Gyroradius

The Larmor radius ( by Joseph Larmor, due to the importance in the cyclotron and cyclotron radius, other designation gyroradius / gyration radius ) is the radius of the circular motion of a charged particle in a uniform magnetic field:

With

  • Mass of the charged particle
  • Velocity component perpendicular to the magnetic field lines
  • Electrical charge of the particle
  • Magnetic flux density of the homogeneous magnetic field.

The frequency of this circular motion is called the cyclotron frequency or gyration:

They must be distinguished from the Larmor frequency, which describes the frequency of the spin precession.

The size is also called magnetic rigidity.

Derivation

On a charged particle moving in a magnetic field, the Lorentz force acts:

With

  • Velocity vector of the particle,
  • Vector of magnetic flux density.

The direction of the force is determined by the cross product of the velocity and the magnetic flux density. Therefore, the Lorentz force is always perpendicular to the direction of movement of the particles and forces on a circular path.

Equating Lorentz force and centripetal force:

Results by solving for the above-mentioned Formula for the radius of gyration.

Normalized gyroradius

In the merger is called the Larmor radius based on a typical expansion of the plasma ( in toroidal geometries of small radius a is used) and normalized gyroradius:

It is an important dimensionless parameter for dimension analysis of fusion machines.

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