth is contributed to beamline elements, the nonlinearity in the solenoid field

Solenoid, Geometric Aberration with Spacecharge

Taking the same setup and adding space charge, it was found that for low enough charge, the ε' metric was able to converge to the theoretical spherical abberation of the solenoid.

Input file: GAwithSpacecharge.rtf

Varying the charge from 1e-15 C to 1e-13 C the beamline element emittance component was plotted as a function of the charge: GeometricAbberationChargeConvergence.pdf

The theoretical emittance growth from the solenoid (44.2 nm) matches to the converged beamline element emittance component (46.7 nm) within the uncertainty due to the timestep chosen (5%)

For large charge, the deviation from the theoretical emittance is attributed to problems with the spacecharge algorithim at the focus of the beam