Experimental study of large-amplitude perturbations in space-charge dominated beams

Detailed experimental measurements are presented concerning the propagation of space-charge waves of varying amplitudes in an intense, charged-particle beam. A short perturbation to the density profile is applied at the electron gun, and both current and mean energy profiles are measured at two locations downstream. The measurements are compared to predictions of a linear 1D cold-fluid model, and self-consistent particle-in-cell simulations. For sufficiently small perturbation amplitudes, the experiment, simulation, and 1D theory agree. For larger amplitudes, the simulation begins to diverge from theoretical predictions due to nonlinear effects. Experimental observations for large-amplitude perturbations differ markedly from either theory or simulation. With the aid of simulations with mismatched and misaligned beams, this departure of experiments from predictions is demonstrated to be caused by the loss of beam current due to scraping aided by the larger radius of the perturbation.

Figure 1

A photo of the upgraded LSE system.

Figure 2

The pulsed voltage signal between the grid and cathode when the perturbation cable is connected to the PFL.

Figure 3

Current profiles of the 4.9 mm beam measured by three Bergoz current monitors when the bias voltage was set to (a) 30 V and (b) 52 V, respectively. In (a), current profiles measured by B2 and B3 are shifted up by 10 and 20 mA, respectively. In (b), current profiles measured by B2 and B3 are shifted up by 20 and 40 mA, respectively.

Figure 4

Mean energy profiles measured at LC1 (black solid lines) and LC2 (red dashed lines) for 4.9 mm beams with different bias voltages. (a) ${\delta }_1=0.0026$, ${\delta }_2=0.0075$; (b) ${\delta }_1=0.01$, ${\delta }_2=0.027$; where ${\delta }_1=d{E}_1/E_0$, ${\delta }_2=d{E}_2/E_0$, and $d{E}_1$ and $d{E}_2$ represent peak-to-peak values of the energy perturbations in LC1 and LC2, respectively.

Figure 5

Current profiles at the location of B3 calculated from 1D theory along with the experimental results (black solid lines). In the 1D theory, the amplitude of initial energy perturbation is assumed to be 0, 15, and 30 eV, respectively. The beam currents are represented by positive values.

Figure 6

Energy profiles at LC2 calculated from 1D theory along with the experimental results (black solid lines). In the 1D theory, the amplitude of initial energy perturbation is assumed to be 0, 15, and 30 eV, respectively.

Figure 7

Comparison of mean energy profiles of the 23 mA parabolic beam between the experimental results, WARP simulations in the beam frame and lab frame: (a) at LC1; (b) at LC2.

Figure 8

Comparison of results from the experiment (blue solid lines), WARP (black broken lines), and 1D theory (red dotted lines) for the 25 mA beam: (a) mean energy profiles at LC2; (b) current profiles at B3.

Figure 9

Comparison of results from the experiment (blue solid lines), WARP (black broken lines), and 1D theory (red dotted lines) for the 40 mA beam: (a) mean energy profiles at LC2; (b) current profiles at B3. Current profiles have been flipped to show positive current values for the convenience of indicating positive perturbations.

Figure 10

Illustration of applying two virtual conducting tubes in WARP code and the particle distribution in the $X\mathrm{\text{−}}Z$ plane at $t=57.2\mathrm{ns}$. The units of both axes are meter. The perturbation is located from 1.22 to 1.7 m.

Figure 11

Comparison of results from the experiment (blue solid lines), WARP simulations with different radii of the virtual tube: 19 mm (black dashed lines), 9 mm (red dotted lines), and 8 mm (green dash-dotted lines): (a) mean energy profiles at LC2; (b) current profiles at B3. Current profiles have been flipped to show positive current values for the convenience of indicating positive perturbations.

Figure 12

Comparison of results from the experiment (blue solid lines), WARP simulations with 19 mm virtual tube (black dashed lines), WARP simulations with the 9 mm virtual tube and the initial beam radius of 4 mm (red dash-dotted lines), and WARP 3D simulations (green dotted lines): (a) mean energy profiles at LC2; (b) current profiles at B3.