A magnetic-confinement design point operates at electron/ion density

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

The Nucleus Resolved, Ch Fusion: the cross section computed and the power balance made honest

Problem

n = 8\times10^{19}\,\mathrm{m^{-3}}

, energy confinement time

\tau_E = 2.1\,\mathrm{s}

and temperature

k_BT = 12\,\mathrm{keV}

. At this temperature the ignition triple product (from the power balance with

\alpha

-particle heating alone) is

n\tau_Ek_BT|_{\rm ignition} = 2.8\times10^{21}\,\mathrm{m^{-3}\,s\,keV}

. ((a)) Calculate the achieved triple product

n\tau_Ek_BT

of the design point. ((b)) State whether the device reaches ignition and by what factor it falls short or exceeds the requirement.