### 6.2.1 Operating principle

The operating principle of sector mass spectrometers is shown in Figure 6.3.

Figure 6.3: Operating principle of the 180° sector mass spectrometer

Neutral gas particles are ionized in an ion source through electron bombardment (Figure 6.4 a). The electrons thus generated with mass $m$ with a load $q$ pass through a potential gradient $U$ towards the magnetic sector field and at the same time take up the kinetic energy,

$E_{kin} = q \cdot U =\frac{m \cdot v^2}{2}$

Formula 6-1: Kinetic energy

i. e. they pass through the sector field at a

speed $v=\sqrt{\frac{2qU}{m}}$. Where the charge is identical,

the speed and thus the time required to pass a given distance depends on the mass. This is exploited directly by time-of-flight mass spectrometers for the purpose of separating masses. In sector field mass spectrometers, the ions describe a circular path in the homogeneous magnetic field caused by the Lorentz force which acts on the moving ions perpendicularly to the speed and perpendicularly to the magnetic field.

$F=q \cdot v \cdot B$

Formula 6-2: Lorentz force

This is used to calculate the radius of the path

$q \cdot v \cdot B = m \cdot v^2 / r$

Formula 6-3: Equilibrium of forces

This is used to calculate the radius of the path

$r=\frac{m \cdot v}{q \cdot B} \mbox{and with Formula 6.1} r=\sqrt{\frac{2mU}{qB^2}}$

The sector field mass spectrometers used for leak detectors are equipped with a permanent magnet which supplies a constant magnetic field and in Figure 6.3 is positioned perpendicular to the image plane. The spectrometers are adjusted in such a way that the trajectory of singly charged helium ions first passes through an orifice and then through the outlet slit and finally strikes the detector. All other molecules are unable to pass through the slit and are re-neutralized. The ion current measured for helium is proportional to the helium partial pressure. As can be seen from Formula 6-4, the radius of the path can be varied through the accelerating voltage $U$. In practice, use is restricted to deflecting not just 4helium but also ions with an $m/e$ ratio of 2 and 3 towards the outlet slit and so detect the gases hydrogen and 3helium.