The most-studied classes of exact solutions of Vlasov—Maxwell equations for stationary neutral current structures in a collisionless relativistic plasma are reviewed which allow the particle distribution functions (PDFs) to be chosen at will. A general classification is presented of the current sheets and filaments described by the method of invariants of motion of particles whose PDF is symmetric in a certain way in coordinate and momentum spaces. The possibility is discussed of using these explicit solutions to model the observed and/or expected features of the current structures in cosmic and laboratory plasmas. Also addressed are how the magnetic field forms and the analytical description of the so-called Weibel instability in a plasma with an arbitrary PDF.

Keywords: neutral current structures, collisionless relativistic plasma, integrals of motion, kinetic theory, magnetosphere PACS: 52.30.−q, 52.35.−g, 94.30.−d (all) DOI: 10.3367/UFNe.2016.08.037893 URL: https://ufn.ru/en/articles/2016/12/b/ 000396007200001 2-s2.0-85014950043 2016PhyU...59.1165K Citation: Kocharovsky V V, Kocharovsky V V, Martyanov V Ju, Tarasov S V "The analytical theory of self-consistent current structures in a collisionless plasma" Phys. Usp. 59 1165–1210 (2016) BibTexBibNote ® (generic)BibNote ® (RIS) MedlineRefWorks PT Journal Article TI The analytical theory of self-consistent current structures in a collisionless plasma AU Kocharovsky V V FAU Kocharovsky VV AU Kocharovsky V V FAU Kocharovsky VV AU Martyanov V Ju FAU Martyanov VJ AU Tarasov S V FAU Tarasov SV DP 10 Dec, 2016 TA Phys. Usp. VI 59 IP 12 PG 1165-1210 RX 10.3367/UFNe.2016.08.037893 URL https://ufn.ru/en/articles/2016/12/b/ SO Phys. Usp. 2016 Dec 10;59(12):1165-1210 Received: 15th, June 2016, revised: 16th, August 2016, accepted: 21st, August 2016 Оригинал: Кочаровский В В, Кочаровский В В, Мартьянов В Ю, Тарасов С В «Аналитическая теория самосогласованных токовых структур в бесстолкновительной плазме» УФН 186 1267–1314 (2016); DOI: 10.3367/UFNr.2016.08.037893