Synchronous acceleration with tapered dielectric-lined waveguides

We present a general concept to accelerate nonrelativistic charged particles. Our concept employs an adiabatically-tapered dielectric-lined waveguide which supports accelerating phase velocities for synchronous acceleration. We propose an ansatz for the transient field equations, show it satisfies Maxwell’s equations under an adiabatic approximation and find excellent agreement with a finite-difference time-domain computer simulation. The fields were implemented into the particle-tracking program astra and we present beam dynamics results for an accelerating field with a 1-mm-wavelength and peak electric field of $100\mathrm{MV}/\mathrm{m}$. Numerical simulations indicate that a $\sim 200$-keV electron beam can be accelerated to an energy of $\sim 10\mathrm{MeV}$ over $\sim 10\mathrm{cm}$ with parameters of interest to a wide range of applications including, e.g., future advanced accelerators, and ultra-fast electron diffraction.

Figure 1

Diagram of the accelerator concept (top) and corresponding evolution of the bunch’s transverse emittance (${ϵ}_r$), rms transverse beam size (${\sigma }_r$), longitudinal bunch length (${\sigma }_z$) (all left axis) and the kinetic energy (right axis) along the accelerator beamline (bottom). The example corresponds to an operating point $(\varphi ,E_0)=(79.3\mathrm{deg},106.875\mathrm{MV}/\mathrm{m})$; see text for details.

Figure 2

(a) Geometry of the dielectric-layer tapering (green shaded area, right axis) over the entrance of the structure; the initial dielectric thickness is $143\mu \mathrm{m}$ ($v_p=0.7c$) and asymptotically approaches $91\mu \mathrm{m}$ ($v_p=c$). In addition we show the comparison between our analytic field ansatz with FDTD code cst-mws over the first 20 mm. (b) Final energy (solid traces, left column) and end phase (dashed lines, right column) as a function of injection phase for various accelerating gradients and initial kinetic energies. The black diagonal dashed line shows ${\varphi }_e={\varphi }_i$, intersections with the phase portraits indicate zero phase-slippage. (c) The compression ratio between the injection phase and end phase, $\mathrm{\Delta }{\varphi }_i/\mathrm{\Delta }{\varphi }_e$ in log-scale as a function of injection energy and accelerating gradient for an input bunch length spanning 60 deg ($\mathrm{\Delta }{\varphi }_i=60\mathrm{deg}$.)

Figure 3

Charge fractional transmission through the structure as a function $B_1$ and $z_s$ for injection parameters $({\mathcal{E}}_i,E_z)=(205\mathrm{keV},105.8\mathrm{MV}/\mathrm{m})$ corresponding to a maximum bunch compression point from Fig. 2. A black dashed line encompasses 100% transmission.

Figure 4

Final bunch energy, inverse bunch length, energy spread, and normalized transverse emittance for the matched case, $(B_1,z_s)=(0.179\mathrm{T},10.5\mathrm{cm})$. In each case we overlay the final bunch charge as white contour levels for 0.3, 0.6, and 0.9 charge transmission. While all final energies are approximately equal ($\sim 11\mathrm{MeV}$), the structure allows for the production of widely-tunable electron beams.

Figure 5

The final beam brightness $B_{6D}=\frac{Q}{{\epsilon }_x{\epsilon }_y{\epsilon }_z}$, is illustrated over ($\varphi$, $E_0$). The maxima correspond very closely with minimum bunch lengths but differentiations arise from charge losses and, e.g., beam dilution.

Figure 6

The longitudinal phase space (LPS) and corresponding current profile is illustrated for the operational point yielding the largest beam brightness, $B_{6D}=1.3\times {10}^{22}$, for $(\varphi ,E_0)=(-41.2\mathrm{deg},123.75\mathrm{MV}/\mathrm{m})$. The maximum peak current of the bunch is $\sim 35\mathrm{A}$.