It has been suggested that fusion reactors are safe from...

It has been suggested that fusion reactors are safe from explosion because the plasma never contains enough energy to do much damage. (a) In $1992,$ the TFTR reactor achieved an ion temperature of $4.0 \times 10^{8} \mathrm{K},$ an ion density of $2.0 \times 10^{13} \mathrm{cm}^{-3},$ and a confinement time of 1.4 s. Calculate the amount of energy stored in the plasma of the TFTR reactor. (b) How many kilograms of water could be boiled away by this much energy? The plasma volume of the TFTR reactor is approximately 50 $\mathrm{m}^{3}$ .

Key Concepts

Plasma Thermal Energy

In a fusion reactor, the plasma contains energy primarily in the form of the random kinetic energy of its particles. This thermal energy is a measure of the total internal energy due to the high-speed motion of the ions and electrons, which is directly related to the temperature of the plasma. Evaluating the energy content of the plasma involves understanding the relationship between particle density, temperature, and the total volume of the plasma, similar to the way one would calculate the internal energy for an ideal gas.

Thermal Energy Calculation

The calculation of thermal energy in a plasma is typically based on kinetic theory, using formulas derived from the ideal gas law. The energy can be estimated via expressions like (3/2)n k T per particle where n is the particle density, k is Boltzmann’s constant, and T is the temperature. Multiplying by the total number of particles within the plasma volume allows one to determine the total stored energy. This method links microscopic particle behavior to macroscopic energy measurements.

Energy Conversion and Latent Heat

Converting the stored thermal energy of a plasma into an equivalent mass of water that could be vaporized involves applying principles of energy conversion and thermodynamics. Specifically, one uses the latent heat of vaporization for water to determine how much energy is needed to boil a given mass. This approach illustrates the broader concept of energy equivalence, connecting high-temperature plasma physics with everyday thermal processes such as boiling water.

Fusion Reactor Safety Considerations

Fusion reactors are considered intrinsically safe with respect to explosive hazards because the total energy stored in the plasma is relatively low compared to conventional chemical explosives. Even in scenarios where the plasma energy might be suddenly released, the amounts involved are insufficient to produce a large-scale explosion. This safety feature arises from both the nature of the plasma confinement and the controlled conditions maintained during fusion operations.

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