Fluid theory for fluctuations in cold inhomogeneous plasmas

Abstract

The theory for potential surface wave fluctuation spectra in cold, inhomogeneous, magnetized plasmas is reconsidered, adopting a transition probability approach. A fluctuation dissipation relation is derived, which is valid for general density profiles and which reduces to the familiar fluctuation dissipation theorem for homogeneous plasmas. Significant corrections to previous work are found. Particular spectra are calculated for the special case of a magnetized plasma with a one-dimensional inhomogeneity.

Theory of Thermal Fluctuations for Leaking and Non Leaking Surface Waves

“…The results from the electrostatic calculation in Ref. [4] are easily recovered from the electroniagnetic theory presented here. m t Equation (2) is valid for isotropic temperatures, but can also be formulated for anisotropic temperatures, by slightly modifying the initial value term.…”

“…of the auto correlation functions have been taken and the initial value of (J1tr)(y, t ) Jl(r'f(~', t ' ) ) a t t = 1' has been included in the right hand side. Notice that the temperature enters in the calculation through the initial value term and that the pressure tern1 is negligible in this case, whereas in UDDHOLM [4] the temperature enters through the pressure term. This is only due to the different ways in which the initial value terms are introduced.…”

“…(5b) is obvious and Eq. (5c) can be derived in the sanie manner as in [4] for non leaking waves; the indices r' denote that the derivatives are to be taken with respect to r'. For leaking surface waves the electric fields need not decay so fast that the surface integrals, which arise in the partial integrations in the derivation of Eq.…”