The distance scale is the gyroradius based on the sound speed:

The formula for the gyroradius also holds for relativistic motion.

Single electrons travel straight through the null point, due to their infinite gyroradius in regions of no magnetic field.

Solving for , the gyroradius is determined to be:

Because particles passed through locations with no magnetic field, their motions could be straight, with an infinite gyroradius.

To be able to proceed we set , where is the gyro frequency and R is the gyroradius.

This centripetal force causes the electron to follow a helical trajectory through the field at a radius called the gyroradius.

This description is most valuable when the gyroradius of the charged particle orbit is small compared to the spatial scale for changes in the field.

Their gyroradius shrinks and when they hit a dense magnetic field they can be reflected using the magnetic mirror effect .

However, the gyroradius in those circumstances is also larger, so that the radial component of the magnetic field seen by the particle is also larger.

In the gyrokinetic model, which is appropriate to systems with a strong background magnetic field, the kinetic equations are averaged over the fast circular motion of the gyroradius.

Thus, the gyroradius is directly proportional to the particle mass and velocity, and inversely proportional to the particle electric charge, and the magnetic field strength.

The radial magnetic field is designed to be strong enough to substantially deflect the low-mass electrons, but not the high-mass ions which have a much larger gyroradius and are hardly impeded.

In the limit where the wavelength of a perturbation of the electric potential is much smaller than the gyroradius based on the sound speed, the Hasegawa-Mima equations become the same as the two-dimensional incompressible fluid.

The gyroradius (also known as radius of gyration, Larmor radius or cyclotron radius) is the radius of the circular motion of a charged particle in the presence of a uniform magnetic field.

If one assumed that magnetopause was just a boundary between a magnetic field in a vacuum and a plasma with a weak magnetic field embedded in it, then the magnetopause would be defined by electrons and ions penetrating one gyroradius into the magnetic field domain.