Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2016 / S4 / 1

A tokamak confines a hot, approximately toroidal plasma using a strong toroidal magnetic field and a poloidal field associated with plasma current and external coils. Helical field lines and suitable magnetic surfaces reduce rapid transverse escape. D-T fusion releases 17.6 MeV, mostly in an uncharged neutron that escapes magnetic confinement and transfers energy to a surrounding blanket. A heat exchanger and thermal power cycle convert some of that energy into electricity.

Essential systems include the vacuum vessel, toroidal and poloidal magnets, current-drive/transformer and auxiliary heating equipment, fueling and exhaust systems, divertor for concentrated heat and particle removal, neutron-absorbing/breeding blanket and shielding. Alpha particles retained in the plasma contribute self-heating. Confinement and controlled exhaust are as important as reaching a high temperature; a magnetic field does not confine the neutrons or make material heat loads vanish.

Lithium in the blanket breeds tritium through neutron reactions, notably ${}^6\mathrm{Li}+n\to {}^4\mathrm{He}+T$. Tritium is not abundant enough in nature to supply a large reactor fleet without breeding. The blanket must also transfer heat and manage neutron damage and losses, and the breeding ratio must exceed consumption after accounting for processing and inventory. Lithium is therefore a fuel-cycle resource rather than the primary charged plasma reactant in the D-T core.

Extraction energy is $6000\mathrm{kg}\times 2500\mathrm{kWh}\mathrm{k}{\mathrm{g}}^{-1}=15$ GWh per year. A continuously operating 2 GW electrical plant generates 17.5 TWh per year, so lithium extraction consumes about $\boxed{0.086\%}$ of its output under the stated estimate. This is energetically favorable even before claiming anything about capital costs or extraction feasibility.

For an ocean mass about $1.4\times 10^{21}$ kg, concentration 0.17 ppm implies about $2.4\times 10^{14}$ kg lithium. At the specified consumption/output ratio, a hypothetical 20 TW electric world would use $6\times 10^7$ kg annually, giving roughly $4\times 10^6$ years. For 3 TW the corresponding scale is $3\times 10^7$ years. State the assumed demand: “power the world” does not uniquely specify electric demand versus primary-energy use. These are inventory quotients ignoring growth, accessible fraction, ecological constraints and processing throughput.

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.