  Slow solitary positive-potential peaks sustained by trapped electron deficit
in a plasma with asymmetric ion velocity distributions are in principle
asymmetric, involving a potential change across the hole. It is shown
theoretically how to construct such asymmetric electron holes, thus providing
fully consistent solutions of the one-dimensional Vlasov-Poisson equation for a
wide variety of prescribed background ion velocity distributions. Because of
ion reflection forces experienced by the hole, there is generally only one
discrete slow hole velocity that is in equilibrium. Moreover the equilibrium is
unstable unless there is a local minimum in the ion velocity distribution, in
which the hole velocity then resides. For stable equilibria with Maxwellian
electrons, the potential drop across the hole is shown to be
$\Delta\phi\simeq{2\over 9}f'''{T_e\over e}({e\psi\over m_i})^2$, where $\psi$
is the hole peak potential, $f'''$ is the third derivative of the background
ion velocity distribution function at the hole velocity, and $T_e$ the electron
temperature. Potential asymmetry is small for holes of the amplitudes usually
observed, $\psi\lesssim 0.5T_e/e$.
