Review problem. To confine a stable plasma, the magnetic...

Review problem. To confine a stable plasma, the magnetic energy density in the magnetic field (Eq. 32.14$)$ must exceed the pressure 2$n k_{\mathrm{B}} T$ of the plasma by a factor of at least $10 .$ In this problem, assume a confinement time $\tau=1.00 \mathrm{s}$ . (a) Using Lawson's criterion, determine the ion density required for the D-T reaction. (b) From the ignition-temperature criterion, determine the required plasma pressure. (c) Determine the magnitude of the magnetic field required to contain the plasma.

Key Concepts

Ignition Temperature Criterion

The ignition temperature criterion specifies the minimum temperature at which a fusion plasma will become self-sustaining—meaning that the energy produced from the fusion reactions is sufficient to overcome losses without external heating. It is a critical parameter in fusion research, as reaching or surpassing this temperature is necessary for 'ignition' and continuous energy production.

Magnetic Energy Density

Magnetic energy density refers to the amount of energy stored in a magnetic field per unit volume, expressed as B²/(2??), where B is the magnetic field magnitude and ?? is the permeability of free space. In confined plasma systems, sufficient magnetic energy density is crucial to counterbalance the plasma pressure and maintain stability, ensuring the plasma remains confined.

D-T Fusion Reaction

The deuterium-tritium (D-T) fusion reaction is one of the most researched fusion processes due to its relatively high reaction cross-section at achievable temperatures. It involves fusing a deuterium nucleus with a tritium nucleus to produce helium, a neutron, and a significant amount of energy, making it a primary candidate for controlled fusion power generation.

Lawson Criterion

The Lawson criterion establishes the minimum conditions necessary for a fusion reaction to achieve net energy output. It relates the plasma density and the energy confinement time (n?) to the temperature and reaction cross-section. In essence, it requires that the product of density and confinement time must exceed a certain threshold to ensure that the energy produced from the fusion reactions is greater than the energy losses, making a reactor viable.

Plasma Pressure

Plasma pressure is the force per unit area exerted by the high-energy particles in the plasma and is typically given by expressions such as 2n kB T, where n is the particle density, kB is the Boltzmann constant, and T is the temperature. It is a key parameter in plasma stability studies because it influences the balance against magnetic forces in a confined system.

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