Let us consider a magnetic field B having constant magnitude lBl but its line of forces curved in the space with constant radius of curvature Rc. Eg : B inside toroid. Such a field doesn't obey Maxwell's equation in a vaccumm so in practice grad B drift will always be added to the effect derived here.

As the particle moves along the field lines in their thermal motion they experience the centrifugal force i.e

Now the drift velocity arising due to the field is

Curvature drift

For curved field, magnitude of B decreases with radius

Drift due to Gradient of magnetic field,

Using equation in 4 we get

The curvature drift arises due to the gradient in the magnetic field strength, causing a net force on charged particles. The total velocity of a particle experiencing curvature drift can be expressed as the sum of two components: the velocity perpendicular to the magnetic field and the velocity along the magnetic field .If magnetic field is bent into a torus for the purpose of confining thermonuclear plasm, the plasma particles will drift out of the torus.

The curvature drift arises due to the gradient in the magnetic field strength perpendicular to the direction of the magnetic field. This gradient results in a change in the direction of the Lorentz force experienced by the particle as it moves along the field lines. As a result, the charged particle experiences a net force pointing toward the region of higher magnetic field strength. This force is perpendicular to both the velocity vector and the magnetic field vector, causing the particle to drift in the direction of increasing magnetic field strength.

The curvature drift plays a crucial role in various plasma phenomena, particularly in magnetized plasmas and magnetic confinement devices such as tokamaks. It contributes to the overall dynamics of charged particles and can influence plasma transport, particle confinement, and the formation of current structures in magnetic fields. Understanding and characterizing curvature drift is important for studying plasma behaviour and designing magnetic confinement systems for fusion research.

This note is a part of the Physics Repository.

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