Particle-in-cell simulation of x-ray wakefield acceleration and betatron radiation in nanotubes

Though wakefield acceleration in crystal channels has been previously proposed, x-ray wakefield acceleration has only recently become a realistic possibility since the invention of the single-cycled optical laser compression technique. We investigate the acceleration due to a wakefield induced by a coherent, ultrashort x-ray pulse guided by a nanoscale channel inside a solid material. By two-dimensional particle-in-cell computer simulations, we show that an acceleration gradient of $\mathrm{TeV}/\mathrm{cm}$ is attainable. This is about 3 orders of magnitude stronger than that of the conventional plasma-based wakefield accelerations, which implies the possibility of an extremely compact scheme to attain ultrahigh energies. In addition to particle acceleration, this scheme can also induce the emission of high energy photons at $\sim O(10–100)\mathrm{MeV}$. Our simulations confirm such high energy photon emissions, which is in contrast with that induced by the optical laser driven wakefield scheme. In addition to this, the significantly improved emittance of the energetic electrons has been discussed.

Figure 1

SEM image of the top surface of a porous alumina sample [30].

Figure 2

The base case wakefield excitation with x-ray laser in a tube, in comparison with a wakefield in a uniform system. Distributions of (a) and (b) the laser field $E_z(\mathrm{V}/\mathrm{m})$, (c) and (d) electron density $n_e({\mathrm{m}}^{-3})$, (e) and (f) longitudinal wakefield $E_x(\mathrm{V}/\mathrm{m})$ including the $E_x$ lineout at $y=0$ axis (the position of dot line), and (g) and (h) transverse wakefield $E_y(\mathrm{V}/\mathrm{m})$ including the $E_y$ lineout at $x=8.24\times {10}^{-7}\mathrm{m}$ axis (the position of dot line) in terms of (a), (c), (e), and (g) tube and (b), (d), (f), and (h) uniform density cases driven by the x-ray pulse.

Figure 3

Evolution of the maximum longitudinal wakefield $E_x(\mathrm{V}/\mathrm{m})$ and the laser field $E_z(\mathrm{V}/\mathrm{m})$ as the function of propagation distance $x(\mathrm{m})$ for both nanotube (red dotted line) and uniform plasma (black dotted line) cases with the same conditions as Fig. 2.

Figure 4

Comparison and a certain scalability between the x-ray regime and the optical one. Distributions of (a) and (b) the longitudinal wakefield $E_x(\mathrm{V}/\mathrm{m})$ and (c) and (d) electron longitudinal momentum $\gamma v_x$ induced by (a) and (c) the x-ray laser pulse and (b) and (d) 1 eV optical laser pulse in a tube when $a_0=10$.

Figure 5

(a) The accelerated electron beam quality in the x-ray wakefield in a tube. The space distribution ($x$, $y$) and (b) the transverse phase space ($y$, $p_y/p_x$) of the top 30% highest energy electrons in the case of x-ray laser. The parameters are the same as in Fig. 4.

Figure 6

The energy spectrum and spatial distribution of photon emitted from the wakefield driven by x-ray laser and optical one. (a) and (b) Photon energy distributions and (c) and (d) photon energy spectrum in the (a) and (c) x-ray driven case and (b) and (d) 1 eV optical laser driven case in a tube. The parameters are the same as in Fig. 5.

Figure 7

Wakefield scalings in the x-ray regime with (a) tube radius, (b) tube wall density when the tube radius is fixed ${\sigma }_{\mathrm{tube}}/{\sigma }_L=1$, and (c) laser intensity when the tube radius is fixed ${\sigma }_{\mathrm{tube}}/{\sigma }_L=0.5$.