Isotope separation is the process of concentrating specific isotopes of a chemical element by removing other isotopes, for example separating natural uranium into enriched uranium and depleted uranium. This is the crucial process in the creation of a nuclear weapon.

Explanation
There are three types of isotope separation techniques:
The third type of separation is still experimental; practical separation techniques all depend in some way on the atomic mass. It is therefore generally easier to separate isotopes with a larger relative mass difference. For example deuterium has twice the mass of ordinary (light) hydrogen and it is generally easier to purify it than to separate uranium-235 from the more common uranium-238. On the other extreme, separation of fissile plutonium-239 from the common impurity plutonium-240, while desirable in that it would allow the creation of gun-type nuclear weapons from plutonium, is generally agreed to be impractical.
See also: Enriched uranium

Those based directly on the atomic weight of the isotope.
Those based on the small differences in chemical reaction rates produced by different atomic weights.
Those based on properties not directly connected to atomic weight, such as nuclear resonances. Separation techniques
All large-scale isotope separation schemes employ a number of similar stages which produce successively higher concentrations of the desired isotope. Each stage enriches the product of the previous step further before being sent to the next stage. Similarly, the tailings from each stage are returned to the previous stage for further processing. This creates a sequential enriching system called a cascade.
There are two important factors that affect the performance of a cascade. First is the separation factor (the square root of the mass ratio of the two isotopes), which is a number greater than 1. Second the number of required stages to get the desired purity.

Enrichment cascades
To date, large-scale commercial isotope separation of only three elements has occurred. In each case, the rarer of the two most common isotopes of an element has been concentrated for use in nuclear technology:
Isotope separation is an important process for both peaceful and military nuclear technology, and therefore the capability that a nation has for isotope separation is of extreme interest to the intelligence community.

Uranium isotopes have been separated to prepare enriched uranium for use as nuclear reactor fuel and in nuclear weapons.
Hydrogen isotopes have been separated to prepare heavy water for use as a moderator in nuclear reactors.
Lithium-6 has been concentrated for use in thermonuclear weapons. Commercial materials
The only alternative to isotope separation is to manufacture the required isotope in its pure form. This may be done by irradiation of a suitable target, but care is needed in target selection and other factors to ensure that only the required isotope of the element of interest is produced. Isotopes of other elements are not so great a problem as they can be removed by chemical means.
This is particularly relevant in the preparation of high-grade plutonium-239 for use in weapons. It is not in practice possible to separate Pu-239 from Pu-240 or Pu-241. Fissile Pu-239 is produced following neutron capture by uranium-238, but further neutron capture will produce non-fissile Pu-240 and worse, then Pu-241 which is a fairly strong neutron emitter. Therefore, the uranium targets used to produce military plutonium must be irradiated for only a short time, to minimise the production of these unwanted isotopes. Conversely, blending plutonium with Pu-241 renders it unsuitable for nuclear weapons.

Alternatives

Practical methods of separation
Often done with gases, but also with liquids, the diffusion method relies on the fact that in thermal equilibrium, two isotopes with the same energy will have different average velocities. The lighter atoms (or the molecules containing them) will travel more quickly and be more likely to diffuse through a membrane. The difference in speeds is proportional to the square root of the mass ratio, so the amount of separation is small and many cascaded stages are needed to obtain high purity. This method is expensive due to the work needed to push gas through a membrane and the many stages necessary.
The first large-scale separation of uranium isotopes was achieved by the United States in large gaseous diffusion separation plants at Oak Ridge Laboratories, which were established as part of the Manhattan Project. These used uranium hexafluoride gas as the process fluid, see gaseous diffusion.

Diffusion
Centrifugal effect schemes rapidly rotate the material allowing the heavier isotopes to go closer to an outer radial wall. This too is often done in gaseous form using a Zippe-type centrifuge.
Gas centrifuges using uranium hexafluoride have largely replaced gaseous diffusion technology for uranium enrichment. As well as requiring less energy to achieve the same separation, far smaller scale plants are possible, making them an economic possibility for a small nation attempting to produce a nuclear weapon. Pakistan is believed to have used this method in developing its nuclear weapons.
Vortex tubes were used by South Africa in their Helikon vortex separation process. The gas is injected tangentially into a chamber with special geometry that further increases its rotation to a very high rate, causing the isotopes to separate. The method is simple because vortex tubes have no moving parts, but energy intensive, about 50 times greater than gas centrifuges. A similar process, known as jet nozzle, was created in Germany, with a demonstration plant built in Brazil, and they went as far as developing a site to fuel the country's nuclear plants.

Centrifugal effect
This method is a form of mass spectrometry, and is sometimes referred to by that name. It uses the fact that charged particles are deflected in a magnetic field and the amount of deflection depends upon the particle's mass. It is very expensive for the quantity produced, as it has an extremely low throughput, but it can allow very high purities to be achieved. This method is often used for processing small amounts of pure isotopes for research or specific use (such as isotopic tracers), but is impractical for industrial use.
At Oak Ridge and at the University of California, Berkeley, Ernest O. Lawrence developed electromagnetic separation for much of the uranium used in the first United States atomic bomb (see Manhattan Project). Devices using his principle are named calutrons. After the war the method was largely abandoned as impractical. It had only been undertaken (along with diffusion and other technologies) to guarantee there would be enough material for use, whatever the cost. Its main eventual contribution to the war effort was to further concentrate material from the gaseous diffusion plants to even higher levels of purity.

Electromagnetic
In this method a laser is tuned to a wavelength which excites only one isotope of the material and ionizes those atoms preferentially. The resonant absorption of light for an isotope is dependent upon its mass and certain hyperfine interactions between electrons and the nucleus, allowing finely tuned lasers to only interact with one isotope. After the atom is ionized it can be removed from the sample by applying an electric field. This method is often abbreviated as AVLIS (atomic vapor laser isotope separation). This method has only recently been developed as laser technology has improved, and is currently not used extensively. However, it is a major concern to those in the field of nuclear proliferation because it may be cheaper and more easily hidden than other methods of isotope separation.
A second method of laser separation is known as MLIS, Molecular Laser Isotope Separation. In this method, an infrared laser is directed at uranium hexafluoride gas, exciting molecules that contain a U-235 atom. A second laser frees a fluorine atom, leaving uranium pentafluoride which then precipitates out of the gas. Cascading the MLIS stages is more difficult than with other methods because the UF₅ must be refluorinated (back to UF₆) before being introduced into the next MLIS stage. Alternative MLIS schemes are currently being developed (using a first laser in the near-infrared or visible region) where an enrichment of over 95% can be obtained in a single stage, but the methods have not (yet) reached industrial feasibility. This method is called OP-IRMPD (Overtone Pre-excitation - IR Multiple Photon Dissociation).
Finally, the SILEX process, developed by Silex Systems in Australia, has recently been licensed to General Electric for the development of a pilot enrichment plant. The method uses uranium hexafluoride as a feedstock, and uses magnets to separate the isotopes after one isotope is preferentially ionized. Further details of the process are unknown.

Laser
Although isotopes of a single element are normally described as having the same chemical properties, this is not strictly true. In particular, reaction rates are very slightly affected by atomic mass.
Techniques using this are most effective for light atoms such as hydrogen. Lighter isotopes tend to react or evaporate more quickly than heavy isotopes, allowing them to be separated. This is how heavy water is produced commercially, see Girdler sulfide process for details. Lighter isotopes also disassociate more rapidly under an electric field. This process in a large cascade was used at the heavy water production plant at Rjukan.
One candidate for the largest kinetic isotopic effect ever measured at room temperature, 305, may eventually be used for the separation of tritium (T). The effects for the oxidation of triated formate anions to HTO were measured as:

Chemical methods
Isotopes of Carbon, Oxygen, and Nitrogen can be purified by chilling these gases or compounds nearly to their liquification temperature in very tall columns (200 to 700 feet tall). The heavier isotopes sink and the lighter isotopes rise, where they are easily collected. The process was developed in the late 1960s by scientists at Los Alamos National Laboratory.[1] This process is also called "cryogenic distillation".[2]

Gravity
Separative Work Unit (SWU) is a complex unit which is a function of the amount of uranium processed and the degree to which it is enriched, ie the extent of increase in the concentration of the U-235 isotope relative to the remainder.
The unit is strictly: Kilogram Separative Work Unit, and it measures the quantity of separative work (indicative of energy used in enrichment) when feed and product quantities are expressed in kilograms. The effort expended in separating a mass F of feed of assay xf into a mass P of product assay xp and waste of mass W and assay xw is expressed in terms of the number of separative work units needed, given by the expression SWU = WV(xw) + PV(xp) - FV(xf), where V(x) is the "value function," defined as V(x) = (1 - 2x) ln ((1 - x) /x).
Separative work is expressed in SWUs, kg SW, or kg UTA (from the German Urantrennarbeit )
If, for example, you begin with 100 kilograms (220 pounds) of natural uranium, it takes about 60 SWU to produce 10 kilograms (22 pounds) of uranium enriched in U-235 content to 4.5%

1 SWU = 1 kg SW = 1 kg UTA
1 kSWU = 1.0 t SW = 1 t UTA
1 MSWU = 1 kt SW = 1 kt UTA