Dynamics of Axisymmetric Loops

  1. C. T. Russell,
  2. E. R. Priest and
  3. L. C. Lee
  1. R. S. Steinolfson

Published Online: 21 MAR 2013

DOI: 10.1029/GM058p0211

Physics of Magnetic Flux Ropes

Physics of Magnetic Flux Ropes

How to Cite

Steinolfson, R. S. (1990) Dynamics of Axisymmetric Loops, in Physics of Magnetic Flux Ropes (eds C. T. Russell, E. R. Priest and L. C. Lee), American Geophysical Union, Washington, D. C.. doi: 10.1029/GM058p0211

Author Information

  1. Department of Space Sciences, Southwest Research Institute, San Antonio, TX 78228

Publication History

  1. Published Online: 21 MAR 2013
  2. Published Print: 1 JAN 1990

ISBN Information

Print ISBN: 9780875900261

Online ISBN: 9781118663868



  • Solar photosphere;
  • Magnetic flux;
  • Astrophysics


The evolution of a magnetic loop in response to rotation within circular sections at the loop ends is investigated using time-dependent, two-dimensional MHD simulations in cylindrical geometry. The magnetic field components at the loop ends are modified by the applied rotating flow in a manner consistent with the generated electric fields. The axisymmetric evolution of the magnetic field and plasma flow within the loop can be characterized as passing through several distinct and identifiable stages. Early on, the magnetic energy increases with the square of time, the current and magnetic field are parallel (force-free), the average kinetic energy remains constant and is negligible compared to the magnetic energy increase, and the solution fluctuates at a characteristic loop frequency. The average kinetic energy then increases rapidly and levels off at a higher value, which is still much less than the magnetic energy increase. The magnetic energy now increases exponentially with time and deviations from a force-free field begin to appear, particularly near the loop axis and ends. In the final phase, the current and field are no longer force-free, and the solution becomes highly nonlinear. The fluctuations that appeared early on continue with ever increasing amplitude into this last stage. Finally, a critical shear level is exceeded and the oscillatory behavior stops and is replaced by an expansion propagating radially outward at large radii, a large radial inflow toward the loop axis within the outward travelling expansion, and a strong cylindrical shock around the axis that brings the inflowing plasma to rest. It is suggested that this shock may produce the heating and particle acceleration in compact loop flares.