Plasma discharge undulator: Concept, theory, and numerical study

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, 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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mo>[</a:mo> <a:mi>O</a:mi> <a:mo>(</a:mo> <a:mtext>kT/m</a:mtext> <a:mo>)</a:mo> <a:mo>]</a:mo> </a:mrow> </a:math> , 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 <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:msub> <b:mi>λ</b:mi> <b:mi>PDU</b:mi> </b:msub> </b:math> , distinct from the natural betatron wavelength <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:msub> <c:mi>λ</c:mi> <c:mi>β</c:mi> </c:msub> </c:math> 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 strong APL 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 are validated through multiparticle simulations of beam dynamics and radiation emission, confirming that the PDU can operate in the short-period regime ( <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:msub> <d:mi>λ</d:mi> <d:mi>PDU</d:mi> </d:msub> </d:math> of millimeters to centimeters) with tunable undulator strength <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:msub> <e:mi>K</e:mi> <e:mi>PDU</e:mi> </e:msub> </e:math> , supporting narrow-band radiation emission. Numerical studies further demonstrate that the PDU is capable of sustaining seeded longitudinal microbunching analogous to that occurring in conventional magnetic undulators. The PDU thus provides a pathway toward miniaturized, tunable, fully plasma based light sources with enhanced control over focusing and spectral properties.