Velocity filter (Wien filter): Explanation |

The speed filter was developed by Wilhelm Wien and is therefore also called Wien Velocity Filter. This can be used to filter charged particles according to their speed and is therefore usually located behind electron or ion sources. You can find out everything about the speed filter in this article.

Structure and function of the speed filter

The velocity filter only works for charged particles, since there are only two forces acting on the charged particles: the Coulomb force and the Lorentz force. An electric field is generated in the filter by a plate capacitor. A pair of Helmholtz coils is located parallel to the direction of flight but perpendicular to the capacitor plates. This generates a homogeneous magnetic field that acts perpendicular to the direction of movement and perpendicular to the electric field.

Now the force exerted by the electric field on the particles acts upwards, for example. In the magnetic field, the particles are deflected by the Lorentz force. The direction of deflection of the particles can be determined by the three-finger rule. The magnetic field must now be aligned in such a way that the Lorentz force acts downwards, i.e. counteracting the deflection by the electric field. Accordingly, the fields are also perpendicular to one another.

Figure 2: Direction of movement of a particle and how the magnetic and electric fields work.

If a particle now moves through the filter, the strength of the deflection by the electric field only depends on its charge and the field strength:

So if only particles of one type (e.g. only electrons) move through the filter, all particles will be deflected in one direction with the same force. This way none of the particles would reach the end of the filter.

In order to prevent all particles from hitting the capacitor plates, the magnetic field must now be set correctly. Since the Lorentz force counteracts the deflection caused by the electric field, both forces must be equal for a particle to be able to pass through the filter.

Figure 3: Balance of forces in linear motion and passing the velocity filter.

The Lorentz force depends on three things: the charge of the particles, the magnetic flux density and the speed of the particles. The latter is the only way in which the particles differ. If the strength of the magnetic field changes, the Lorentz force is different for the different particles. The force acts more strongly on the faster particles than on the slower ones. Only at a certain speed of the particles is the Lorentz force just as great as the force that acts on the particles through the electric field.

Figure 4: Deflection of the particles through interaction with the Coulomb and Lorentz forces.

If a particle is moving too fast, the Lorentz force is greater than the Coulomb force. Then it becomes cathode distracted and doesn’t make it through the aperture. On the other hand, if a particle is too slow, the Lorentz force is not sufficient to compensate for the deflection by the capacitor. The particle then becomes anode distracted.

The particle can only pass through the pinhole at the optimal speed. Then the forces are perfectly balanced.

Derivation of the velocity formula

Of course, it is important how you can calculate the speed with which the particles can pass through the filter. Also because you can only set your filter correctly then. You can only use the experiment if you master these calculations.

The basic condition for this calculation is that the Lorentz force, which acts in one direction through the magnetic field, and the electric force, which acts in the opposite direction through the electric field, must balance out:

The electric force is defined as the product of the electric field strength E and the charge of the particle in the field Q. The Lorentz force is the product of this same charge, the speed of the particle v and the magnetic flux density B:

Since the charge refers to the same particle, it can be canceled out. As a result, only the speed and the two variables that influence it are left in the formula. The charge of the particle is irrelevant.

Figure 5: Deflection of the particles to the cathode or anode.

If a particle is too fast, the Lorentz force is too large. Then it is deflected towards the cathode and does not make it through the filter. On the other hand, if a particle is too slow, the Lorentz force is not sufficient to compensate for the deflection by the capacitor. The particle is then deflected towards the anode.

What is the Wien Velocity Filter for?

Use on the mass spectrometer

The velocity filter is able to only let charged particles of a certain velocity through. This makes it an important component for all experiments that require a particle beam with a certain speed. This includes, for example, the mass spectrometer, with which the masses of the accelerated particles can be measured. For the measurement results of this experiment, it is absolutely necessary to know the speed of the particles, as this is used later for further calculations.

Figure 6: Particle passing through the velocity filter and deflection on a circular path to determine the particle mass in the mass spectrometer.

For more details on the mass spectrometer, be sure to check out our article on it.

Velocity filter in the particle accelerator

At particle accelerators, the particles have many different properties. In order for an experiment to work, the right ones must be selected. Among other things, the particles must have exactly the right speed. Only then are the results truly revealing. Wien’s velocity filter is also used here for this purpose.

Since the particles must also have other properties, the filter here is part of a complicated selection system.

Particle Velocity Measurement

The velocity filter can also be used to measure the velocities of particles, for example at the end of an experiment, and thus to confirm other measurement results. Since the speed only depends on the strength of the fields, by adjusting the fields, the speed can be calculated. To do this, you change them until the particles can pass and then calculate the speed they need to have in this case.

The limits of possible uses

In the case of uncharged particles, however, Wien’s velocity filter fails. The Coulomb force and the Lorentz force are responsible for how it works. Both act only on electric charges. Uncharged particles would therefore pass through the filter regardless of their speed.

Normally, however, this does not matter. In most experiments using the filter, the particles are already accelerated by the Coulomb force. Uncharged particles are therefore not present in the particle stream.