And you can see how this flux density follows the scheme of the flux lines. The highest density is behind the MOVING MAGNET, but inside the STATOR MAGNETS, and there is also a little part of high density ahead the MOVING MAGNET edges.
THE FINAL EXPLANATION - ENERGY DIFFERENCE:
At the present moment, we have seen a lot of effects produced on flux lines, flux density and magnetization on magnets due to the configuration and materials of the device. All these things claim the generation of a unidirectional force. Here is the more powerful argument: ENERGY.
The MOVING MAGNET has not a symmetrically distributed energy, and it doesn't matter where the MOVING MAGNET is respect to the TRACK!
Usually, the magnetic energy on a magnet is equal from the middle to both sides. The energy is equally distributed along the magnet, so it doesn't move. When you place a STATOR MAGNET near one side, the energy level of this side increases or decreases, and the moving magnet approaches or moves away. Also, the STATOR MAGNET feels the opposite force, but it is cancelled by mechanical tension, so the STATOR MAGNET doesn't move.
On the PM3, the magnetic energy levels on MOVING MAGNET are ALWAYS different on both sides. The simulations gave 19.5 Joules / m from the middle to the left and 22.3 Joules / m from the middle to the right, with little variations while the MOVING MAGNET moves, but always a difference of 2.8 Joules / m approx. is maintained.
The magnetic energy on MOVING MAGNET is always less from the middle to the left than from the middle to the right (whatever the position respect to the TRACK is), so a force is generated. Also, the STATOR MAGNETS near the MOVING MAGNET have different energy levels too (more on the left STATORS than on the right!), but the forces generated on near STATOR MAGNETS are compensated with mechanical tension forces as explained before.
Here is a simple graphical explanation of energy distribution:
Due to this difference on energy distribution (greater on the right side), the MOVING MAGNET feels a force and the near STATOR MAGNETS feel the opposite reaction (energy levels on near STATOR MAGNETS increase to the left).
The energy distribution takes this configuration because of the presence of the MOVING MAGNET between the STATOR MAGNETS, so it doesn't matter where we put the MOVING MAGNET, it will change the energy distribution around, so the position of the magnet causes the energy distribution to change and that energy distribution makes the MOVING MAGNET to move.
THE FORCES MEASURED ON THE DEVICE:
Here is a graphical measurement of the forces along the path of MOVING MAGNET that confirms the motion: