A tokamak held at a fixed field and beta is to burn an equal mixture of deuterium and…

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 tokamak held at a fixed field

B

and beta

\beta

is to burn an equal mixture of deuterium and helium-3 at

100\,\mathrm{keV}

instead of deuterium-tritium at

10\,\mathrm{keV}

. Helium-3 carries charge

2

, so each helium-3 ion brings two electrons. Take the plasma pressure as

p = (n + n_e)k_BT

, with

n

the total ion density,

n_e

the electron density, and ions and electrons at the same temperature. The rate coefficients are

1.14\times10^{-22}\,\mathrm{m^3\,s^{-1}}

for deuterium-tritium at

10\,\mathrm{keV}

and

1.7\times10^{-22}\,\mathrm{m^3\,s^{-1}}

for deuterium-helium-3 at

100\,\mathrm{keV}

. Each deuterium-tritium fusion releases

17.6\,\mathrm{MeV}

and each deuterium-helium-3 fusion

18.3\,\mathrm{MeV}

. ((a)) Find the ratio of the deuterium-helium-3 fusion power density to the deuterium-tritium one at the same pressure. ((b)) At

\beta = 0.03

and ITER's

5.3\,\mathrm{T}

, deuterium-tritium at

10\,\mathrm{keV}

gives about

0.9\,\mathrm{MW\,m^{-3}}

. What field would deuterium-helium-3 at

100\,\mathrm{keV}

need, at the same

\beta

, to give the same power density? ((c)) At that field the two plasmas give the same fusion power per cubic metre. Deuterium-tritium sends

80

per cent of it out as neutrons, and deuterium-helium-3, through side deuterium-deuterium reactions, under

5

per cent. Find the largest ratio of their neutron powers per cubic metre, and say what the saving in neutrons has been bought with.