  We study the dust surface potential for the complex dusty plasma with
negative ions and with a three-parameter non-Maxwell velocity distribution. The
plasma contains electrons, positive ions, negative ions, and negatively charged
dust particles. By using the current equilibrium condition, we derive the
relationship between the normalized dust surface potential and the dusty plasma
parameters such as the normalized dust number density, the temperature ratio of
negative ions to electrons, the density ratio of negative ions to positive
ions, and the charge number of negative ions. The numerical analyses show that
the relationship depends evidently on the three parameters in the non-Maxwell
distribution when the dust surface potential is relatively smaller, but with
increase of the potential, such dependence will weaken soon. The dust surface
potential is negative and increases monotonously with increase of the dust
density, and for the complex dusty plasma with the three-parameter non-Maxwell
distribution, it is generally greater than that in the same plasma with the
kappa-distribution and the Maxwellian distribution.
