use a 9-point difference equation for Poisson's equation (suggested by M. Greenberg) as given in Appendix A. The A clouds-interacting-with-clouds, clouds-in-cells method (CIC) is presented for many-body nonlinear plasma problems. Density and motion of the individual charged particles is obtained by force are obtained by assuming that the particles have finite size,
integrating the Newton-Lorentz equation, are tenuous, and may pass through one another; the particles are thus called clouds. They obey a Coulomb force (ȁ1/r or 1/r 3 ) when separated and a linear force (ȁr ) when overlapping, allowing simple harmonic oscillations at small separation. CIC is contrasted with
the zero-size particle and nearest-grid-point approach, ZSP-NGP. CIC appears to have substantially less unwanted noise than ZSP-NGP and should be more useful in simulating dense plasmas. Initial runs have been encouraging. The methods may find use in other The electric field E is Ϫٌ. The magnetic field B is the many-body simulations, such as with stars, or with particles in phase applied field, given analytically. This integration uses the space. ᮊ 1969 Academic Press orbit fitting scheme given by Hockney .
The special problem addressed here is how to convert charge positions into charge density, and then how to ob-1 This work was performed under the auspices of the U.S. Atomic monic oscillation frequency for small perturbations from Energy Commission.