Speed ​​filter

A velocity filter , according to its developer Wilhelm Wien also Wienfilter called, is mainly used in the particle beam of the ion source , only those particles to let pass through the filter which have a certain speed, while all "stuck" remaining in the filter - in other words, one can thus “preparing” a particle flow with only a precisely defined speed, but also determining the speed of unknown charged particles.

Structure and functionality

Qualitative functioning of the speed filter

Balance of forces of the moving load

Electrically charged particles are sent through a plate capacitor , which is itself completely within a homogeneous magnetic field . All vector parameters of this arrangement (the electric field generated by the capacitor, the magnetic field and the path of the charged particle) are all perpendicular to each other (" three-finger rule ").

If positively charged particles come from the left in the picture on the right, they are deflected downwards by the electric field and upwards by the magnetic field. If both forces are equal, the total force is zero and the particles fly straight ahead. Since the Lorentz force is proportional to the speed, only particles of a certain speed stay on a straight path in the filter, all other particles are deflected up or down and can be intercepted by a shutter at the exit.

Since both forces only act on charged particles, the particles may first have to be ionized (e.g. by means of an electric arc).

Mathematical consideration

The weight of the particle can be neglected in all calculations because of its small size.

In the following, the condition is derived that the particle is not deflected with:

• B : magnetic flux density
• E : Electric field strength
• q : charge
• v : speed

Scalar viewing

There is an equilibrium of forces and thus a straight crossing of the filter if the following applies to the electrical force and the magnetic force (Lorentz force) : ${\displaystyle F_{\text{C}}}$ ${\displaystyle F_{\text{L}}}$

${\displaystyle \,F_{\text{C}}=F_{\text{L}}}$

${\displaystyle q\,E=q\,v\,B}$

${\displaystyle E=v\,B}$

This results in the passage speed:

${\displaystyle v_{\text{0}}={\frac {E}{B}}={\frac {\left|{\vec {E}}\right|}{\left|{\vec {B}}\right|}}}$

With the use of the vector product

With the help of Newton's second law, the following applies to movement in the field :

${\displaystyle \sum {\vec {F}}=m\,{\dot {\vec {v}}}=m\,{\vec {a}}=q\,({\vec {E}}+{\vec {v}}\times {\vec {B}})}$

Means non-distraction . ${\displaystyle \sum {\vec {F}}=m\,{\vec {a}}=0}$

${\displaystyle q\,{\vec {E}}=-q\,({\vec {v}}\times {\vec {B}})}$

If speed, electric field and magnetic field are perpendicular to each other, as required, the following applies:

${\displaystyle v_{\text{0}}={\frac {\left|{\vec {E}}\right|}{\left|{\vec {B}}\right|}}}$

Areas of application

Use of a Wien filter in a mass spectrometer

In order to filter out particles at a certain speed, the magnetic and electric fields must be adjusted accordingly. The speed of the particles that can pass the Wien filter at a certain magnetic flux density or electric field strength is known from the above relationship.

The mass and charge of the particles play no role in the function of the filter, as can be seen from the formulas.

In the case of a mass spectrometer, a speed filter usually selects particles of a certain (known) speed from an ion beam in order to then separate the different masses (e.g. by means of a magnetic field).

Velocity filters are often used in particle accelerators . Together with other electrostatic and magnetic filters, they form an often complex system for selecting particles of a certain mass, charge and speed.

Web links

• freepatentsonline: Vienna filter, United States Patent 4019989 (English)
• Java applet to demonstrate a Wien filter

Individual evidence

1. ↑ Lecture notes at the University of Essen (p. 13) (PDF; 1.7 MB)