A magnetically confined deuterium-tritium plasma has equal deuterium and tritium ion…

PHYSICS · Multi-part · Fermi University Physics · Plasma Physics · Fusion plasmas · Fusion plasmas

Energy from Physics, Ch Fusion as a power plant: gain, beta, wall loading and breeding

Problem

A magnetically confined deuterium-tritium plasma has equal deuterium and tritium ion densities and an ion temperature of

10\,\mathrm{keV}

. It is held at a plasma beta (plasma pressure over magnetic pressure) of

\beta = 0.025

in a magnetic field of

B = 6.0\,\mathrm{T}

. Take the Bosch-Hale fusion rate coefficient at

10\,\mathrm{keV}

\langle\sigma v\rangle = 1.14\times10^{-22}\,\mathrm{m^3\,s^{-1}}

and the energy released per D-T fusion as

17.6\,\mathrm{MeV}

. The plasma's total pressure is shared equally between ions and electrons of equal density

n

(the ion density,

n = n_D + n_T

). ((a)) Find the plasma pressure. ((b)) Find the total ion density

n

. ((c)) Find the fusion power density.