On cubic non-linearities in fluid and kinetic models

The kinetic origin of the cubic terms found in electromagnetic reduced fluid models of magnetized plasmas is identified and analyzed. The transition from cartesian to guiding center variables in kinetic systems is responsible for the introduction of such cubic terms, and the derivation of a set of such terms is explicitly shown. The role of these terms in fluid simulations, and their importance for energy conservation of cubic terms in both frameworks is discussed