 Solution

The supplied confinement criterion alone fixes a product, not a unique current or machine size. Choose a representative ion density $n_i=10^{20}{\mathrm{m}}^{-3}$. ThenFor $n_i=10^{19}$ to $10^{21}{\mathrm{m}}^{-3}$, the same criterion gives $\tau \gtrsim 10$ to $0.1\mathrm{s}$. These are illustrative density choices, not additional source data.

For a current estimate, assume a large-aspect-ratio circular tokamak with major radius $R_0=3\mathrm{m}$, minor radius $a=1\mathrm{m}$, toroidal field $B_{\varphi }=5\mathrm{T}$ and edge tokamak safety factor $q_s\simeq 3$. The geometrical winding relation and Ampère's law giveFor the stated assumptions,so toroidal plasma currents of order megaamperes are a natural scale. As a consistency check at $T\sim 10^8\mathrm{K}$, quasineutral singly charged heavy hydrogen has total thermal pressure $p\simeq 2n_i{k}_{B}T\simeq 2.8\times 10^5\mathrm{Pa}$. With $5\mathrm{T}$, $2{\mu }_{0}p/B^2\simeq 0.028$, so the assumed magnetic pressure exceeds the thermal pressure. The particular current depends on geometry and field-line pitch; it cannot be inferred from the confinement product alone.