Weibel Instability in Collisionless Plasmas Across Astrophysical and Laboratory Shocks
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2026
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| author | Shrivastav, Vivek Chettri, Mani K Singh, Hemam D Singh, Britan Mukherjee, Rupak |
| author_facet | Shrivastav, Vivek Chettri, Mani K Singh, Hemam D Singh, Britan Mukherjee, Rupak |
| contents | We present a cold-fluid analysis of the purely transverse Weibel (current-filamentation) instability across four regimes: non-relativistic (NR) single-species, NR multi-species, relativistic single-species, and relativistic multi-species (electron--positron and electron--proton). Beginning from linearized fluid equations, we derive the dispersion relations in each regime and extract scaling laws for the maximum growth rate $γ_{\rm max}$ and characteristic unstable wavenumber $k_{\rm max} = ω_{pi}/c$. Relativistic corrections suppress $γ_{\rm max}$ by up to 40 per cent above $v_0 \approx 0.2c$, peaking near $v_0 \approx 0.9c$. Multi-species effects are significant only for $m_e/m_i \gtrsim 1/500$. For the tabletop laser experiment of Bai et al., Nat.Commun., 16, 3770 (2025), the cold-fluid prediction gives $d_i = c/ω_{pi} \approx 31.7\,μ{\rm m}$, within 2 per cent of the measured filament spacing $λ_F \approx 31\,μ{\rm m}$. The saturation field estimate $B_{\rm sat} \approx 2.3\times10^4$ T is an upper bound, consistent with the measured $\approx 5000$ T under kinetic suppression. Two MMS burst-mode bow shock crossings (October 16, 2015 and November 25, 2017) confirm $k_{\rm max} d_i = 1$ from FGM/FPI data. A multi-environment scatter plot spans 21 orders of magnitude in $n_i$, with all points within a factor of 3 of the 1:1 line. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_12747 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weibel Instability in Collisionless Plasmas Across Astrophysical and Laboratory Shocks Shrivastav, Vivek Chettri, Mani K Singh, Hemam D Singh, Britan Mukherjee, Rupak Plasma Physics High Energy Astrophysical Phenomena Solar and Stellar Astrophysics Space Physics We present a cold-fluid analysis of the purely transverse Weibel (current-filamentation) instability across four regimes: non-relativistic (NR) single-species, NR multi-species, relativistic single-species, and relativistic multi-species (electron--positron and electron--proton). Beginning from linearized fluid equations, we derive the dispersion relations in each regime and extract scaling laws for the maximum growth rate $γ_{\rm max}$ and characteristic unstable wavenumber $k_{\rm max} = ω_{pi}/c$. Relativistic corrections suppress $γ_{\rm max}$ by up to 40 per cent above $v_0 \approx 0.2c$, peaking near $v_0 \approx 0.9c$. Multi-species effects are significant only for $m_e/m_i \gtrsim 1/500$. For the tabletop laser experiment of Bai et al., Nat.Commun., 16, 3770 (2025), the cold-fluid prediction gives $d_i = c/ω_{pi} \approx 31.7\,μ{\rm m}$, within 2 per cent of the measured filament spacing $λ_F \approx 31\,μ{\rm m}$. The saturation field estimate $B_{\rm sat} \approx 2.3\times10^4$ T is an upper bound, consistent with the measured $\approx 5000$ T under kinetic suppression. Two MMS burst-mode bow shock crossings (October 16, 2015 and November 25, 2017) confirm $k_{\rm max} d_i = 1$ from FGM/FPI data. A multi-environment scatter plot spans 21 orders of magnitude in $n_i$, with all points within a factor of 3 of the 1:1 line. |
| title | Weibel Instability in Collisionless Plasmas Across Astrophysical and Laboratory Shocks |
| topic | Plasma Physics High Energy Astrophysical Phenomena Solar and Stellar Astrophysics Space Physics |
| url | https://arxiv.org/abs/2603.12747 |