Editing Magnetic reconnection (section)

===Stochastic reconnection===

In stochastic reconnection,<ref>{{cite journal|author1-link=Alexandre Lazarian|last1=Lazarian|first1=Alex|last2=Vishniac|first2=Ethan|title=Reconnection in a Weakly Stochastic Field|journal=The Astrophysical Journal|date=1999|volume=517|issue=2|pages=700–718|doi=10.1086/307233|arxiv = astro-ph/9811037 |bibcode = 1999ApJ...517..700L |s2cid=119349364}}</ref> magnetic field has a small scale random component arising because of turbulence.<ref>{{cite journal|last1=Jafari|first1=Amir|last2=Vishniac|first2=Ethan|title=Topology and stochasticity of turbulent magnetic fields |journal=Physical Review E|date=2019|volume=100|issue=1|pages=013201|doi=10.1103/PhysRevE.100.013201|pmid=31499931|bibcode=2019PhRvE.100a3201J|s2cid=199120046}}</ref> For the turbulent flow in the reconnection region, a model for magnetohydrodynamic turbulence should be used such as the model developed by Goldreich and Sridhar in 1995.<ref>{{cite journal|last1=Goldreich|first1=P.|last2=Sridhar|first2=S.|title=Toward a theory of interstellar turbulence. 2: Strong Alfvenic turbulence|journal=The Astrophysical Journal|date=1995|volume=438|page=763|doi=10.1086/175121|bibcode = 1995ApJ...438..763G |url=https://authors.library.caltech.edu/38003/}}</ref> This stochastic model is independent of small scale physics such as resistive effects and depends only on turbulent effects.<ref>{{cite journal|last1=Jafari|first1=Amir|last2=Vishniac|first2=Ethan|last3=Kowal|first3=Grzegorz|last4=Lazarian|first4=Alex|title=Stochastic Reconnection for Large Magnetic Prandtl Numbers|journal=The Astrophysical Journal|date=2018|volume=860|issue=2|pages=52|doi=10.3847/1538-4357/aac517|bibcode=2018ApJ...860...52J|s2cid=126072383|doi-access=free}}</ref> Roughly speaking, in stochastic model, turbulence brings initially distant magnetic field lines to small separations where they can reconnect locally (Sweet-Parker type reconnection) and separate again due to turbulent super-linear diffusion (Richardson diffusion <ref>{{cite journal|last1=Jafari|first1=Amir|last2=Vishniac|first2=Ethan|title=Magnetic stochasticity and diffusion|journal=Physical Review E|date=2019|volume=100|issue=4|pages=043205|doi=10.1103/PhysRevE.100.043205|pmid=31770890|arxiv=1908.06474|bibcode=2019PhRvE.100d3205J|s2cid=201070540}}</ref>). For a current sheet of the length <math>L </math>, the upper limit for reconnection velocity is given by

<math display="block">v = v_\text{turb} \; \operatorname{min}\left[\left( {L \over l} \right)^\frac{1}{2}, \left( {l \over L} \right)^\frac{1}{2} \right],</math>

where <math>v_\text{turb} = v_l^2/v_A</math>. Here <math>l</math>, and <math>v_l</math> are turbulence injection length scale and velocity respectively and <math>v_A </math> is the Alfvén velocity. This model has been successfully tested by numerical simulations.<ref>{{cite journal|last1=Kowal|first1=G.|title=Numerical Tests of Fast Reconnection in Weakly Stochastic Magnetic Fields|last2=Lazarian|first2=A.|last3=Vishniac|first3=E.|last4=Otmianowska-Mazur|first4=K.|journal=The Astrophysical Journal|year=2009|volume=700|issue=1|pages=63–85|doi=10.1088/0004-637X/700/1/63|arxiv = 0903.2052 |bibcode = 2009ApJ...700...63K |s2cid=4671422}}</ref><ref>{{cite journal| last1=Kowal|first1=G| last2=Lazarian|first2=A.| last3=Vishniac|first3=E.| last4=Otmianowska-Mazur|first4=K.| title=Reconnection studies under different types of turbulence driving| journal=Nonlinear Processes in Geophysics|date=2012|volume=19|issue=2|pages=297–314|doi=10.5194/npg-19-297-2012| arxiv = 1203.2971 |bibcode = 2012NPGeo..19..297K |s2cid=53390559|doi-access=free}}</ref>