# What is magnetic acceleration

Physicists use electric fields to accelerate particles to higher energies. To bring the particles onto the crooked path, they use magnetic fields.

Again and again it is necessary to redirect charged particles. This is the case, for example, in circular accelerators, in which the particles repeatedly travel through the same acceleration paths on a circular path. Or if the particles are to be guided from one accelerator into another or if they are to be bundled into compact beams.

In all of this, one uses the effect that electrical particles fly in magnetic fields along a circular path. The so-called Lorentz force is responsible for this. Their direction depends on the charge of the particle and the direction of the magnetic field.

Goal wall shooting with Henry Lorentz.

The force of a magnetic field B on an electric charge q with the velocity v is described by the magnetic component of the Lorentz force:

The force is always perpendicular to the speed (which is indicated by the cross product symbol "x’ "). Therefore, a magnetic field can only change the direction of the speed, but not increase or decrease its magnitude. In this case, too, physicists speak of acceleration.

In order to calculate the radius of the circular path of a charged particle in a magnetic field, one has to equate the centripetal force with the magnetic force. For a non-relativistic particle - that is, one with a speed further below that of light - the following derivation applies.

The centripetal force of a particle of mass m on a circular path with velocity v and radius R is determined by:

The magnetic force on the charged particle with the charge q in the magnetic field B is:

These two forces are equal on the circular path. This gives for the radius:

The higher the speed, the lower the magnetic field can be. The higher the mass, the stronger the magnetic field has to be. So for protons you need much stronger magnets than for electrons.