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# Calculating Effective Pumping Speeds

Before we can calculate effective pumping speeds, we must know how pumping speed and conductances are combined. The raw equations and some examples are given in Combining Conductances. This section is simply an alternative, more pictorial approach.

It never hurts to “eyeball” the situation before you start number crunching. Here we use intuition to set outer limits of the EPS. The question we want to answer is: If we attach a 500L/sec pump via a 500 L/sec conductance port, what is the EPS from the chamber. But let us ease into that gently.

1. If a 500L/sec pump is connected by some infinite conductance port, would the gas notice the presence of the port?

Answer - No. The EPS from the chamber would be 500L/sec.

2. If two 500L/sec pumps are connected to the chamber by separate, infinite conductance ports, what would the EPS be?

Answer - 1000 L/sec. (500 L/sec + 500 L/sec)

3. If one 500L/sec pump is connected to the chamber via a 500L/sec port would the EPS be higher or lower than 500L/sec?

Answer - Lower. (We have put something between pump and chamber that will reduce the “ease” with which gas flows between them.)

Since we know the conductance and pumping speed are measured in the same units, the intuitive approach suggests

• adding pumping speed and conductance in series lowers the EPS
• adding pumping speeds in parallel increases the EPS

This sounds identical to the series/parallel connections of electrical capacitances. Indeed, pumping speeds and gas conductances are added using exactly the same mathematic forms as used in electrical capacitances. So, for series connection (that is, connecting a chamber to a pump via a port):

1/EPS = 1/PS + 1/C

PS = manufacturer's pumping speed (L/sec)
C = conductance of port (L/sec).

4. Now, we can calculate the EPS from the chamber which has a 500 L/sec pump attached via a 500L/sec port. Substituting the numbers in the equation above gives:

1/EPS = 1/500 + 1/500
1/EPS = 2/500
1/EPS = 1/250
EPS = 250 L/sec

That is, when a pumping speed and a conductance of equal value are connected, the EPS is half the quoted pumping speed.

5. Let us expand on our knowledge by asking: what is the EPS if we add an LN2 trap with 500L/sec conductance between the port and pump in the example above?

1/EPS = 1/500 + 1/500 + 1/500
1/EPS = 3/500
1/EPS = 1/167
EPS = 167 L/sec

Clearly, using the manufacturer's quoted pumping speed (500 L/sec) as the EPS (which is really 167L/sec) will causes serious errors in modeling the vacuum chamber's characteristics.

6. Make it ridiculous. Connect a 2000L/sec pump to a chamber by a 10 L/sec tube, what is the EPS?

1/EPS = 1/2000 + 1/10
1/EPS = 1/2000 + 200/2000
1/EPS = 201/2000
EPS = slightly less than 10 L/sec

### Conclusion

The critical fact to extract from this segment is:

The effective pumping speed never exceeds the value of the minimum conductance (or pumping speed) of the individual parts that are stacked together.

Expressed differently, if one component in the stack has a 10 L/sec conductance, the effective pumping speed cannot exceed 10 L/sec even if a 2,000,000 L/sec pump is used.