Description
Plasma streaming instabilities driven by ultrarelativistic charged particle beams in dense ambient plasmas play a central role in astrophysical and laboratory settings [1]. However, their numerical modeling is hampered by the large disparity in dynamical scales between the beam and plasma particles.
Here, we leverage the quasistatic approximation (QSA)–widely used in the context of plasma accelerators [2]–to develop a unified model of unstable modes in the realistic case where the beam continuously encounters fresh plasma at its leading edge. Unlike previous works [3,4], we do not adopt the slowly varying envelope approximation (SVEA). This allows us to capture the unstable modes developing throughout the beam region, and thus to clarify the interplay of the current filamentation (CFI) and oblique-two-stream (OTSI) instabilities, under conditions where standard theory predicts dominance of the OTSI [1]. By contrast, we find that spatiotemporal CFI modes prevail near the front–precisely where the SVEA breaks down–and are superseded by the spatiotemporal OTSI further away.
We benchmark our theory against high-resolution particle-in-cell (PIC) simulations and QSA-based PIC (QS-PIC) simulations performed using our newly developed QuaSSis code [5]. We demonstrate that the dramatic computational speedup offered by the QS-PIC method makes it possible to probe extreme beam-plasma interactions, such as those expected in the context of blazar jets.
Finally, we extend our theory to collisional systems. We show analytically that the collisionality of the background plasma entails a more complex instability dynamics, involving a succession of spatiotemporal and temporal variants of the CFI and OTSI, which is well reproduced by low-noise collisional QS-PIC simulations.
References
[1] A. Bret et al., Phys. Plasmas 17, 120501 (2010).
[2] P. Sprangle et al., Phys. Rev. A 41, 4463 (1990).
[3] V. B. Pathak et al., New J. Phys. 17, 043049 (2015).
[4] P. San Miguel Claveria et al., Phys. Rev. Res. 4, 023085 (2022).
[5] Q. Labro et al., arXiv:2506.18567v1 (2025).