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Pumping Speed

This error is easily exposed. Think of two identical pumps and chambers: one set is connected via a short, wide-diameter tube; the other is connected by a long, narrow tube. Which arrangement pumps the chamber faster and why?

From the first great principle, 'vacuum doesn't suck', we know that gas molecules enter the pumping mechanism via a series of random collisions with each other and with chamber walls. The narrower the tube, the lower the probability that a molecule will enter it. The longer the tube, the greater the chance of the molecule hitting a wall while passing through. But molecules, unlike light, do not bounce off walls at the same angle as they arrive. They are just as likely to bounce backward as forward.

That is, the shorter, wider connection gives the faster pump-down, since its higher conductance leads to a higher effective pumping speed from the chamber.

Effective Pumping Speed

• A 500L/s pump is connected to the chamber by some magical 'infinite' conductance port, would the pump's pumping speed be affected?

  
  Answer - No. EPS is 500 L/s

• Two 500L/s pumps are connected to the same chamber by separate, 'infinite' conductance ports, what is the EPS?
  

  Answer - EPS is 1000 L/sec.

• A 500L/s pump is connected to the chamber by a 500L/sec port, would the EPS be higher or lower than 500L/sec?
  

  Answer - Lower.

  This indicates that adding pumping speed and conductance in series lowers the overall pumping speed, while adding them in parallel increases the pumping speed. This sounds identical to the series/parallel connections of electrical capacitances. Indeed, pumping speeds (PS) and conductances (C) are added to give effective pumping speed (EPS) using exactly the same mathematic form as capacitances. To calculate series connection of chamber and pump noted above:

  1/EPS = 1/PS + 1/C

  Substituting the numbers from our initial example, we find 1/EPS = 1/500 + 1/500
  1/EPS = 2/500
  1/EPS = 1/250

  EPS = 250 liter per sec That is, when the pumping speed and conductance are of equal value, the effective pumping speed is half the quoted pumping speed. Newcomers to vacuum technology, and even some old-timers, are surprised by this number.
  
    Adding other components only worsens the problem. For example, what if we put an LN2 trap with 500L/sec conductance between the port and pump?

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

  EPS = 167 liter per sec

  Clearly, using the quoted PS as the effective PS will cause serious errors in estimating base pressure and pump down time.
  
    Now, we will take the ridiculous situation and connect a 2000L/sec pump to a chamber by a tube with 10L/sec conductance and calculate the EPS. 1/EPS = 1/2000 + 1/10
  1/EPS = 201/2000
  1/EPS = 1/9.95

  EPS = <10 liter per sec

Conclusions

One critical fact should be extracted from this segment. 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 10L/sec conductance, the effective pumping speed cannot exceed 10L/sec even if a 2,000,000L/sec pump is attached to it! (Remember - vacuum doesn't suck!

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