  An optically thin $p$-$^{11}$B plasma loses more energy to bremsstrahlung
than it gains from fusion reactions, unless the ion temperature can be elevated
above the electron temperature. In thermal plasmas, the temperature differences
required are possible in small Coulomb logarithm regimes, characterized by high
density and low temperature. The minimum Lawson criterion for thermal
$p$-$^{11}$B plasmas and the minimum $\rho R$ required for ICF volume ignition
are calculated. Ignition could be reached more easily if the fusion reactivity
can be improved with nonthermal ion distributions. To establish an upper bound
for this utility, we consider a monoenergetic beam with particle energy
selected to maximize the beam- thermal reactivity. Channeling fusion alpha
energy to maintain such a beam facilitates ignition at lower densities and
$\rho R$, improves reactivity at constant pressure, and could be used to remove
helium ash. The gains realized with a beam thus establish an upper bound for
the reductions in ignition threshold that can be realized with any nonthermal
distribution; these are evaluated for $p$-$^{11}$B and DT plasmas.
