### 4.9.1.2 Holweck stage operating principle

A Holweck stage (Figure 4.26) is a multi-stage Gaede type molecular pump having a helical pump channel. Due to the rotation of the rotor, gas molecules entering the pump channel receive a stimulus velocity in the direction of the channel. Backflow losses occur through gaps between the barriers that separate the Holweck channels from each other and the rotor. The gap widths must be kept small to minimize backflow. Cylindrical sleeves (1) that rotate about helical channels in the stator (2) are used as Holweck stages. Arranging stators both outside as well as inside the rotor enables two Holweck stages to be easily integrated within one and the same pump. This means that the displaced gas particles are transported outside the rotor through the stator channel and then inside the rotor through further stator channels until they are conveyed back up to the backing pump through a collecting channel. Some modern turbopumps have several of these ”pleated“ Holweck stages.

The pumping speed $S_0$ of the Holweck stages is equal to:

\[S_0=\frac{1}{2} \cdot b \cdot h \cdot v \cdot \mbox{cos}\alpha \]

**Formula 4-12:** Holweck stage pumping speed

Where $b \cdot h$ is the channel cross section and $v \cdot \mbox{cos}\alpha$ the velocity component in the channel direction.

The compression ratio increases exponentially as a function of channel length $L$ and velocity $v \cdot \mbox{cos}\alpha$ [4]:

\[K_0=\frac{v \cdot \mbox{cos}\alpha \cdot L}{\bar{c} \cdot g \cdot h} \mbox{with 1 < g < 3}\]

**Formula 4-13:** Holweck stage compression ratio

The values yielded with this formula are not attained in real Holweck stages since backflow over the barrier from the neighboring channel dramatically reduces the compression ratio, and this influence is not taken into account in Formula 4-13.

To set up a turbo pumping station with diaphragm pumps with a
final pressure of between 0.5 and 5 hPa, turbopumps are today equipped
with Holweck stages. These kinds of pumps are termed turbo drag pumps.
Since only low pumping speeds are required to generate low base
pressures due to the high pre-compression of the turbopump, the
displacement channels and, in particular, both the channel height as
well as the clearances to the rotors can be kept extremely small, thus
still providing a molecular flow in the range of 1 hPa. At the same
time, this increases the compression ratios for nitrogen by the
required factor of 10^{3}. The shift of the compression ratio curves to
higher pressure by approximately two powers of ten can be seen from
Figure 4.27.

**Figure 4.27:** Compression ratios of pure turbopumps
and turbo drag pumps

For turbopumps which are designed for high gas throughput, a compromise is made where the gas throughput, fore-vacuum compatibility and particle tolerance are concerned and the distance between the gaps in the Holweck stages is increased.