New method for generating linear transfer matrices through combined rf and solenoid fields

We present a new method for computing the transverse transfer matrix for superimposed axisymmetric rf and solenoid field maps. The algorithm constructs the transfer matrix directly from one-dimensional rf and solenoid field maps without computing numerical derivatives or eigenfunction expansions of the field map data. In addition, this method accurately describes the dynamics of low energy particles starting from a solenoid-immersed cathode, allowing the method to simulate transport through both rf and electrostatic guns. Comparison of particle tracking with the transfer matrix, and direct integration of the equations of motion through several field setups, shows excellent agreement between the two methods.

Figure 1

The fields and energy gain for a 500 kV gun voltage, 0.04 T maximum solenoid field setting, and 1 eV initial kinetic energy.

Figure 2

Comparison of Runge-Kutta integration (blue) and the tracking using the transfer matrix (green) through the DC gun and solenoid fields.

Figure 3

The field map for the SRF injector cavity and the corresponding energy gain. The cavity voltage is 3 MV, the initial kinetic energy is 1 MeV, and the phase is on-crest.

Figure 4

Comparison of direct integration (blue) and tracking using the transfer matrix (green) of the two principle trajectories.

Figure 5

The fields and energy gain for the rf gun setup. The cavity field is scaled so that the cavity voltage is 1 MV, and the phase is set to the on-crest value for a 1 MeV electron.

Figure 6

Comparison of direct integration (blue) and tracking using the transfer matrix (green) of the two principle trajectories.