  We study an unconventional two-dimensional, two-component classical plasma on
a sphere, with emphasis on detecting signatures of melting transitions. This
system is relevant to Ising-type quantum Hall states, and is unconventional in
the sense that it features particles interacting via two different
two-dimensional Coulomb interactions. One species of particles in the plasma
carries charge of both types (Q_1,Q_2), while the other species carries only
charge of the second type (0,-Q_2). We find signatures of a freezing transition
at Q_1^2 approximately 140. This means that the species with charge of both
types will form a Wigner crystal, whereas the species with charge of the second
type also shows signatures of being a Wigner crystal, due to the attractive
inter-component interaction of the second type. Moreover, there is also a
Berezinskii-Kosterlitz-Thouless phase transition at Q_2^2 approximately 4, at
which the two species of particles bind to form molecules that are neutral with
respect to the second Coulomb interaction. These two transitions appear to be
independent of each other, giving a rectangular phase diagram. As a special
case, Q_2=0 describes the (conventional) two-dimensional one-component plasma.
Our study is consistent with previous studies of this plasma, and sheds new
light on the freezing transition of this system.
