{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T01:25:29Z","timestamp":1771982729699,"version":"3.50.1"},"reference-count":51,"publisher":"AIP Publishing","issue":"4","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2013,4,1]]},"abstract":"<jats:p>Collisionless shocks are ubiquitous in astrophysics and in the lab. Recent numerical simulations and experiments have shown how they can arise from the encounter of two collisionless plasma shells. When the shells interpenetrate, the overlapping region turns unstable, triggering the shock formation. As a first step towards a microscopic understanding of the process, we analyze here in detail the initial instability phase. On the one hand, 2D relativistic Particle-In-Cell simulations are performed where two symmetric initially cold pair plasmas collide. On the other hand, the instabilities at work are analyzed, as well as the field at saturation and the seed field which gets amplified. For mildly relativistic motions and onward, Weibel modes govern the linear phase. We derive an expression for the duration of the linear phase in good agreement with the simulations. This saturation time constitutes indeed a lower-bound for the shock formation time.<\/jats:p>","DOI":"10.1063\/1.4798541","type":"journal-article","created":{"date-parts":[[2013,4,29]],"date-time":"2013-04-29T13:46:29Z","timestamp":1367243189000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":89,"title":["Collisionless shock formation, spontaneous electromagnetic fluctuations, and streaming instabilities"],"prefix":"10.1063","volume":"20","author":[{"given":"A.","family":"Bret","sequence":"first","affiliation":[{"name":"ETSI Industriales, Universidad de Castilla-La Mancha 1 , 13071 Ciudad Real, Spain"},{"name":"Instituto de Investigaciones Energ\u00e9ticas y Aplicaciones Industriales, Campus Universitario de Ciudad Real 2 , 13071 Ciudad Real, Spain"},{"name":"Harvard-Smithsonian Center for Astrophysics 5 , 60 Garden Street, MS-51 Cambridge, Massachusetts 02138, USA"}]},{"given":"A.","family":"Stockem","sequence":"additional","affiliation":[{"name":"GoLP\/Instituto de Plasmas e Fus\u00e3o Nuclear\u2013Laborat\u00f3rio Associado, Instituto Superior T\u00e9cnico 3 , Lisboa, Portugal"}]},{"given":"F.","family":"Fiuza","sequence":"additional","affiliation":[{"name":"GoLP\/Instituto de Plasmas e Fus\u00e3o Nuclear\u2013Laborat\u00f3rio Associado, Instituto Superior T\u00e9cnico 3 , Lisboa, Portugal"}]},{"given":"C.","family":"Ruyer","sequence":"additional","affiliation":[{"name":"CEA, DAM 4 , DIF F-91297 Arpajon, France"}]},{"given":"L.","family":"Gremillet","sequence":"additional","affiliation":[{"name":"CEA, DAM 4 , DIF F-91297 Arpajon, France"}]},{"given":"R.","family":"Narayan","sequence":"additional","affiliation":[{"name":"Harvard-Smithsonian Center for Astrophysics 5 , 60 Garden Street, MS-51 Cambridge, Massachusetts 02138, USA"}]},{"given":"L. 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