Exact aymptotic expansions for the thermodynamics of hydrogen gas in the Saha regime

We consider the hydrogen quantum plasma in the Saha regime, where it almost reduces to a partially ionized atomic gas. We briefly review the construction of systematic expansions of thermodynamical functions beyond Saha theory, which describes an ideal mixture of ionized protons, ionized electrons and hydrogen atoms in their ground-state. Thanks to the existence of rigorous results, we first identify the simultaneous low-temperature and low-density limit in which Saha theory becomes asymptotically exact. Then, we argue that the screened cluster representation is well suited for calculating corrections, since that formalism accounts for all screening and recombination phenomena at work in a more tractable way than other many-body methods. We sketch the corresponding diagrammatical analysis, which leads to an exact asymptotic expansion for the equation of state. That scaled low-temperature expansion improves the analytical knowledge of the phase diagram. It also provides reliable numerical values over a rather wide range of temperatures and densities, as confirmed by comparisons to quantum Monte Carlo data.Comment: 10 page

Helioseismic analysis of the hydrogen partition function in the solar interior

The difference in the adiabatic gradient gamma_1 between inverted solar data and solar models is analyzed. To obtain deeper insight into the issues of plasma physics, the so-called ``intrinsic'' difference in gamma_1 is extracted, that is, the difference due to the change in the equation of state alone. Our method uses reference models based on two equations of state currently used in solar modeling, the Mihalas-Hummer-Dappen (MHD) equation of state, and the OPAL equation of state (developed at Livermore). Solar oscillation frequencies from the SOI/MDI instrument on board the SOHO spacecraft during its first 144 days in operation are used. Our results confirm the existence of a subtle effect of the excited states in hydrogen that was previously studied only theoretically (Nayfonov & Dappen 1998). The effect stems from internal partition function of hydrogen, as used in the MHD equation of state. Although it is a pure-hydrogen effect, it takes place in somewhat deeper layers of the Sun, where more than 90% of hydrogen is ionized, and where the second ionization zone of helium is located. Therefore, the effect will have to be taken into account in reliable helioseismic determinations of the astrophysically relevant helium-abundance of the solar convection zone.Comment: 30 pages, 4 figures, 1 table. Revised version submitted to Ap

Correlations in two-component log-gas systems

A systematic study of the properties of particle and charge correlation functions in the two-dimensional Coulomb gas confined to a one-dimensional domain is undertaken. Two versions of this system are considered: one in which the positive and negative charges are constrained to alternate in sign along the line, and the other where there is no charge ordering constraint. Both systems undergo a zero-density Kosterlitz-Thouless type transition as the dimensionless coupling $\Gamma := q^2 / kT$ is varied through $\Gamma = 2$. In the charge ordered system we use a perturbation technique to establish an $O(1/r^4)$ decay of the two-body correlations in the high temperature limit. For $\Gamma \rightarrow 2^+$, the low-fugacity expansion of the asymptotic charge-charge correlation can be resummed to all orders in the fugacity. The resummation leads to the Kosterlitz renormalization equations.Comment: 39 pages, 5 figures not included, Latex, to appear J. Stat. Phys. Shortened version of abstract belo

Climatology of aerosol optical properties and black carbon mass absorption cross section at a remote high-altitude site in the western Mediterranean Basin

Aerosol light scattering (&sigma;_sp), backscattering (&sigma;_bsp) and absorption (&sigma;_ap) were measured at Montsec (MSC; 42°3' N, 0°44' E, 1570 m a.s.l.), a remote high-altitude site in the western Mediterranean Basin. Mean (±SD) &sigma;_sp, &sigma;_bsp and &sigma;_ap were 18.9 ± 20.8, 2.6 ± 2.8 and 1.5 ± 1.4 Mm⁻¹, respectively at 635 nm during the period under study (June 2011–June 2013). Mean values of single-scattering albedo (SSA, 635 nm), the scattering Ångström exponent (SAE, 450–635 nm), backscatter-to-scatter ratio (<i>B</i> / <i>S</i>, 635 nm), asymmetry parameter (<i>g</i>, 635 nm), black carbon mass absorption cross section (MAC, 637 nm) and PM_2.5 mass scattering cross section (MSCS, 635 nm) were 0.92 ± 0.03, 1.56 ± 0.88, 0.16 ± 0.09, 0.53 ± 0.16, 10.9 ± 3.5 m² g⁻¹ and 2.5 ± 1.3 m² g⁻¹, respectively. The scattering measurements performed at MSC were in the medium/upper range of values reported by Andrews et al. (2011) for other mountaintop sites in Europe due to the frequent regional recirculation scenarios (SREG) and Saharan dust episodes (NAF) occurring mostly in spring/summer and causing the presence of polluted layers at the MSC altitude. However, the development of upslope winds and the possible presence of planetary boundary layer air at MSC altitude in summer may also have contributed to the high scattering observed. Under these summer conditions no clear diurnal cycles were observed for the measured extensive aerosol optical properties (&sigma;_sp, &sigma;_bsp and &sigma;_ap). Conversely, low &sigma;_sp and &sigma;_ap at MSC were measured during Atlantic advections (AA) and winter regional anticyclonic episodes (WREG) typically observed during the cold season in the western Mediterranean. Therefore, a season-dependent decrease in the magnitude of aerosol extensive properties was observed when MSC was in the free troposphere, with the highest free-troposphere vs. all-data difference observed in winter and the lowest in spring/summer. The location of MSC station allowed for a reliable characterization of aerosols as a function of the main synoptic meteorological patterns. The SAE was the lowest during NAF and showed an inverse correlation with the outbreak intensity, indicating a progressive shift toward larger particles. Moreover, the strength of NAF episodes in the region led to a slope of the scattering vs. absorption relationship among the lowest reported for other mountaintop sites worldwide, indicating that MSC was dominated by dust aerosols at high aerosol loading. As a consequence, SSA showed a nearly monotonic increase with increasing particle concentration and scattering. The SAE was the highest during SREG, indicating the presence of polluted layers dominated by smaller particles. Correspondingly, the asymmetry parameter was lower under SREG compared with NAF. The MAC and MSCS were significantly higher during NAF and SREG compared to AA and WREG, indicating an increase of absorption and scattering efficiencies associated with the summer polluted scenarios. The optical measurements performed at the MSC remote site were compared with those simultaneously performed at a regional background station in the western Mediterranean Basin located at around 700 m a.s.l. upstream of the MSC station

Variability of aerosol optical properties in the Western Mediterranean Basin

Aerosol light scattering, absorption and particulate matter (PM) concentrations were measured at Montseny, a regional background site in the Western Mediterranean Basin (WMB) which is part of the European Supersite for Atmospheric Aerosol Research (EUSAAR). Off line analyses of 24 h PM filters collected with Hi-Vol instruments were performed for the determination of the main chemical components of PM. Mean scattering and hemispheric backscattering coefficients (@ 635 nm) were 26.6±23.2 Mm&lt;sup&gt;−1&lt;/sup&gt; and 4.3±2.7 Mm&lt;sup&gt;−1&lt;/sup&gt;, respectively and the mean aerosol absorption coefficient (@ 637 nm) was 2.8±2.2 Mm&lt;sup&gt;−1&lt;/sup&gt;. Mean values of Single Scattering Albedo (SSA) and Ångström exponent (&lt;i&gt;å&lt;/i&gt;) (calculated from 450 nm to 635 nm) at MSY were 0.90±0.05 and 1.3±0.5 respectively. A clear relationship was observed between the PM&lt;sub&gt;1&lt;/sub&gt;/PM&lt;sub&gt;10&lt;/sub&gt; and PM&lt;sub&gt;2.5&lt;/sub&gt;/PM&lt;sub&gt;10&lt;/sub&gt; ratios as a function of the calculated Ångström exponents. Mass scattering cross sections (MSC) for fine mass and sulfate at 635 nm were 2.8±0.5 m&lt;sup&gt;2&lt;/sup&gt; g&lt;sup&gt;−1&lt;/sup&gt; and 11.8±2.2 m&lt;sup&gt;2&lt;/sup&gt; g&lt;sup&gt;−1&lt;/sup&gt;, respectively, while the mean aerosol absorption cross section (MAC) was 10.4±2.0 m&lt;sup&gt;2&lt;/sup&gt; g&lt;sup&gt;−1&lt;/sup&gt;. The variability in aerosol optical properties in the WMB were largely explained by the origin and ageing of air masses over the measurement site. The MAC values appear dependent of particles aging: similar to the expected absorption cross-section for fresh emissions under Atlantic Advection episodes and higher under aerosol pollution episodes. The analysis of the Ångström exponent as a function of the origin the air masses revealed that polluted winter anticyclonic conditions and summer recirculation scenarios typical of the WMB led to an increase of fine particles in the atmosphere (&lt;i&gt;å&lt;/i&gt; = 1.5±0.1) while the aerosol optical properties under Atlantic Advection episodes and Saharan dust outbreaks were clearly dominated by coarser particles (&lt;i&gt;å&lt;/i&gt; = 1.0±0.4). The sea breeze played an important role in transporting pollutants from the developed WMB coastlines towards inland rural areas, changing the optical properties of aerosols. Aerosol scattering and backscattering coefficients increased by around 40 % in the afternoon when the sea breeze was fully developed while the absorption coefficient increased by more than 100 % as a consequence of the increase in the equivalent black carbon concentration (EBC) observed at MSY under sea breeze circulation

Surface correlations for two-dimensional Coulomb fluids in a disc

After a brief review of previous work, two exactly solvable two-dimensional models of a finite Coulomb fluid in a disc are studied. The charge correlation function near the boundary circle is computed. When the disc radius is large compared to the bulk correlation length, a correlation function of the surface charge density can be defined. It is checked, on the solvable models, that this correlation function does have the generic long-range behaviour, decaying as the inverse square distance, predicted by macroscopic electrostatics. In the case of a two-component plasma (Coulomb fluid made of two species of particles of opposite charges), the density correlation function on the boundary circle itself is conjectured to have a temperature-independent behaviour, decaying as the -4 power of the distance.Comment: 15 pages, Latex, submitted to J.Phys.:Condens.Matte