# Electrostatic module

The EM-electrostatic module of PLASIMO calculates the electrostatic potential and the electric field distributions in plasma and dielectric materials with a specified dielectric permittivity. The volume and surface charge density profiles are user-specified. The custom expressions in PLASIMO allow any function of time to be specified.

Below are examples of steady-state and time-dependent electrostatic models.

## One dimensional electrostatic model

One dimensional model describing the potential distribution of a parallel plate. The grounded electrode is covered with dielectric with relative permittivity of 6. The volume charges are prescribed with uniform density of 3$$\cdot$$10-2 C m-3.

A time dependent amplitude modulated voltage is applied to the powered electrode. The exact specification of the applied voltage is shown on the screen-shot below:

Screen capture of 1D EM simulation. Calculated spatial potential distribution (left) and the applied time-dependent voltage (right).

## 1, 2 and 3 dimensional electrostatic models

The screen-shots below show electrostatic potential distribution solved in 1, 2 and 3 dimensions with prescribed volume and surface charge densities. The electrostatic potential is solved inside two materials with different relative dielectric permittivity: $$\epsilon_r$$ = 1.0 for the left region and $$\epsilon_r$$ = 6.0 for right region.

1, 2 and 3 dimensional calculations of the electrostatic potential