Wien filter

A velocity filter, named after its developer Wilhelm Wien and Wien filter, is mainly intended to let out of the particle of an ion source, only those particles pass through the filter, which have a certain speed, while all remaining in the filter " stuck" - in other words, one can so that a particle " prepare " with only a precisely defined speed, but also determine the speed of unknown charged particles.

Design and operation

Electrically charged particles are passed through a plate capacitor, which is itself completely within a homogeneous magnetic field. All relevant parameters of this arrangement ( the electric field generated by the capacitor, the magnetic field and the path of the charged particle ) are doing to each other in pairs vertically.

If in the picture positively charged particles coming from the left, they are deflected by the electric field down by the magnetic field upwards. Are the two forces of equal size, the total force is zero and the particles fly straight. Since the Lorentz force is proportional to velocity, only particles of a certain velocity in the filter to stay on a straight path, all other particles are deflected up or down and can be intercepted by an aperture at the output.

Since both forces act only on charged particles, the particles may have to first be ionized ( by an arc, for example ).

Mathematical viewing

The weight of the particle can be neglected in all calculations.

In the following, the condition is derived that the particle will not be distracted by:

• B: magnetic flux density
• E: electric field strength
• Q: charge
• V: speed

Scalar viewing

A balance of forces and thus a linear traversal of the filter is when applies to the electric force and the magnetic force ( Lorentz force )

This results in the transmission rate:

With use of the vector product

For the motion in the field applies using the Newton's second law:

Does not mean distraction.

Areas of application

To filter out particles of a certain speed, the magnetic and the electric field must be so adjusted accordingly. Of the particles that can pass through the Wien filter at a given magnetic flux density and electric field strength, we know by the above relation, the speed.

Mass and charge of the particles for the play function of the filter does not matter, as shown in the formulas.

In a mass spectrometer selected usually out a velocity filter of a ion beam particles with a specific ( known order ) rate to then be separated ( for example by means of a magnetic field ) the different masses.

Velocity filters are often used in particle accelerators. Together with other electrostatic and magnetic filters they often form a rather complex system to select particles of a certain mass, charge and velocity.