Experimental and numerical study of phase mixing of an intense beam

We study, experimentally and numerically, the relaxation of an initially nonuniform intense beam in an alternating-gradient transport line. A nonlinear distribution consisting of five interacting beamlets is created and tracked for longer than seven plasma periods with the help of tomographic phase-space mapping. Emittance growth is initially rapid, but slows down as the nonuniform distribution homogenizes in a few plasma periods. Both growth rates are found to depend on the beam current.

Figure 1

Schematic layout of the UMER five-beamlet mask. Parameters $j$ and $b$ are the beamlet and pipe radius, respectively. For our experiment, $2j=1.75\mathrm{mm}$, $2\delta =5.22\mathrm{mm}$, and $2b=50\mathrm{mm}$. Distances are to scale.

Figure 2

Merger of the five beamlets at a distance $\approx 0.6{\lambda }_p$ from the source. Configuration space (left) and $x{x}^{\prime }$ phase space (right) from (a) experiment and (b) WARP simulation. The measured emittance in terms of the initial $4\times \mathrm{rms}$ emittance,${\epsilon }_i$, is $1.05{\epsilon }_i$.

Figure 3

Beam evolution at different locations inside the UMER ring in configuration space (left) and $x{x}^{\prime }$ phase space (right). The measured emittances in terms of the initial $4\times \mathrm{rms}$ emittance, ${\epsilon }_i$, are (a) $1.09{\epsilon }_i$, (b) $1.08{\epsilon }_i$, (c) $1.11{\epsilon }_i$, and (d) $1.10{\epsilon }_i$. Those values are also shown with red squares in Fig. 4.

Figure 4

Evolution of phase mixing from simulation: (a) emittance growth rates for beam parameters as in the experiment ($\chi =0.7$). The red squares are experimental data. (b) Dependence of growth rates with the beam intensity $\chi$ in logarithmic scale. The mathematical expressions are obtained by fitting the data (red lines).