Fokker-Planck equation for a test-particle weakly coupled to a magnetized plasma

We consider the derivation of a kinetic equation for a charged test particle weakly interacting with an electrostatic plasma in thermal equilibrium, subject to a uniform external magnetic field. The Liouville equation leads to a generalized master equation to second order in the `weak' interaction; a Fokker-Planck-type equation then follows as a `Markovian' approximation. It is shown that such an equation does not preserve the positivity of the distribution function f(x,v;t). By applying techniques developed in the theory of open systems, a correct Fokker-Planck equation is derived. Explicit expressions for the diffusion and drift coefficients, depending on the magnetic field, are obtained.

nero- a post-maximum supernova radiation transport code

The interpretation of supernova (SN) spectra is essential for deriving SN ejecta properties such as density and composition, which in turn can tell us about their progenitors and the explosion mechanism. A very large number of atomic processes are important for spectrum formation. Several tools for calculating SN spectra exist, but they mainly focus on the very early or late epochs. The intermediate phase, which requires a non-local thermodynamic equilibrium (NLTE) treatment of radiation transport has rarely been studied. In this paper, we present a new SN radiation transport code, nero, which can look at those epochs. All the atomic processes are treated in full NLTE, under a steady-state assumption. This is a valid approach between roughly 50 and 500days after the explosion depending on SN type. This covers the post-maximum photospheric and the early and the intermediate nebular phase. As a test, we compare nero to the radiation transport code of Jerkstrand, Fransson & Kozma and to the nebular code of Mazzali et al. All three codes have been developed independently and a comparison provides a valuable opportunity to investigate their reliability. Currently, nero is one-dimensional and can be used for predicting spectra of synthetic explosion models or for deriving SN properties by spectral modelling. To demonstrate this, we study the spectra of the 'normal' Type Ia supernova (SN Ia) 2005cf between 50 and 350 days after the explosion and identify most of the common SN Ia line features at post-maximum epochs. © 2011 The Authors Monthly Notices of the Royal Astronomical Society © 2011 RAS.