{"paper":{"title":"Acoustic instability at shock-wave precursors","license":"http://creativecommons.org/licenses/by/4.0/","headline":"With realistic Mach numbers and cosmic-ray efficiencies, the acoustic instability grows small density perturbations into large nonlinear structures as plasma crosses a shock precursor.","cross_cats":["hep-ph","physics.plasm-ph"],"primary_cat":"astro-ph.HE","authors_text":"Antonio Capanema, Emanuele Sobacchi, Pasquale Blasi","submitted_at":"2026-04-14T09:47:55Z","abstract_excerpt":"Magnetic field amplification is an integral part of the process of particle acceleration at non-relativistic shocks. It is necessary to reach the maximum energies required by observations, especially in supernova remnants, thought to be sources of the bulk of Galactic cosmic rays. Such amplification can be caused by the acoustic instability that develops when small density perturbations interact with the cosmic-ray pressure gradient in the upstream of a cosmic-ray-modified shock. The vorticity induced by the nonlinear development of the instability may lead to turbulence, which amplifies the p"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Adopting more realistic values of Mach number and cosmic-ray acceleration efficiency than previously assumed in the literature, we show that the acoustic instability can transform small density perturbations into large nonlinear structures while the fluid crosses the precursor region of a cosmic-ray-modified shock.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That an externally assigned cosmic-ray pressure gradient accurately captures the self-consistent precursor structure of a cosmic-ray-modified shock and that two-dimensional simulations suffice to capture the essential nonlinear evolution and resulting turbulence.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Numerical simulations show acoustic instability transforms small density perturbations into nonlinear structures across realistic cosmic-ray-modified shock precursors, generating turbulent magnetic fluctuations.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"With realistic Mach numbers and cosmic-ray efficiencies, the acoustic instability grows small density perturbations into large nonlinear structures as plasma crosses a shock precursor.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"4db7e7ce8e45fbeb427701e2f5397d8d99a1d994584e466e5edaa7a22f79ddd6"},"source":{"id":"2604.12514","kind":"arxiv","version":1},"verdict":{"id":"a90680ae-61ef-4bf2-9bb6-79cfbc3f6341","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T15:27:33.448103Z","strongest_claim":"Adopting more realistic values of Mach number and cosmic-ray acceleration efficiency than previously assumed in the literature, we show that the acoustic instability can transform small density perturbations into large nonlinear structures while the fluid crosses the precursor region of a cosmic-ray-modified shock.","one_line_summary":"Numerical simulations show acoustic instability transforms small density perturbations into nonlinear structures across realistic cosmic-ray-modified shock precursors, generating turbulent magnetic fluctuations.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That an externally assigned cosmic-ray pressure gradient accurately captures the self-consistent precursor structure of a cosmic-ray-modified shock and that two-dimensional simulations suffice to capture the essential nonlinear evolution and resulting turbulence.","pith_extraction_headline":"With realistic Mach numbers and cosmic-ray efficiencies, the acoustic instability grows small density perturbations into large nonlinear structures as plasma crosses a shock precursor."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.12514/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":4,"sample":[{"doi":"","year":null,"title":"For density fluctuations, the field isf=δρ/ρ 0, and we chooseC=1 such thatX n Eδρ/ρ0(¯kn)∆kn = X ab ∆2k P(kab)=ξ(0) = 1 A X i j ∆x∆y \" δρ ρ0 (xi j) #2 = δρrms ρ0 !2 ,(B.12) whereδρ rms /ρ0 is the RMSδ","work_id":"e96d5567-8729-4e0b-9701-4dea178ad686","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"In other words, δBrms(¯kn)= q 8πEturb,mag(¯kn)∆kn (B.14) is the RMS value of magnetic field fluctuations with charac- teristic scaleℓ=2π/ ¯kn","work_id":"6b38158e-6a25-48c1-833a-e636c83c4956","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"For velocity fields,e.g.δu, we chooseC=ρ 0/2 such that X n Eδu(¯kn)∆kn = 1 A X i j ∆x∆y ρ0|δu(xi j)|2 2 = ρ0δu2 rms 2 . (B.15) Analogously to the magnetic field case, the RMS amplitude of velocity per","work_id":"37e34865-6f48-4b15-856c-ab4eac79e395","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1990,"title":"For studies of compressible turbulence, it is common to consider the density-weighted velocityw= √ρuto de- fine kinetic energy spectra (Kida & Orszag 1990; Grete et al. 2017). Letδwbe its fluctuations","work_id":"82563fda-b4ef-4eb3-ab50-ffd3c2c47667","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":4,"snapshot_sha256":"ab49a18d8a184714db90fc9bbcb47c2a2703641c005815ac474ab34573e0b4a2","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}