Solenoid transport of beams with current-dependent initial conditions
We present that intense charged particle beams will generally be formed with an initial correlation between their longitudinal properties, including longitudinal variations in current, and their transverse properties, including their radius and divergence. This is due to the competition between the transverse focusing fields in the beam source and the time-varying space charge forces in the beam. In DC electron guns where the current modulation is slow compared to the electron transit time, the nature of these correlations was previously shown to depend on the gun geometry, exhibiting a linear dependence of the beam radius and divergence on the beam current at the gun exit. Here, we extend the previous work to study the transport of beams with such correlation in uniform and periodic solenoid channels. For each transport channel configuration studied, the transverse envelope equation is used to calculate the envelope of 101 beam slices differing in their slice currents, as well as initial radius and divergence (due to their dependence on slice current). For each channel configuration, these calculations are performed 546 times, with each of these iterations considering a different degree of correlation between the radius and divergence, and the slice current. It is found that some degree of correlation between the initial radius and slice current actually aids in beam transport, and the required strength of correlation can be estimated with simple models. Finally, increasing the degree of correlation between the initial divergence and slice current is generally counterproductive, and the degree of sensitivity to such correlations depends on the design of the transport channel.