Why current-carrying magnetic flux tubes gobble up plasma and become thin as a result

Suppose an electric current I flows along a magnetic flux tube that has poloidal flux c and radius a5a(z), where z is the axial position along the flux tube. This current creates a toroidal magnetic field Bf . It is shown that, in such a case, nonlinear, nonconservative J3B forces accelerate plasma axially from regions of small a to regions of large a and that this acceleration is proportional to ]I/]z . Thus, if a current-carrying flux tube is bulged at, say, z50 and constricted at, say, z 56h , then plasma will be accelerated from z56h towards z50 resulting in a situation similar to two water jets pointed at each other. The ingested plasma convects embedded, frozen-in toroidal magnetic flux from z56h to z50. The counterdirected flows collide and stagnate at z50 and in so doing ~i! convert their translational kinetic energy into heat, ~ii! increase the plasma density at z'0, and ~iii! increase the embedded toroidal flux density at z'0. The increase in toroidal flux density at z'0 increases Bf and hence increases the magnetic pinch force at z'0 and so causes a reduction of a(0). Thus, the flux tube develops an axially uniform cross section, a decreased volume, an increased density, and an increased temperature. This model is proposed as a likely hypothesis for the long-standing mystery of why solar coronal loops are observed to be axially uniform, hot, and bright. It is furthermore argued that a small number of tail particles bouncing between the approaching counterstreaming plasma jets should be Fermi accelerated to extreme energies. Finally, analytic solution of the Grad–Shafranov equation predicts that a flux tube becomes axially uniform when the ingested plasma becomes hot and dense enough to have 2m0nkT/Bpol 2 5(m0Ia(0)/c) /2; observed coronal loop parameters are in reasonable agreement with this relationship which is analogous to having bpol51 in a tokamak. © 2003 American Institute of Physics. @DOI: 10.1063/1.1558275#