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The Darwin approximation is investigated for its possible use in simulationof electromagnetic effects in large size, high frequency capacitively coupleddischarges. The approximation is utilized within the framework of two differentfluid models which are applied to typical cases showing pronounced standingwave and skin effects. With the first model it is demonstrated that Darwinapproximation is valid for treatment of such effects in the range of parametersunder consideration. The second approach, a reduced nonlinear Darwinapproximation-based model, shows that the electromagnetic phenomena persist ina more realistic setting. The Darwin approximation offers a simple andefficient way of carrying out electromagnetic simulations as it removes theCourant condition plaguing explicit electromagnetic algorithms and can beimplemented as a straightforward modification of electrostatic algorithms. Thealgorithm described here avoids iterative schemes needed for the divergencecleaning and represents a fast and efficient solver, which can be used in fluidand kinetic models for self-consistent description of technical plasmasexhibiting certain electromagnetic activity.

Simulations of electromagnetic effects in high frequency capacitively coupled discharges using the Darwin approximation