Sizing up the scales

Exploring the breaking and rejoining of magnetic-field lines requires simulations and computation. A simulation’s accuracy, however, depends on various issues of scale.

Magnetic reconnection’s multiscale nature exacerbates the challenge of simulating it. Early research was based entirely on fluid models in just two dimensions, since kinetic simulations were infeasible.

Kinetic modeling requires the space and time scales associated with charged-particle motion to be resolved at the level of protons and electrons in a plasma. The separation between these scales is determined by the proton-to-electron mass ratio, which is 1,836. In a plasma, the electrons gyrate about the magnetic field 1,836 times faster than the protons, and the physical size of the electron-gyration radius is 43 – the square root of 1,836 – times smaller than a proton’s.

To model reconnection, the simulation size must be much larger than the proton gyroradius. This suggests some of the huge range of space and time scales the simulations require. Only recent advances in algorithms, hardware and software allow three-dimensional simulations.

Vadim Roytershteyn, a plasma physicist at SciberQuest in Del Mar, Calif., notes that recent studies demonstrate a deep link between turbulence and magnetic reconnection. Scientists have speculated about this association “from very early on in this field.” Without 3-D simulations, this relationship could not be explored.