currentconserving

Currentconserving, often written as current-conserving, is a term used to describe methods, models, or formulations that preserve electric current and, by extension, charge conservation in physical and numerical contexts. At its core, it denotes adherence to the continuity equation, ∂ρ/∂t + ∇·J = 0, which expresses the conservation of charge in space and time. In circuit theory, this parallels the idea behind Kirchhoff’s current law, while in electromagnetism and plasma physics it underpins stable and physically meaningful evolution of fields and charges.

In computational settings, current-conserving schemes deposit or update currents on a grid in a way that exactly satisfies the discrete continuity equation. This prevents artificial accumulation or depletion of charge, eliminates certain numerical artefacts, and improves long-time stability. Notable implementations include current deposition schemes used with particle-in-cell (PIC) and finite-difference time-domain (FDTD) methods. Classic examples are the Villasenor-Buneman current deposition and the Esirkepov algorithm, both designed to maintain local charge conservation across multidimensional grids.

Applications of current-conserving approaches span plasma physics, accelerator physics, laser–plasma interactions, and related areas where accurate evolution of charges and currents is critical. They help reduce numerical noise, mitigate self-forces on particles, and ensure reliable field growth and energy transfer over many time steps. Trade-offs can include increased computational complexity and stricter requirements on grid geometry and time stepping.

See also: charge conservation, continuity equation, Esirkepov current deposition, Villasenor-Buneman scheme, PIC, FDTD.