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

Abstract

Suppose an electric current I flows along a magnetic flux tube that has poloidal flux ψ and radius a=a(z), where z is the axial position along the flux tube. This current creates a toroidal magnetic field Bφ. It is shown that, in such a case, nonlinear, nonconservative J×B forces accelerate plasma axially from regions of small a to regions of large a and that this acceleration is proportional to ∂I2/∂z. Thus, if a current-carrying flux tube is bulged at, say, z=0 and constricted at, say, z=±h, then plasma will be accelerated from z=±h towards z=0 resulting in a situation similar to two water jets pointed at each other. The ingested plasma convects embedded, frozen-in toroidal magnetic flux from z=±h to z=0. The counterdirected flows collide and stagnate at z=0 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 Bφ 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 2μ0nκT/Bpol2=(μ0Ia(0)/ψ)2/2; observed coronal loop parameters are in reasonable agreement with this relationship which is analogous to having βpol=1 in a tokamak.