Experimental study of transverse effects in planar dielectric wakefield accelerating structures with elliptical beams

The main obstacle to the practical implementation of the dielectric wakefield acceleration (DWA) concept is the development of the beam breakup instability due to transverse dipole wakefields generated when the beam propagates off axis in the accelerating structure. One of the methods to suppress this instability is to elliptically shape the beam and accelerate it in a planar structure. Here, we report a detailed experimental investigation of the transverse dynamics of elliptical beams in planar dielectric structure with parameters mimicking future DWA modules. Both dipole and quadrupole wakefields’ effects on beam stability and projected emittance were studied. This study has highlighted the importance of counteracting quadrupole wakefields in future DWA implementations.

Figure 1

Schematic of the experiment performed at CLARA BA1, with an inset showing the DWA structure and coordinate system used for defining structure gaps and beam offsets.

Figure 2

Top: Beam images on the S5 screen at various offsets in the structure with the half-gap of $a=2.0\mathrm{mm}$. The bunch length is 800 fs and the rms horizontal beam size ${\sigma }_{x0}=360\mu \mathrm{m}$. Bottom: vertical projections at $y_0=0$ and 1.54 mm.

Figure 3

Comparison of simulated longitudinal $E_z$ (top) and vertical $F_y$ (bottom) wakefields for an 85-pC Gaussian bunch with lengths ${\sigma }_t=800$ and 300 fs, and ${\sigma }_x={\sigma }_y=150\mu \mathrm{m}$. The longitudinal coordinate is normalized to the bunch ${\sigma }_t$ and the $F_y$ field is plotted at $y=2{\sigma }_y=300\mu \mathrm{m}$. The DWA structure half-gap is $a=1\mathrm{mm}$.

Figure 4

Beam divergence calculated as ${\sigma }^{\prime }=({\sigma }_{S5}-{\sigma }_{S4})/L$ where $L=2.05\mathrm{m}$ is the distance between screens in horizontal (a) and vertical (b) planes. Dashed lines are third order polynomial fits to aid legibility. Measurements are presented for structure half-gaps of $a=0.5$, 0.75, and 1.0 mm. The beam is set on axis of the structure at each gap and the bunch length is ${\sigma }_t=800\mathrm{fs}$. Error bars shown for $a=0.5\mathrm{mm}$ data are representative of errors for other half-gaps, which are omitted to aid legibility.

Figure 5

Top: horizontal phase spaces of the beam with ${\sigma }_{x0}=0.75\mathrm{mm}$ propagating in the free path (left) and through the structure set to $a=0.5\mathrm{mm}$ (right). Bottom: dependence of the horizontal projected emittance on beam size ${\sigma }_{x0}$.

Figure 6

Average longitudinal $E_z$ and transverse $F_y$ wakefield strengths as a function of the rms beam size at the position of the DLW. $E_z$ is measured with the structure half-gap of $a=1.0\mathrm{mm}$ and beam centered. $F_y$ is measured with $a=2.0\mathrm{mm}$ and $y_0=1.34\mathrm{mm}.\mathrm{rms}$ bunch lengths of ${\sigma }_t=800$ and 300 fs were used. The lines are corresponding simulation results.

Figure 7

(a) Average transverse $F_y$ wakefield strengths as a function of ${\sigma }_{x0}$. $F_y$ is measured with a structure half-gap of $a=2.0\mathrm{mm}$, and offsets $y_0=1.14$ and 1.54 mm. rms bunch length is set to 800 fs. Lines—corresponding simulation results. (b) Normalized simulated dependencies of $E_z$ and $F_y$ on ${\sigma }_{x0}$ from Figs. 6 and 7.

Figure 8

(a) Skew Gaussian longitudinal bunch profile used in simulations at 1 GeV and 10 nC. Five longitudinal slices of 0.4 ps width each that were studied individually are also shown. (b) Transverse wakefield forces along the bunch on the structure axis. Horizontal $F_x$ is calculated at coordinates $(x,y)=(2{\sigma }_x,0)$ and vertical $F_y$ at $(x,y)=(0,2{\sigma }_y)$, where ${\sigma }_x=500\mu \mathrm{m}$ and ${\sigma }_y=50\mu \mathrm{m}$.

Figure 9

Variation of horizontal rms beam sizes along the DWA structure. Initial beam size is ${\sigma }_{x0}=500\mu \mathrm{m}$ but 5% of particles with largest deviation from the axis are discounted. The beam is set on axis. Vertical wakefields $F_y$ are removed. (a, b) five slices as shown in Fig. 8. (c) projected size of the whole beam.

Figure 10

Horizontal beam profiles at $s=0$ (initial) and at $s=1.0$ and 2.5 m. The beam is set on axis and vertical wakefields $F_y$ removed.

Figure 11

Bunch charge as a function of propagation distance through the structure. Plots are shown for $F_x$ removed (dotted line) and included (solid line). The beam is on the structure axis.

Figure 12

Transverse-longitudinal distribution of particles after propagation distances of $s=1.5$ and 2.5 m from the beginning of the structure ($s=0$). The beam is on the structure axis. $F_x$ is included.

Figure 13

Bunch charge as a function of propagation distance through the structure with the beam offset vertically by $y_0=50\mu \mathrm{m}$. Plots are shown for $F_x$ removed (dotted line) and included (solid line).

Figure 14

Transverse-longitudinal distribution of particles after 1.5 and 2.5 m propagation distance through the structure. The beam is initially offset vertically by $y_0=50\mu \mathrm{m}$. $F_x$ is included.

Figure 15

Bunch charge in five longitudinal slices (shown in Fig. 8) as a function of propagation distance through the structure. The beam is initially offset vertically by $y_0=50\mu \mathrm{m}$. $F_x$ is included.