δf Algorithm

The ?f Algorithm is a low noise particle code algorithm. The perturbation of the distribution function (?f) away from a large equilibrium is evolved rather than the total distribution function. "Particles" in the code are actually Lagrangian markers at which the value of the distribution function is known, The magnitude of the numerical noise is characteristic of the size of the perturbation rather than the equilibrium and scales roughly as the inverse of the number of particles, In this paper, the algorithm is described, and conserved energies are derived for linear and nonlinear sets of equations. Two different forms of the energy principle test separately adequate resolution in time and space and adequacy of the number of simulation particles. A semi-implicit time step method is described which allows violation of the Courant condition. Low noise capabilities of a linear code using the algorithm are demonstrated.