Single-shot reconstruction of core 4D phase space of high-brightness electron beams using metal grids

This paper details the development of a single-shot diagnostic technique for the 4D average and core phase space densities of low-charge, high-brightness electron beams, based on the analysis of shadow point-projection images of metal grids. This technique is similar to the standard pepper pot method, although it allows much greater transmission of the beam and therefore is more suitable for low-charge electron beams. Transverse coupling terms are included in the analysis, allowing the complete 4D transverse beam matrix to be reconstructed. The 4D beam phase space information is extremely important for the characterization of nonround beams. An analysis of the resolution limits and experimental benchmarking of the technique with pepper-pot emittance measurements are presented.

Figure 1

Top: intensity plot of a sample image at the screen, generated from the output of a simulation (details in Sec. 3) of an electron beam masked with a TEM300 grid. Axis labels of the image are in pixels and the pixel size is $15\mu \mathrm{m}$. Middle: sheared image with horizontal and vertical lines showing detected minima of the projections onto the axis. These projections are also shown as red lines on the image. Bottom: screen intensity profile showing points where the fits are done.

Figure 2

A schematic of the beam propagating from the TEM grid to the screen, showing how it spreads by ${\sigma }_{x^{\prime }}$.

Figure 3

Relative error of the rms divergence ${\sigma }_{x_{ij}^{\prime }}$ fit from the simulations of a fixed phase space distribution, as a function of the number of particles in the beam, intercepted by one bar of a TEM grid ($85\mu \mathrm{m}$ pitch, $31\mu \mathrm{m}$ bar width) and one hole of a pepper pot mask ($15\mu \mathrm{m}$ hole diameter).

Figure 4

Reconstruction of the 4D trace space density of the beam simulation in Fig. 1, shown as 2D projections of subspaces $(x,x^{\prime })$, $(y,y^{\prime })$, $(x,y)$, $(x,y^{\prime })$, $(x^{\prime },y)$, and $(x^{\prime },y^{\prime })$.

Figure 5

Solid blue line represents the fractional emittance of the particle distribution comprised in different fractions of the beam, obtained from the reconstruction of the 4D trace space density of the simulation in Fig. 1. The solid green line shows the tangent line to the reconstructed curve at the core to linearly extrapolate the core emittance. The dashed pink line is the analytical curve of a 4D Gaussian distribution with the same rms emittance.

Figure 6

Space charge effects on the reconstruction of the horizontal emittance of a geometric phase space distribution in different energy and charge scenarios.

Figure 7

Schematic of the grid-lens configuration. Distances $p_0$ and $q_0$ satisfy the imaging condition $1/p_0+1/q_0=1/f$ for a lens of focal length $f$.

Figure 8

A schematic of the Pegasus beamline.

Figure 9

Photographs of 300-mesh copper TEM grid 1GC300 (left) and pepper pot (right) used for the experiments, taken with a microscope.

Figure 10

Sample intensity plot of an image taken in experiments at Pegasus using a TEM grid (top) and a pepper pot (bottom). The images have been cropped to remove the edge of the YAG screen, which was emitting radiation.

Figure 11

Reconstructed 4D trace space density of a bunch measured with a TEM300 grid, shown as 2D projections of subspaces $(x,x^{\prime })$, $(y,y^{\prime })$, $(x,y)$, $(x,y^{\prime })$, $(x^{\prime },y)$ and $(x^{\prime },y^{\prime })$.

Figure 12

Reconstruction of the cumulative charge distribution with respect to the fractional emittance (blue solid line) from the measurement of Pegasus electron beam with a TEM300. The solid green line shows the tangent line to the reconstructed curve at the core to linearly extrapolate the core emittance. The dashed pink line is the analytical curve of a 4D Gaussian distribution.