# Magneto-Fluid Dynamics Seminar

#### Magnetic Reconnection in Three Dimensional Space

**Speaker:**
Allen Boozer, Columbia University

**Location:**
Warren Weaver Hall 905

**Date:**
Tuesday, January 30, 2018, 11 a.m.

**Synopsis:**

The breaking of magnetic field line connections is of fundamental importance in essentially all applications of plasma physics: laboratory to astrophysics. For sixty years the theory of magnetic reconnection has been focused on two-coordinate models. When dissipative time scales far exceed natural evolution times, such models are not realistic for ordinary three dimensional space. The ideal (dissipationless) evolution of a magnetic field is shown to in general lead to a state in which the magnetic field lines change their connections on an Alfvénic (inertial), not resistive, time scale. Only a finite mass of the lightest current carrier, the electron, is required. During the reconnection, the gradient in *j_*||/*B* relaxes while conserving magnetic helicity in the reconnecting region. This implies a definite amount of energy is released from the magnetic field and transferred to shear Alfvén waves, which in turn transfer their energy to the plasma. When there is a strong non-reconnecting component of the magnetic field, called a guide field, *j_*||/*B* obeys the same evolution equation as that of an impurity being mixed into a fluid by stirring. Although the enhancement of mixing by stirring has been recognized by every cook for many millennia, the analogous effect in magnetic reconnection is not generally recognized. An interesting mathematical difference is a three-coordinate model is required for the enhancement of magnetic reconnection while only two coordinates are required in fluid mixing. The issue is the number of spatial coordinates required to obtain an exponential spatial separation of magnetic field lines versus streamlines of a fluid flow.