Two arguments are quoted below

PHYSICS · Multi-part · Fermi University Physics · Nuclear Physics · Plasma Physics · Fission, fusion and nuclear energy

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

Problem

Two arguments are quoted below. Find the error in each. ((a)) "Deuterium-tritium fusion is used in preference to deuterium-deuterium because it releases more energy per reaction:

17.6\,\mathrm{MeV}

against a mean of

3.65\,\mathrm{MeV}

for the two

dd

branches, a factor of

4.8

. Since a bigger

Q

value means a deeper, more attractive nuclear interaction, the reaction should proceed faster, and this factor of

4.8

is roughly what should be seen in the cross sections at the same energy." ((b)) "The first capsule to produce more fusion energy than laser energy delivered

3.15\,\mathrm{MJ}

from

2.05\,\mathrm{MJ}

of laser input, with

\rho R = 1.3\,\mathrm{g\,cm^{-2}}

. Using

f_b = \rho R/(\rho R + H_B)

with

H_B = 7\,\mathrm{g\,cm^{-2}}

gives

f_b = 1.3/(1.3+7) = 16\,\mathrm{per\ cent}

. Working back from the

\approx 0.2\,\mathrm{mg}

of DT fuel and the measured yield gives a burn fraction of only about

5\,\mathrm{per\ cent}

. Since

5\,\mathrm{per\ cent}

is far below the

16\,\mathrm{per\ cent}

the formula predicts at the stated

\rho R

, and the shot still exceeded breakeven, the burn-fraction formula itself must be wrong for inertial capsules."

Related theory

Nuclear Physics

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