  Random electromagnetic fields are ubiquitous in plasmas, the most common
example being electromagnetic radiation of thermal origin. They should exert a
random force on electrons and ions in a plasma, adding a random component to
their motion. Products of randomly fluctuating quantities, such as velocity and
magnetic field, which are correlated through the dynamical equations of the
two-fluid model of plasma, should then exhibit non-zero average values.
Investigation of such effects requires spatial-spectral representation of the
non-linear equations of the two-fluid model. Chandrasekhar-Kendall (CK)
functions, their generating function and its gradient defined over an infinite
domain are shown to simultaneously provide orthogonal basis for solenoidal,
scalar and irrotational fields respectively, facilitating transformation from
coordinate space to mode number space and back. This paper constructs a
theoretical framework for studying coherent effects of random forces due to
random electromagnetic fields in a two-fluid plasma and discusses some results
which follow from its structure. Azimuthally symmetric modes are shown to be
the sole beneficiaries of the cooperation of random modes in generating
non-random effects. The formalism also facilitates investigation of the
interaction between compressible dynamics, which plays a central role in plasma
compression, heating and confinement and incompressible dynamics, which is
involved in phenomena like turbulence and self-organization.
