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I have been reading about nuclear fusion, and tokamak reactors, and I have a question: how do they achieve the high temperatures of several hundred million degrees? I know that in a hydrogen bomb, which uses fusion,. the use atomic bombs to generate the temperatures to initiate the fusion process. But I do not think that they use atomic bomb blasts in a controlled reactor. So by what means do they use to achieve these spectacular temperatures? to start the fusion reaction?

In tokomak's, heating up to a million degrees or more is usually accomplished by resistance (ohmic) heating, just as a wire is heated by passing current through it. In this case the current is generated by coils which induce a current in the plasma. This type of heating is sometimes referred to as I^2 R heating from the formula P=I^2 R. This says that the heating is proportional to the square of the induced current and directly proportional to the resistance. One problem with this method of heating is that the resistance of the plasma can become too small as the plasma temperature increases to allow sufficient heating. Thus supplemental heating is sometimes required. Supplemental heat can be provided by techniques such as: magnetic compression, neutral beam injection, magnetic pumping, laser beam heating, electron beam heating, ion beam heating, or microwave (or radio frequency) radiation. Primarily, though, ohmic heating is the answer to your question.

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