Control variate hybrid particle-in-cell method with exact energy conservation

Kinetic plasma simulations based on the particle-in-cell (PIC) technique routinely employ control variates to reduce deleterious marker particle noise in fluid moment computations. However, when using the standard delta-f technique, noise reduction comes at the cost of unphysical total energy errors. We will report on a new approach to the delta-f PIC method in the context of a collisionless hybrid fluid electron - kinetic ion system that preserves total energy exactly. To achieve exact conservation, the method is deduced from a continuous-time particle discretization that modifies the electron pressure evolution equation with small, low-noise counterterms. Time is then discretized using a skew-gradient method. Notably, the scheme conserves the variance-reduced total energy, and not the standard full-f energy expression.