text: As for ideal MHD, the plasma can be considered as tied to the magnetic field lines when certain conditions are fulfilled. One often says that the magnetic field lines are frozen into the plasma. The frozen-in conditions can be derived from Vlasov equation.
  We introduce the scales , , and  for time, distance and speed respectively. They represent magnitudes of the different parameters which give large changes in . By large we mean that
  We then write
  Vlasov equation can now be written
  So far no approximations have been done. To be able to proceed we set , where  is the gyro frequency and  is the gyroradius. By dividing by , we get
  If  and , the two first terms will be much less than  since  and  due to the definitions of , , and  above. Since the last term is of the order of , we can neglect the two first terms and write
  This equation can be decomposed into a field aligned and a perpendicular part:
  The next step is to write , where
  It will soon be clear why this is done. With this substitution, we get
  If the parallel electric field is small,
  This equation means that the distribution is gyrotropic. The mean velocity of a gyrotropic distribution is zero. Hence,  is identical with the mean velocity, , and we have
  To summarize, the gyro period and the gyro radius must be much smaller than the typical times and lengths which give large changes in the distribution function. The gyro radius is often estimated by replacing  with the thermal velocity or the Alfvén velocity. In the latter case  is often called the inertial length. The frozen-in conditions must be evaluated for each particle species separately. Because electrons have much smaller gyro period and gyro radius than ions, the frozen-in conditions will more often be satisfied.