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You're referencing the Chernobyl accident, which actually didn't even have a containment structure. Now I'm sure you've probably heard many comparisons to the Three Mile Island and Chernobyl accidents in past few days. If you don't mind, I'd like to illustrate how each of these reactor accidents relates to the Japanese problems.
While these two events are often lumped together, they were the results of very different phenomenon and had very different effects. The Chernobyl accident was a true disaster, resulted in a serious threat to the local public, and lead to numerous fatalities. The reactor was destroyed and the surrounding region was scarred. Three mile island, on the other hand, was posed little threat to the public and resulted in only a small release of radioactivity when during a ventilation process. The Three Mile Island plant actually still operates to this day.
In the case of Three mile island, this comparison is quite fair. As is the case now, difficulty at three mile island stemmed from trouble providing cooling water to the core following pump failure and lead to a partial meltdown. In japan's case, the primary pumps were lost when the plant was isolated from the power grid during the earthquake. When the plant was isolated from the power grid, the reactor was "scramed" which means that control rods were inserted into the core to prevent further fission.
Had the earthquake been the only tribulation, all would have been fine and dandy because there are diesel powered backup pumps which kicked on in response to this sort of situation, cooling the core to remove what is called "decay heat". Decay heat is heat generation (orders of magnitude lower than heat generation in normal operations) from the radioactive materials in the pressure vessel which continues for a finite amount of time after shutdown. However, in the tsunami following the earthquake, many of these pumps were disabled and since then, there has been difficulty providing coolant to the core to remove this decay heat. As a result, some "fuel rods" have been damaged and a portion of the fuel may have melted. While this means that the reactor will probably never run again, it isn't the sort of disaster many people think of. As with the case of three mile island, there is likely little threat posed to the public.
The difficulties with the Japanese reactors is very different from what happened in the reactor at Chernobyl. The trouble facing the Japanese reactors is providing coolant to remove decay heat from the core. The trouble at Chernobyl was what is called a "run away criticality accident". This occurs when the fission rate increases with increasing reactor temperature. This is a result of the core geometry and materials used. What was particularly troublesome was the use of graphite moderator/water coolant combination. As you might guess, more fission means more heat, which leads to higher temperatures, which in turn leads to even more fission! When this configuration was achieved, within a very short period of time, the reactor exploded. As I mentioned previously, the Chernobyl reactor had no containment structure, only a containment building so there was little to prevent radiation material from escaping into the environment.
The reactors distressed in japan and any reactor in the United States have been engineered such that this could never happen. Beyond a certain operating temperature, any further increase in temperature will lead to a REDUCED fission rate, which in turn reduces to temperature to the operation temperature. It's conceptually similar to how the cruise control works in a car. This achieved by using water as a coolant AND moderator. As water is boiled, density drops, moderation decreases,and fewer fissions can occur. But the problem now isn't fission, its decay heat.
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