Plasma, often called the fourth state of matter, is a gas brought to temperatures high enough to free some of the electrons that were previously attached to the neutral atoms. Since a given volume of plasma contains approximately the same amount of free electrons as there is the excess positive charge, it is quasi-neutral. This condition is however violated if the control volume is smaller than that enclosed by a sphere of a certain critical radius. This critical radius is called the Debye Length and is defined as follows:

where e₀ is the permittivity of free space, given as 8.84x10^-12 C²/ (N*m²). The Debye Length is commonly used as the spatial parameter is computer simulation since quasi-neutrality condition allows for a simpler computational algorithm.

Plasma conducts electricity and as such, it responds to an electromagnetic field according to the Newton-Lorentz equations of motion:

where E is the electric field, V is the flow velocity and B is the magnetic field.

The vector equation immediately reveals that the plasma will accelerate in the direction of the electric field. The rotational force generated by the magnetic field is directed in a direction normal to the plane defined by the magnetic field and the velocity vector. Thus, it is possible to generate propulsive force by accelerating the heavier ions out of the spacecraft thruster using a high E field. This principle is used in electrostatic thrusters, which disregard the VxB component. The magnetic field is still employed in these thrusters, however, it is used to prevent the impingement of ions onto the thruster walls, since plasma cannot easily travel across the lines of the B field. The applied magnetic field is used in electromagnetic thrusters to generate the thrust using a self-induced current, however, this is out of the scope of currently ongoing research.

The electric field can also be rewritten using the gradient of the electric potential f:

Laplacian of which relates it to the charge density by the Poisson's equation:

NOTE: The force acting on two charged particles is given by the Coulomb's Law:

This relationship is seldom used in computer plasma simulation, due to the large number of computations required to obtain the force. A single time step in a system consisting of only 100 particles would require almost 10¹⁵⁸ applications of the Coulomb's Law. The number of particles used in a typical plasma simulation is often on the order of one million. Obviously, the time required to compute such a system using the Coulomb's Law would approach infinity.