Time-dependent phase-space characterization of intense charged particle beams

Knowledge of the three-dimensional structure of a charged particle beam bunch is essential for understanding its evolution and for initializing computer simulations, especially when space charge is involved. This paper presents a novel experimental method for time-sliced mapping of the transverse phase space of a space-charge dominated beam based on tomographic principles. The combination of a high precision tomographic diagnostic with fast imaging screens and a gated camera are used to produce phase-space maps of two beams: one with a parabolic current profile and another with a short perturbation atop a rectangular pulse. The correlations between longitudinal and transverse phase spaces are apparent and their impact on the dynamics is discussed.

Figure 1

Experimental configuration of the LSE: (a) Schematic layout; (b) actual configuration.

Figure 2

Beam signal at the Bergoz showing the rectangular beam with a negative perturbation. The red/black traces show the beam current with perturbation on/off. The perturbation aptitude is roughly 25% of that of the main beam. The camera gates used were 10 ns (solid line) and 100 ns (dotted line).

Figure 3

Beam phase-space distribution in $x\mathrm{\text{−}}{x}^{\prime }$ within a 10 ns gate centered around the perturbation, recovered by tomography and backprojected to the gun aperture ($z=0\mathrm{cm}$). (a) Without, and (b) with the perturbation. The subtracted slope $\varphi$ is shown in Table .

Figure 4

Beam configuration space (top) and measured $x\mathrm{\text{−}}{x}^{\prime }$ phase space by tomography (bottom) reconstructed at LC1: (a) Without, and (b) with the perturbation. The subtracted slope $\varphi$ is shown in Table .

Figure 5

Beam configuration space (top) and measured $x\mathrm{\text{−}}{x}^{\prime }$ phase space by tomography (bottom) reconstructed at the screen location: (a) Without, and (b) with the perturbation. The subtracted phase-space slopes, $\varphi$, are $7.4\mathrm{mrad}/\mathrm{mm}$ in both cases. Images are obtained within a 100 ns gate encompassing the entire beam.

Figure 6

Signal collected at the Bergoz coil showing the longitudinal current profile of the parabolic beam, and indicating the approximate locations of the camera gates.

Figure 7

Beam in configuration space (top) and in $x\mathrm{\text{−}}{x}^{\prime }$ phase space (bottom) for slices a, b, c, d, e, and f, reconstructed at LC1. Phase spaces are generated using the initial conditions shown in Fig. 8.

Figure 8

Beam parameters measured in the experiment as a function of time along the pulse, at the screen location: (a) Beam size; (b) emittance; (c) slope of the phase space [from Eq. (10)]. The solid line corresponds to measurements at LC1 ($z=43.0\mathrm{cm}$) and the dashed line at the aperture ($z=0\mathrm{cm}$).