Radius at which a charged particle gyrates in a magnetic field.
The force F exerted on a charged particle of mass m and charge q and velocity v in a uniform magnetic field B is given by
For simplicity, consider a magnetic field with a z component
in the z
direction is zero while acceleration in the x and y direction is given by
is the cyclotron frequency
(eB/m). The solution to these equations
implies a Larmor Radius, L
L= √(2) mvthermal/qB
is the thermal velocity of the charged particles. Thus, the higher the magnetic field, the smaller the Larmor radius and the more tightly bound
the charged particle will be to the magnetic field. A proton
will gyrate at a larger Larmor radius than an electron
(its mass is much greater).
In order to contain a plasma, it is important to ensure that the device can contain particles gyrating at the Larmor radius.