Terahertz-driven acceleration of subrelativistic electron beams using tapered rectangular dielectric-lined waveguides

We investigate the use of tapered rectangular dielectric-lined waveguides (DLWs) for the acceleration of low-energy, subrelativistic, electron bunches by the interaction with multicycle narrowband terahertz (THz) pulses. A key challenge exists in this subrelativistic regime; the electron velocity changes significantly as energy is gained. To keep electrons in the accelerating phase, the phase velocity must also be increased to match. We present simulations which demonstrate that the dielectric thickness can be kept constant and the width of the dielectric lining can be tapered along the direction of travel to vary the phase velocity, an approach only possible by the use of a rectangular waveguide geometry. The properties of tapered DLWs are discussed and following this, a design process is presented to demonstrate that the way this tapering can be optimized for different pulse and beam parameters. The minimum accelerating gradient for electron bunch capture is derived and compared to simulations. As examples of this design process, designs are considered based on considerations of the THz source, incoming electron beam, and manufacturing tolerances. A maximum THz pulse energy of $22.5\mathrm{\mu }\mathrm{J}$ in the DLW was considered, which represents what is readily achievable using mJ-level regenerative amplifier laser systems together with optical-to-terahertz conversion in lithium niobate crystals. This will be more than double the energy of a 100 keV electron beam, increasing it to 205 keV. We describe the optimization process and present a detailed exploration of the beam dynamics, discussing how the performance will further improve with compressed bunches.

Figure 1

Cutaway view of a width-tapered rectangular DLW with metal width $w$, dielectric width $w_d$, vacuum gap height $a$, dielectric thickness $t_d$, full height $h$, and length $L$. The direction of propagation is the $z$ direction with the axis defined as the center line of the waveguide.

Figure 2

Illustration of field trapping in DLWs. (a) The maximum longitudinal electric field (for arbitrary total mode energy) in DLWs with the same gap height and increasing dielectric thickness. (b) Characteristic impedance and minimum synchronous energy for 0.2 THz DLWs with increasing thickness of dielectric layer and constant $a$ and $w$.

Figure 3

(a) Widths required to synchronize the phase velocity of a 0.2 THz pulse and an electron of a given energy in a fused silica DLW with $a=0.48\mathrm{mm}$ and $t_d=0.38\mathrm{mm}$. (b) Group velocity and characteristic impedance on axis (for arbitrary total mode energy) in waveguide sections synchronized to electron energy.

Figure 4

Field profiles along vertical axis of the vacuum gap in example 0.2 THz and 0.4 THz DLWs. Both examples used a gap height of 0.48 mm and are normalized to set the 0.2 THz amplitude on axis to 1.

Figure 5

Modeled phase of the accelerating field at the position of a reference electron during the mismatched section in our two designs.

Figure 6

Widths of the dielectric lining and metal channel along the length of the structure. The gap height (0.48 mm) and dielectric thickness (0.38 mm) are constant.

Figure 7

Energy growth for the captured bunch in a 0.3 fC bunch from a commercially available electron gun [42] during propagation through the DLW. The solid line shows the mean energy of the captured bunch, and the dashed lines indicate the energy spread of the captured bunch.

Figure 8

Velocity of particles and waves along the structure length for (a) the $12\mathrm{\mu }\mathrm{J}$ design and (b) the $22.5\mathrm{\mu }\mathrm{J}$ design. The particle data show the full bunch at 5 ps snapshots with each dot representing a single electron.

Figure 9

Electric field phase experience by the bunch for a realistic bunch tracked from the gun using gpt and injected into the structure. (a) shows the phase of the electron bunch throughout interaction in the $12\mathrm{\mu }\mathrm{J}$ design along with the corresponding field. In (b), this is compared with the higher energy design, which requires less phase overshoot.

Figure 10

Energy distribution of the whole bunch at the waveguide exit, with a realistic 100 keV 0.5 fC bunch tracked using gpt (a) and an idealized input bunch with 10% of the longitudinal size and 50% of the vertical size (b).

Figure 11

Emittance growth for the captured bunch of a 0.3 fC bunch injected by a commercially available electron gun. (a) Normalized horizontal rms emittance, (b) normalized vertical rms emittance, (c) squared-mean vertical size, (d) squared-mean vertical momentum, and (e) correlation squared between vertical position and momentum.

Figure 12

Particle trajectories for a realistic 0.3 fC bunch from a commercially available electron gun propagating through the DLW. Trajectories for electrons which are lost due to being deflected into the dielectrics are highlighted in red, and electron trajectories for the particles in the captured bunch are highlighted in blue. The subplots show the (a) horizontal trajectories and (b) vertical trajectories.

Figure 13

Energy and $y$ and $z$ coordinates of particles immediately before the bunch leaves the DLW.

Figure 14

Charge deposition rate vs longitudinal position for a realistic 0.3 fC bunch from a commercially available electron gun propagating through the tapered DLW. By shortening the length $L$ of the DLW from 30 to 25 mm, some of the particle deposition (light red) was eliminated.

Figure 15

Variation in the total transmitted charge and the accelerated charge for a 0.5 fC input bunch compressed by varying amounts. The proportion of charge that is accelerated increases for more compressed input bunches, while the total transmitted charge shows some decrease.

Figure 16

Distribution of electron positions in $y$ in a compressed 185 fs bunch upon entering the DLW. Particles that form the captured bunch begin close to on axis and are shown in blue. Particles that enter the DLW $>25\mathrm{\mu }\mathrm{m}$ vertically off axis have a much higher chance to be deposited in the dielectrics downstream.

Figure 17

Minimum accelerating field required to overcome the velocity mismatch in structures with different minimum phase velocities for a selection of example electron beam energies.

Figure 18

A possible scheme for achieving fully relativistic energies by a multistage approach. Each stage would provide higher energy gain than the previous one, and the number of stages depends on the available THz pulse energy.