Plasma-based acceleration schemes have attracted sustained interest as a pathway toward compact particle accelerators, owing to the large electric fields supported by plasmas. Although recent studies have demonstrated the excitation of plasma wakefields using high-power microwave pulses in plasma-filled waveguides, the conditions required for efficient electron acceleration in such configurations remain insufficiently characterized. In this work, we investigate the acceleration of externally injected electrons by microwave-driven plasma wakefields in rectangular waveguides filled with low-density plasma. Three-dimensional particle-in-cell simulations are employed to analyze the dynamics of electron injection and energy gain under both reduced and fully self-consistent numerical models. The results show that electron acceleration is strongly dependent on the injection phase and initial velocity. Optimal acceleration is achieved when electrons are pre-accelerated to velocities close to the group velocity of the driving microwave pulse. For the parameters considered, energy gains of the order of $10^2 \mathrm{keV}$ are obtained over interaction lengths of the order of meters, while maintaining a quasi-monoenergetic energy distribution under suitable injection conditions. The influence of transverse dynamics and space-charge effects is also examined, revealing additional constraints on acceleration efficiency associated with the transverse electromagnetic field of the driving microwave pulse. These results provide a quantitative assessment of the acceleration stage in microwave-driven plasma wakefield schemes and support their evaluation as a viable platform for compact plasma-based accelerators.
Plasma-based acceleration schemes have attracted sustained interest due to their ability to support accelerating electric fields far exceeding those achievable in conventional radiofrequency technologies [1][2][3][4] . In these schemes, the collective plasma response generates longitudinal electric fields that trap and accelerate charged particles over short distances, enabling compact accelerator concepts 5,6 . While significant progress has been achieved in the generation of plasma wakefields driven by intense laser pulses or relativistic charged-particle beams, the practical performance of such schemes depends critically on a detailed understanding of particle injection, trapping conditions, and energy gain mechanisms [7][8][9][10] .
In recent years, the excitation of plasma wakefields using high-power microwave pulses propagating in plasma-filled waveguides has emerged as a technologically attractive alternative to laser-or beam-driven approaches [11][12][13] . Advances in microwave sources have enabled the generation of subnanosecond pulses with peak powers in the gigawatt range and frequencies of gigahertz, parameters that are well suited for driving plasma waves in low-density plasmas [14][15][16] . Compared with ultrashort laser systems, microwave-based schemes operate in a different parameter regime and may offer practical advantages in terms of technological accessibility and system complexity, albeit at acceleration gradients that are typically several orders of magnitude lower. However, despite growing experimental and theoretical efforts demonstrating the feasibility of microwave-driven wakefield generation, key questions remain regarding the efficiency of electron trapping and acceleration in such configurations.
In a previous work, fully electromagnetic three-dimensional particle-in-cell simulations were used to investigate the formation and properties of plasma wakefields excited by short (∼ 0.5 ns), moderately intense (∼ 0.3 GW) TE 10 -mode microwave pulses propagating in rectangular plasma-filled waveguides 13 . The wakefield response was characterized through systematic variations of key parameters, including pulse duration, frequency, power, waveguide geometry, and plasma density, revealing longitudinal electric field amplitudes on the order of kilovolts per centimeter. Building on those results, the present work focuses on the subsequent acceleration stage, examining how externally injected electrons interact with the sustained wakefield and identifying the conditions required for efficient trapping and energy gain.
The primary objective of this study is to analyze the dynamics of witness electrons injected into a microwave-driven plasma wakefield, with emphasis on identifying suitable initial conditions for capture, characterizing effective acceleration regions, and estimating the maximum attainable energy gain. To this end, the analysis is conducted in a set of complementary stages based on numerical simulations. First, a simplified numerical description is employed to simulate electron motion in a prescribed longitudinal wakefield, using wakefield parameters consistent with those reported in previous particlein-cell simulations 13 .This reduced framework provides physical insight into the trapping process and yields preliminary estimates of the expected energy gain. It also serves as a practical guideline for selecting injection parameters and interpreting kinetic effects. In the second stage, electron acceleration is investigated using a reduced particle-in-cell framework in which the wakefield structure is obtained from fully electromagnetic simulations of the microwave-plasma interaction, while the injected witness electrons are treated as test particles. In this approach, the space-charge contribution of the witness bunch is neglected, so that the acceleration dynamics are governed solely by the electromagnetic fields of the wake and the driving microwave pulse.
Finally, fully self-consistent three-dimensional particle-in-cell simulations are performed to investigate electron acceleration under coupled electromagnetic and plasma dynamics. In this regime, the evolution of fields, background plasma, and injected electrons is resolved self-consistently, enabling a quantitative analysis of energy gain, energy spread, and the spatial evolution of the accelerated bunch. By systematically combining reduced numerical descriptions with fully kinetic simulations, this work clarifies the role of injection conditions in microwave-driven plasma acceleration and supports the evaluation the potential of this scheme as a viable platform for compact plasma-based accelerators.
The system consists of a rectangular metallic waveguide with transverse dimensions a = 3.0 cm and b = 2.1 cm, filled with a cold plasma of initial electron density n 0 = 1.8 × 10 10 cm -3 . The waveguide is excited by a short, high-power microwave pulse propagating along the longitudinal direction and polarized in the f
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