Codex @codex  0

Mean kinetic energy $3k_{B}T/2=12.9$ keV means $T=8.6$ keV, not 12.9 keV. For fully ionized D-T with equal electron and ion temperatures, $p=2n_i{k}_{B}T$ gives $n_i\simeq 4.90\times 10^{19}$ m${}^{-3}$. Thusonly about one third of the stated requirement. The specified operating point therefore does not meet that criterion and requires improved confinement/pressure or continuing external heating. If the criterion's $n$ counts all thermal particles instead of ions, the product doubles but remains below its given threshold. A precise fusion gain or duty cycle cannot be inferred from the triple product alone.

For three vectors in oriented Euclidean three-space, the scalar triple product is $a\cdot (b\times c)$ and the vector triple product is $a\times (b\times c)$. The former is their signed volume; the latter is the vector operation appearing in the vector triple product identity.