Numerical Simulation About The Electric Field Environment Of The Lunar Surface

In this paper, we have simulated the electrical field environment of the lunar surface in depth. Different kinds of sheaths are formed on the lunar surface for the different space environment. Even for the same kind of sheath, because of different angles the photons flux hitting the Moon, electrical field environment is different from each other.The Moon stays in the solar wind, so the Bohm sheath is formed on the lunar surface. The electrons in the solar wind hit the surface and make the potential of the surface to be negative. On the day-side of the Moon, because of photons to the surface, photoelectric effect is happened, and which will increase the potential of lunar surface. According to these conditions, we model three kinds of sheaths: sheath A, which have a potential barrier; sheath B in which the potential decreases monotonically, and the photoelectrons play the domain role; sheath C in which the potential increases monotonically. We get the densities of different particles in the condition that the electrons and photoelectrons satisfy half-Maxwellian distribution. By derivation, we get the boundary condition equations, Poisson's equation and the expression of electrical field intensity for every sheath model.Some of parameters in the sheath models are unknown, but they can be solved by boundary condition equations. After all parameters obtained, we can get the electrical potential and electrical field intensity by solving the Poisson's equation with Runge-Kutta method. We change the density of photoelectrons on the lunar surface to simulate the different angle of photons hitting the Moon. By numerical simulation and data analysis, we believe that on the night-side of the Moon, sheath C is formed and the angle of photons hitting the Moon has large impact on the electrical potential and electrical field intensity. On the day-side, both sheath A B and C could be formed. When the photoelectrons density at origin is small, sheath C will be formed; when n_p,ogrows bigger, both sheath A and B could be formed. For the sheath which contains a smaller energy is more stable. Then we can compute the potential energy to decide which sheath would be formed. We also find the Mach number M has a great influence on the sheath A. Combining the range of n(p,o), we can give the critical curve between A B and C for different n(p,o) and M.