  The Darwin approximation is investigated for its possible use in simulation
of electromagnetic effects in large size, high frequency capacitively coupled
discharges. The approximation is utilized within the framework of two different
fluid models which are applied to typical cases showing pronounced standing
wave and skin effects. With the first model it is demonstrated that Darwin
approximation is valid for treatment of such effects in the range of parameters
under consideration. The second approach, a reduced nonlinear Darwin
approximation-based model, shows that the electromagnetic phenomena persist in
a more realistic setting. The Darwin approximation offers a simple and
efficient way of carrying out electromagnetic simulations as it removes the
Courant condition plaguing explicit electromagnetic algorithms and can be
implemented as a straightforward modification of electrostatic algorithms. The
algorithm described here avoids iterative schemes needed for the divergence
cleaning and represents a fast and efficient solver, which can be used in fluid
and kinetic models for self-consistent description of technical plasmas
exhibiting certain electromagnetic activity.
