Probing Flying-Focus Wakefields

TL;DR

Probing Flying-Focus Wakefields investigates whether flying-focus wakefields generated with an axiparabola can achieve dephasingless acceleration by tuning the wake velocity along $z$, maintaining phase with trapped electrons under the resonance condition $c\tau \approx \lambda_p$. The study combines direct imaging via femtosecond relativistic electron microscopy (FREM), with Axiprop optical propagation simulations and PIC simulations (FBPIC) to map wakefield structure as a function of plasma density $n_0$ and focusing depth. It finds a stable, V-shaped wakefield structure that shifts with density, with the on-axis field $E_z$ becoming more nonlinear at higher $n_0$ (e.g., $E_z/E_0$ rising from about 0.16 to 0.52 as $n_0$ increases), and shows ionization dynamics—especially for helium—significantly alter wake evolution, while small nitrogen additions have limited effect on structure but can impact electron-injection energy. Focusing depth relative to the gas plateau also qualitatively changes wakefield topology, highlighting the need to optimize interaction geometry for reliable dephasingless LWFA performance.

Abstract

Flying-focus wakefields, which can propagate with a tunable velocity along the optical axis, are promising solutions to electron dephasing in laser-wakefield accelerators. This is accomplished by a combination of spatio-temporal couplings and focusing with an axiparabola, a specialized optical element which produces a quasi-Bessel beam. If implemented, dephasingless acceleration would allow for a hitherto unachievable mixture of high acceleration gradients and long acceleration lengths. Here, we conduct an in-depth study of the structure and behavior of such a flying-focus wakefield, through a combination of direct imaging and simulations. We show the stability of the wakefield structures, explore how the wakefield evolves with changes of density, study the effects of ionization on the wakefield structure with a variety of gases, and analyze the importance of the focusing position. These insights shed light onto this novel wakefield regime and bring understanding that is important to the realization of dephasingless acceleration.

Figures (5)

• Figure 1: (a) Schematic of the experimental setup. The axiparabola focuses one beam onto jet 1, a slit nozzle, generating a flying-focus wakefield. A second beam, temporally synchronized with the first, is focused by an off-axis parabola (OAP, not shown) onto jet 2, a converging-diverging nozzle, generating a second wakefield. This wakefield accelerates electrons, referred to on the figure as the probe bunch. This bunch is allowed to propagate further, spatially expanding. It then impinges upon the flying-focus wakefield. The fields inside of the wakefield give momentum kicks to the probe electrons. After further free-space propagation, these momentum kicks become density perturbations which can be seen on a Ce:YAG scintillating screen. (b) Three 2D focal spot measurements at 1 mm intervals along the focal line of the axiparabola. Color bar shows relative intensity. Taken in vacuum.
• Figure 2: (a--d) Experimental FREM images. (e) Simulated FREM image with parameters reported in section \ref{['sec:methods:PIC']} at the plasma density of $n_0 = 5e17cm^{-3}$. (f) Simulated wakefield corresponding to the FREM image. Colorbar in (a--e) shows relative intensity of signal from scintillating screen, where 0 is the intensity of the unperturbed probe beam. Blue colorbar in (f) shows relative electron density distribution $n_{\textup{e}}/n_0$ and red color shows the intensity of the axiparabola laser field.
• Figure 3: (a--d) Relative electron density distribution $n_{\textup{e}}/n_0$ and intensity of the axiparabola laser field for flying focus wakefield at different densities. The dashed lines show the FWHM duration of the laser beam as a function of the transverse coordinate. (e--h) Corresponding simulated FREM images at the different densities. Colorbar shows relative intensity of signal from scintillating screen, where 0 is the intensity of the unperturbed probe beam. (i--l) Corresponding spatial distributions of the normalized longitudinal electric field, $E_z/E_0$. Colorbar shows strength of the electric field.
• Figure 4: Comparison of relative electron density distribution $n_{\textup{e}}/n_0$ and intensity of the axiparabola laser field for flying focus wakefield using (a) preionized plasma, (b) pure hydrogen, (c) pure helium, and (d) helium-nitrogen mixture. (e--h) Corresponding simulated FREM images. Colorbar shows relative intensity of signal from scintillating screen, where 0 is the intensity of the unperturbed probe beam.
• Figure 5: (a--d) Comparison of relative electron density distribution $n_{\textup{e}}/n_0$ and intensity of the axiparabola laser field for flying focus wakefield at different focusing locations relative to beginning of the plateau in the gas density distribution. The simulation iterations are adjusted relative to the change in $\Delta f_0$ and correspond to the position of 2 mm after the beginning of the focal line. (e--h) Corresponding simulated FREM images. Colorbar shows relative intensity of signal from scintillating screen, where 0 is the intensity of the unperturbed probe beam.