The Rate of Separation of Magnetic Lines of Force in a Random Magnetic Field

The mixing of magnetic lines of force, as represented by their rate of separation, as a function of distance along the magnetic field, is considered with emphasis on neighboring lines of force. This effect is particularly important in understanding the transport of charged particles perpendicular to the average magnetic field. The calculation is carried out in the approximation that the separation changes by an amount small compared with the correlation scale normal to the field, in a distance along the field of a few correlation scales. It is found that the rate of separation is very sensitive to the precise form of the power spectrum. For a power-law spectrum cc k - a with a < 2, the rate of separation can be quite rapid, and is insensitive to the initial value of the separation. Application to the interplanetary and interstellar magnetic fields is discussed, and it is shown that in some cases field lines, much closer together than the correlation scale, separate at a rate which is effectively as rapid as if they were many correlation lengths apart. In such cases the scale of coherent flux tubes is much less than the correlation scale of the field. Subject headings: hydromagnetics - interplanetary medium - interstellar medium