Simulation of incoherent ion effects in electron storage rings

Ion trapping occurs when a negatively charged beam ionizes residual gas inside an accelerator vacuum chamber, and the resulting ions become trapped in the beam potential. In addition to the well-understood coherent instability, trapped ions can cause incoherent effects, such as emittance growth and tune spread. Typically, simulation of ion effects is done using a weak-strong model, in which the ions are modeled using macroparticles, but the beam is assumed to be a fixed Gaussian distribution, with only centroid motion allowed. This type of model necessarily neglects intra-bunch effects. Recently, a residual gas ion modeling capability has been incorporated into the particle tracking code elegant. Both the beam and ions are modeled using macroparticles, so incoherent effects can be studied. The code models ion generation, movement of ions between bunches, and beam-ion interactions. It has also been parallelized and can be used in combination with other elegant elements. The code has been used to study ion instability in the present APS storage ring. Once several important effects are included (multiple ionization, transverse impedance, and charge variation between bunches), the simulations show good agreement with the measured data.

Figure 1

Run time vs number of processors for a typical APS simulation (1000 turns).

Figure 2

Total charge of each ion species in the baseline APS simulation.

Figure 3

Ion density at different interaction points in the baseline APS simulation.

Figure 4

Vertical instability amplitude for the baseline simulation.

Figure 5

Amplitude of lower vertical betatron sidebands in the baseline simulation, compared to a simulation with no ions.

Figure 6

Vertical ion distribution, after three turns, at IP1.

Figure 7

Ion density (top) and instability amplitude (bottom), comparing simulations with increasing bunch charge variation.

Figure 8

Ion density (top) and instability amplitude (bottom), comparing different effects: multiple ionization (red), transverse impedance (green), and 10% rms charge variation (blue). The result of including all three effects is shown in cyan.

Figure 9

Measured and simulated vertical beam spectrum for normal 324 bunch operation. The points shown are the lower vertical betatron sidebands.

Figure 10

Top: measured bunch pattern corresponding to Fig. 9. Bottom: FFT of this pattern.

Figure 11

Ion density for different pressure values. Note the log scale on the vertical axis.

Figure 12

Vertical instability amplitude (top) and rms beam size (bottom), for different pressure values.

Figure 13

Horizontal instability amplitude (top) and rms beam size (bottom), for different pressure values.

Figure 14

Effective emittance in the vertical (top) and horizontal (bottom) planes, for different pressure values.