# How many cetrafuges?

1. May 6, 2008

Dear All
How many U235 Centrafuges we need to produce nuclear weapon? and for how long they will work in cascade to produce a bomb? Is there any formula or equations for that?

Best regards

2. May 6, 2008

Staff Emeritus
You can use one. If you are willing to wait long enough.

I don't think you will find many people who are willing to explain to you how to build your very own working nuclear device.

3. May 6, 2008

### humanino

:uhh:
We can discuss the principles of nuclear weapons, but I have no clue what a centrafuge is.

4. May 6, 2008

### vanesch

Staff Emeritus
The formula for "units of separation work" given an inflow with concentration x_f, a desired product concentration x_p and a waste concentration x_w is given by:

USW = P V(x_p) + W V(x_w) - F V(x_f)

with V(x) = (1-2x) log((1-x)/x)

and P, W and F the respective quantities of product, waste and feed (input). Of course, F = W + P, and we also have that W = (x_p - x_f) / (x_f - x_w) P

See http://en.wikipedia.org/wiki/Isotope_separation

So, you have your natural uranium concentration, x_f = 0.007 (0.7% is U-235). You have your desired product concentration x_p (say, 80%). Now you have to pick your waste concentration yourself. The lower it is, the less natural uranium you'll need, but the more separation work you will have to do. Say you put x_w = 0.0025.

Say you need 200 kg of 80% U-235. That means that you will have 35200 kg of waste, and hence you need 35 400 kg of natural uranium.
If you pick your waste concentration to be 0.0005, you will only need 24 600 kg of uranium.

However, for the first case, you will need 37 000 "units of separation work", while in the second case, you will need 65240 "units of separation work".

A given centrifuge or diffusion apparatus will correspond to a certain amount of "units of separation work" it can do per week, month or year, and the above quantities will then indicate how many of them you need to do the work in one week, month or year, or, on the other hand, how many weeks, months or years you will need to do the work with one centrifuge.

To give you an idea, the French Pierlatte factory has a total potential of about 11 million "units of separation work" per year.

Last edited: May 6, 2008
5. May 9, 2008

### BishopUser

A single centrifuge might produce about 30 grams of HEU per year, about the equivalent of five Separative Work Unit (SWU). As as a general rule of thumb, a cascade of 850 to 1,000 centrifuges, each 1.5 meters long, operating continuously at 400 m/sec, would be able to produce about 20-25 kilograms of HEU in a year, enough for one weapon. One such bomb would require about 6,000 SWU.

according to:
http://www.globalsecurity.org/wmd/intro/u-centrifuge.htm