Electron Beam Driven Generation of Frequency-Tunable Isolated Relativistic Subcycle Pulses

We propose a novel scheme for frequency-tunable subcycle electromagnetic pulse generation. To this end a pump electron beam is injected into an electromagnetic seed pulse as the latter is reflected by a mirror. The electron beam is shown to be able to amplify the field of the seed pulse while upshifting its central frequency and reducing its number of cycles. We demonstrate the amplification by means of 1D and 2D particle-in-cell simulations. In order to explain and optimize the process, a model based on fluid theory is proposed. We estimate that using currently available electron beams and terahertz pulse sources, our scheme is able to produce millijoule-strong midinfrared subcycle pulses.

Figure 1

Schematic representation of the electron beam driven amplification scheme. (a) The counterpropagating seed electromagnetic pulse and pump electron beam are moving towards a mirror (thin foil). (b) The electromagnetic pulse is reflected by the mirror and interacts with the electron beam as it exits through the mirror, leading to the generation and amplification of an intense subcycle pulse.

Figure 2

(a) Electric field snapshot after the interaction of a strongly focused low-frequency pulse with a monoenergetic electron beam passing the standing mirror at $x=0$. Corresponding on-axis signal (b) and spectrum (c) demonstrating the generation of an intense higher-frequency subcycle pulse with a cold monoenergetic electron beam (solid red lines), a beam with 150% energy spread having the same total energy (dash-dotted blue lines), and without the electron beam (dashed gray lines). (d) Conversion efficiency vs seed field strength. (e) Amplified peak electric field dependence on delay time $t_d$. The parameters are $t_e=0.016T_0$, $y_e=0.3{\lambda }_0$, $n_e^{\max }=28.3n_c$, ${\gamma }_e=20$, $t_0=0.21T_0$, and $E_0^{\mathrm{in}}=E_c$ [except in (d)]. The simulation was performed with 1600 points per electromagnetic pulse carrier wavelength along $x$, 100 points along $y$, 1608 points per electromagnetic pulse carrier oscillation, and 100 macroparticles per cell. We consider an aluminium foil of thickness $1.4c/{\omega }_0$ acting as a mirror. Since such a foil does not stop mega-electron-volt electrons (Ref. [21], p. 376) and ensures the reflection of the low-frequency seed pulse, we simply model it as a dense electron plasma.

Figure 3

Space-time diagrams visualizing the electron beam (blue line) moving with speed $v_b$ and electromagnetic pulse (red lines) without (a) or with (b) the standing mirror at $x=x_0$ [black line in (b)]: Without the mirror the whole electromagnetic pulse and with the mirror only part of the electromagnetic pulse interacts with the electron beam allowing for subcycle pulse generation.

Figure 4

(a) Visualization of the amplification mechanism. Electric field approximated by the unperturbed reflected seed pulse field (dashed line), corresponding vector potential (solid line), electron density (dotted line), and time-dependent energy density gain $U_{\mathrm{gain}}$ (dash-dotted line). (b) Electric field after the interaction of the incoming plane wave single-cycle pulse (dashed line) with the electron beam according to the fluid model (dotted line) and PIC (solid line). (c) Spectra according to PIC simulation. The parameters are $t_e=0.016T_0$, $t_d=0$, $n_e^{\max }=28.3n_c$, ${\gamma }_e=20$, $t_0=0.21T_0$, $E_0^{\mathrm{in}}=0.001E_c$. The distance from the mirror to the detector is $6.37c/{\omega }_0$. (d) Peak electric field amplitude amplification for different incoming seed pulse amplitudes according to PIC simulations. The remaining parameters are the same as above.

Figure 5

Electric field time traces before (dashed lines) and after (solid lines) the interaction using a few-cycle seed pulse and an underdense electron beam without (a) or with (b) the mirror. The field after the interaction without the mirror [solid line in (a)] has been magnified by a factor of 10 for a better comparison. The parameters are $t_e=0.016T_0$, $n_e^{\max }=5.66n_c$, ${\gamma }_e=10$, $t_0=0.85T_0$, $E_0^{\mathrm{in}}=0.1E_c$. The simulations were performed with 1600 points per electromagnetic pulse carrier wavelength and with 1000 particles per cell. The mirror has been modeled as a dense electron plasma with thickness $0.22{\lambda }_0$.