In Chap. 4, we saw that the guiding centers of ions and electrons gyrating in a tor­oidal magnetic field have vertical drifts because the field is nonuniform; that is, it varies horizontally. The reason is that the particle feels a different magnetic field on

each side of its Larmor orbit. A similar effect occurs in the presence of an electric field. This is shown in Fig. 5.4. There, the magnetic field (B-field) is coming out of the paper, and the electric field (E-field) points from left to right. Consider first the positive ion. It tries to follow its usual circular path, but it is pushed to the right by the E-field. Having higher energy, its orbit becomes larger. As it cycles back to the left, it moves against the E-field and is slowed up, so its orbit is smaller on the left side. This clearly causes the center of the orbit, the guiding center, to drift down­wards. Now consider the electron on the left. Since it has opposite charge, it gyrates counterclockwise instead of clockwise, and is pushed to the left instead of to the right by the E-field. The result is that it also drifts downwards. Furthermore, since it is lighter and moves faster than the ion, it executes more orbits in the same time interval, ending up with exactly the same downward drift! The result is that parti­cles have an E x B (E-cross-B) drift that is perpendicular to both the B-field and the E-field, and which has the same speed and same direction for ions and electrons regardless of their energies.

It may seem strange that when you push in one direction, the particle goes in a perpendicular direction, but this effect is the same as that in a toy gyroscope. When the gyroscope tips down from vertical, gravity pulls it downwards, but the gyro­scope precesses horizontally. If you follow a point on the rotating ring, you will see that under gravitational pull the whole ring will move sideways, just as do the orbits in Fig. 5.4. The same effect causes a rolling hoop to go a long way before falling over. When the hoop starts to lean over to the left, say, gravity will pull the hoop downwards, and the gyroscopic effect will turn the hoop to the left, so that it travels in a direction that will straighten it up. The front wheel of a bicycle also benefits from this effect, but only in a small way. There are stronger stabilizing forces in a bicycle.