On the entropy of plasmas described with regularized κ\kappa-distributions

In classical thermodynamics the entropy is an extensive quantity, i.e.\ the sum of the entropies of two subsystems in equilibrium with each other is equal to the entropy of the full system consisting of the two subsystems. The extensitivity of entropy has been questioned in the context of a theoretical foundation for the so-called $\kappa$-distributions, which describe plasma constituents with power-law velocity distributions. We demonstrate here, by employing the recently introduced {\it regularized $\kappa$-distributions}, that entropy can be defined as an extensive quantity even for such power-law-like distributions that truncate exponentially.Comment: Preprint accepted for publication in Phys. Rev.

A criterion to discriminate between solar and cosmic ray forcing of the terrestrial climate

International audienceThere is increasing evidence that there exist interstellar-terrestrial relations and that the heliosphere's effectivity to serve as a protecting shield for the Earth, specifically against cosmic rays, is varying in time. Nonetheless, a debate is going on whether, amongst other drivers, the Sun or the cosmic rays are influencing the terrestrial climate, particularly on periods of hundred years and shorter. As the modelling of the transport of cosmic rays in the heliosphere has evolved from pure test particle simulations to far more consistent treatments, one can explain various correlations within the framework of physical models and one can make quantitative predictions regarding terrestrial indicators of interstellar-terrestrial relations. This level of understanding and modelling allows to identify a criterion with which one can discriminate between solar and cosmic ray forcing on a period of several decades. We define such a criterion and discuss related existing observations

MHD Simulation of the Inner-Heliospheric Magnetic Field

Maps of the radial magnetic field at a heliocentric distance of ten solar radii are used as boundary conditions in the MHD code CRONOS to simulate a 3D inner-heliospheric solar wind emanating from the rotating Sun out to 1 AU. The input data for the magnetic field are the result of solar surface flux transport modelling using observational data of sunspot groups coupled with a current sheet source surface model. Amongst several advancements, this allows for higher angular resolution than that of comparable observational data from synoptic magnetograms. The required initial conditions for the other MHD quantities are obtained following an empirical approach using an inverse relation between flux tube expansion and radial solar wind speed. The computations are performed for representative solar minimum and maximum conditions, and the corresponding state of the solar wind up to the Earths orbit is obtained. After a successful comparison of the latter with observational data, they can be used to drive outer-heliospheric models.Comment: for associated wmv movie files accompanying Figure 7, see http://www.tp4.rub.de/~tow/max.wmv and http://www.tp4.rub.de/~tow/min.wm

Electron holes in a regularized kappa background

The pseudopotential method is used to derive electron hole structures in a suprathermal plasma with a regularized κ probability distribution function background. The regularized character allows the exploration of small κ values beyond the standard suprathermal case for which κ&gt;3/2 is a necessary condition. We found the nonlinear dispersion relation yielding the amplitude of the electrostatic potential in terms of the remaining parameters, in particular the drift velocity, the wavenumber and the spectral index. Periodic, solitary wave, drifting and non-drifting solutions have been identified. In the linear limit, the dispersion relation yields generalized Langmuir and electron acoustic plasma modes. Standard electron hole structures are regained in the κ≫1 limit.</p

On the Role of Risk Aversion and Market Design in Capacity Expansion Planning

Investment decisions in competitive power markets are based upon thorough profitability assessments. Thereby, investors typically show a high degree of risk aversion, which is the main argument for capacity mechanisms being implemented around the world. In order to investigate the interdependencies between investors\u27 risk aversion and market design, we extend the agent-based electricity market model PowerACE to account for long-term uncertainties. This allows us to model capacity expansion planning from an agent perspective and with different risk preferences. The enhanced model is then applied in a multi-country case study of the European electricity market. Our results show that assuming risk-averse rather than risk-neutral investors leads to slightly reduced investments in dispatchable capacity, higher wholesale electricity prices, and reduced levels of resource adequacy. These effects are more pronounced in an energy-only market than under a capacity mechanism. Moreover, uncoordinated changes in market design may also lead to negative crossborder effects