Plasma Discharge Undulator: a novel concept for plasma-based radiation sources

Abstract

Plasma discharge devices have recently emerged as compact and versatile tools for particle beam manipulation. Building upon the Active Plasma Lens (APL) and its curved extension, the Active Plasma Bending (ABP), this work introduces the concept of the Plasma Discharge Undulator (PDU). In a PDU, a high-current discharge within a capillary generates an azimuthal magnetic field providing strong linear focusing ($O(1)$ (kT/m)), while a controlled and periodical spatial modulation of the discharge axis acts as a geometric driving term. The resulting beam dynamics can be modeled as a forced harmonic oscillator, yielding a well-defined oscillation at wavelength $λ_{\mathrm{PDU}}$, distinct from the natural betatron wavelength $λ_β$ related to APL focusing. Proper injection conditions result in the suppression of collective betatron oscillations, significantly reducing the intrinsic undulator strength spread typical of conventional plasma undulators, while allowing for matched beam transport thanks to APL strong focusing. Analytical models for particle trajectories and radiation emission are developed, and the one-dimensional requirements for free-electron laser (FEL) emission are evaluated, providing scaling relations and feasibility criteria for FEL operation in the proposed scheme. Theoretical estimates and multi-particle simulations indicate that the PDU can operate in the short-period regime ($λ_{\mathrm{PDU}} = $ mm-cm) with tunable undulator strength $K_{\mathrm{PDU}}$, supporting narrow-band radiation emission. The PDU thus provides a pathway toward miniaturized, tunable, fully-plasma-based light sources with enhanced control over focusing and spectral properties.

Figures (6)

• Figure 1: Conceptual sketch of the Plasma Discharge Undulator (PDU). Top: azimuthal magnetic field distribution induced by the discharge current in a capillary. Bottom: example of possible geometrical implementation of the periodic discharge modulation.
• Figure 2: (a) Matched beam propagation in PDU field for proper centroid injection offset $x_{inj}=x_0$, which provide collective oscillation at $\lambda=\lambda_\mathrm{PDU}$ only (solid black). Single particle trajectories will be anyway subject to mixed betatron/undulator motion (solid red as an example) (b) Geometric constraints on capillary offset $\Delta x$ normalized over capillary diameter $d_c$ as a function of $\lambda_{\mathrm{PDU}}/\lambda_\beta$, showing that for $\lambda_{\mathrm{PDU}}<\lambda_{\mathrm{\beta}}$ the system necessarily needs clearance (i.e. a line of sight through the device).
• Figure 3: Comparison between the two asymptotic regimes of the single particle undulator strength $K$ as a function of the transverse injection position in the plasma channel. For small amplitudes, $K$ converges to the forced value $K_{\mathrm{PDU}}$; for increasing amplitudes, it approaches the betatronic limit $K_{\beta,inj} = r_{inj}\gamma k_\beta$, following a hyperbolic trend.
• Figure 4: On-axis radiation spectra for representative PDU parameters. (a) Single-particle spectrum (solid blue), showing excellent agreement with the theoretical incoherent undulator emission (dashed orange) at the fundamental wavelength and its harmonics. (b) Spectrum emitted by a matched Gaussian beam (solid blue), exhibiting a slight broadening and deviation from the ideal undulator case (dashed orange) due to the superposition of betatron motion on the forced oscillatory motion, which leads to the appearance of both even and odd harmonics on-axis, associated with mixed-frequency radiation components.
• Figure 5: (a) Photon spectrum integrated within a 1% bandwidth as a function of the radiation spot radius (color scale), for 4 kA discharge current, $\sigma_r = 4~\upmu\mathrm{m}$, $K_{\mathrm{PDU}} = 0.45$, and undulator length $L_{\mathrm{PDU}} = 6~\mathrm{cm}$. The inset plot shows the cumulative photon number. (b) Frequency-integrated radiation spot at 10 m from the source, showing the expected divergence of $\pm 1/\gamma$ in the $K_{\mathrm{PDU}} < 1$ regime.