It is well known that classical varieties of $\Sigma$ -algebras correspond bijectively to finitary monads on $\mathsf{Set}$ . We present an analogous result for varieties of ordered $\Sigma$ -algebras, that is, categories of algebras presented by inequations between $\Sigma$ -terms. We prove that they correspond bijectively to strongly finitary monads on $\mathsf{Pos}$ . That is, those finitary monads which preserve reflexive coinserters. We deduce that strongly finitary monads have a coinserter presentation, analogous to the coequalizer presentation of finitary monads due to Kelly and Power. We also show that these monads are liftings of finitary monads on $\mathsf{Set}$ . Finally, varieties presented by equations are proved to correspond to extensions of finitary monads on $\mathsf{Set}$ to strongly finitary monads on $\mathsf{Pos}$ .

Laser–plasma interaction (LPI) at intensities $10^{15}{-}10^{16}~\text{W}\cdot \text{cm}^{-2}$ is dominated by parametric instabilities which can be responsible for a significant amount of non-collisional absorption and generate large fluxes of high-energy nonthermal electrons. Such a regime is of paramount importance for inertial confinement fusion (ICF) and in particular for the shock ignition scheme. In this paper we report on an experiment carried out at the Prague Asterix Laser System (PALS) facility to investigate the extent and time history of stimulated Raman scattering (SRS) and two-plasmon decay (TPD) instabilities, driven by the interaction of an infrared laser pulse at an intensity ${\sim}1.2\times 10^{16}~\text{W}\cdot \text{cm}^{-2}$ with a ${\sim}100~\unicode[STIX]{x03BC}\text{m}$ scalelength plasma produced from irradiation of a flat plastic target. The laser pulse duration (300 ps) and the high value of plasma temperature (${\sim}4~\text{keV}$) expected from hydrodynamic simulations make these results interesting for a deeper understanding of LPI in shock ignition conditions. Experimental results show that absolute TPD/SRS, driven at a quarter of the critical density, and convective SRS, driven at lower plasma densities, are well separated in time, with absolute instabilities driven at early times of interaction and convective backward SRS emerging at the laser peak and persisting all over the tail of the pulse. Side-scattering SRS, driven at low plasma densities, is also clearly observed. Experimental results are compared to fully kinetic large-scale, two-dimensional simulations. Particle-in-cell results, beyond reproducing the framework delineated by the experimental measurements, reveal the importance of filamentation instability in ruling the onset of SRS and stimulated Brillouin scattering instabilities and confirm the crucial role of collisionless absorption in the LPI energy balance.

The Cambrian–Ordovician metasedimentary rocks of the Meguma terrane (Canadian Appalachians) were extensively intruded by silicic plutons during Middle Devonian to Early Carboniferous times. Syn-plutonic but volumetrically minor mafic-ultramafic intrusions were also emplaced. In most localities, the silicic plutons and mafic-ultramafic intrusions do not appear to be petrogenetically related and are likely derived from different sources. The Attwoods Brook gabbronorite of SW Nova Scotia yielded an in situ zircon weighted-mean 206Pb–238U age of 357.9 ± 3.3 Ma that is within the uncertainty of the age of the neighbouring Wedgeport pluton (357 ± 1 Ma). The Wedgeport pluton is a rare example of a mantle-derived, peraluminous A-type granite within the Meguma terrane. The similar ages and Nd isotopes of the Attwoods Brook gabbronorite (εNd(t) = +1.1 to +4.0) and Wedgeport pluton (εNd(t) = +2.1 to +3.3) suggest the two intrusions are petrogenetically related. Fractional crystallization modelling demonstrates that a parental magma similar to the Attwoods Brook gabbronorite can produce residual silicic liquids that resemble the granites of the Wedgeport pluton, indicating that they could be members of the same intrusive complex. The emplacement of the gabbronorite and Wedgeport pluton occurred during a period of tensional plate stress that was contemporaneous with rifting of the Maritimes Basin that produced the Fountain Lake continental flood basalts and A-type granites of the Cobequid Highlands within the Avalon terrane. It is possible that the Early Carboniferous rocks of SW Nova Scotia are related to the rifted-related magmatism within the Maritimes Basin.

This paper provides a summary of recent research connected with the shock ignition (SI) concept of the inertial confinement fusion which was carried out at PALS. In the experiments, Cu planar targets coated with a thin CH layer were used. Two-beam irradiation experiment was applied to investigate the effect of preliminary produced plasma to shock-wave generation. The 1ω or 3ω main beam with a high intensity >1015 W/cm2 generates shock wave, while the other 1ω beam with the intensity below 1014 W/cm2 creates CH pre-plasma simulating the pre-compressed plasma related to SI. Influence of laser wavelength on absorbed energy transfer to shock wave was studied by means of femtosecond interferometry and measuring the crater volume. To characterize the hot electron and ion emission, two-dimensional (2D) Kα-imaging of Cu plasma and grid collector measurements were used. In single 1ω beam experiments energy transport by fast electrons produced by resonant absorption made a significant contribution to shock-wave pressure. However, two-beam experiments with 1ω main beam show that the pre-plasma is strongly degrading the scalelength which leads to decreasing the fast electron energy contribution to shock pressure. In both the single 3ω beam experiments and the two-beam experiments with the 3ω main beam, do not show any clear influence of fast electron transport on shock-wave pressure. The non-monotonic behavior of the scalelength at changing the laser beam focal radius in both presence and absence of pre-plasma reflects the competition of plasma motion and electron heat conduction under the conditions of one-dimensional and 2D plasma expansion at large and small focal radii, respectively.

The study focuses on the distribution of B, Be, Li, rare earth elements (REE), high-field-strength elements (HFSE), Th, U and Pb in fresh and hydrothermally altered ocean island basalts (OIB) from French Polynesia, and evaluates B/Be and Li/Be ratios as potential tracers of subducted components in the mantle. Hydrothermal solutions affecting the rocks during cooling were derived from meteoric water, sea water and magmatic fluids. The concentrations of REE, HFSE, Th and Be in the OIB were not affected by secondary processes except during advanced stages of subaerial hydrothermal alteration where saponite was a dominant secondary phase. This alteration modified the contents of these elements, changed REE patterns and produced a positive Ce anomaly. The subaerial and submarine hydrothermal alteration (T ∼ 70–100°C) may change U concentrations in OIB, whereas Pb was only marginally redistributed during alteration.

Boron was enriched during submarine and subaerial hydrothermal alteration but was not noticeably affected in basalts altered by magmatic fluids at T > 200°C. Like B, the mobility of Li during the alteration varies with fluid temperature. Lithium became enriched in the basalts during advanced stages of lower T hydrothermal alteration (<100°C). However, this element was partly removed from the rocks during higher T alteration (>200°C) by magmatic fluids. Boron, Be and Li behave as incompatible trace elements in basaltic magmas. Beryllium content in primitive mantle is estimated to be 0.07 ppm. Fresh Polynesian OIB have low abundances of B and Li and low B/Be (2–5) and Li/Be (2.5–5) ratios compared with volcanic arc rocks, marine sediments and altered oceanic crust. Various OIB including even those which have HIMU- and EM-affinities have similar overlapping B/Be and Li/Be ratios. Both B and Li are probably stripped from a lithospheric slab during subduction-related metamorphism and are, thus, not involved in deep mantle recycling. The mantle-normalized trace element abundances of MORB and OIB usually display patterns characterized by negative B, Pb and Li anomalies. The patterns of continental crust and crustal rocks have distinct positive anomalies for these elements whereas continental basaltic rocks have variable relative abundances of B, Pb and Li. The anomalies of these elements in basalts can be useful in discriminating their tectonic setting and constraining the mantle source regions of basalts.

Ultramafic xenoliths enclosed in Plio-Quaternary alkali basalts from Tallante near Cartagne (southern Spain) are composed mainly of spinel lherzolites which are probably upper mantle residues. In many xenoliths, the spinel lherzolite is cut by pyroxenite or gabbroic anorthosite veinlets generally 0.2–3 cm thick. The clinopyroxenite veinlets were formed by high-pressure crystal-liquid segregation from alkali basalt magmas formed earlier than the host basalts, whereas mantle metasomatism played a role in the genesis of gabbroic anorthosites. Close to the contact with the veinlets, the spinel lherzolites are enriched in Ca, Fe, and some incompatible elements including light REE due to the migration of a fluid from the veinlets into the surrounding lherzolites. The host alkali basalts were derived from a heterogeneous, incompatible element-enriched upper-mantle source probably similar in composition and nature to the composite xenoliths, but were formed in a garnet stability field.

Small (m-scale) peridotite enclaves at Planany (central Czech Republic) are separated from their gneissic host rocks by a narrow (cm-scale) reaction rim comprising an inner, tremolite + phlogopite zone and an outer, essentially monomineralic phlogopite zone. Both retain an Mg# very similar to that of the peridotite (Mg# = 81), but relative to this reference frame, show large increases in LILE (K, Rb, Ba) and radionuclides (U, Th). On a smaller scale, however, there has been a mineralogically-controlled decoupling of various components, particularly among the HFSE and REE, the former favouring the phlogopite-rich outer layer of the reaction rim, the latter the amphibole-rich inner zone. Taken together, however, the reaction zones preserve key compositional features of their inferred protolith.

Metasomatic interaction on a cm scale between calc-silicate pods and the enclosing sillimanite + biotite + tourmaline gneiss at Partridge Breast Lake, northern Manitoba, Canada, led to the development of an inner (by calc-silicate rock), hornblende-rich reaction zone and an outer, biotite-rich zone. The boundary between the reaction zones is interpreted as the original calc-silicate/metapelite interface. Compared with its metapelitic protolith, the biotite zone shows a two- to twenty-fold depletion in the concentrations of incompatible trace elements (notably the light rare earths, U, Th, Nb, Ta, Zr and Hf). In contrast, the relative concentrations of trace elements remained nearly constant during the mineralogical transformation of the calc-silicate rock to the hornblende zone. The depletion of trace elements in the biotite zone is attributed to the dissolution of accessory phases (e.g. monazite). Although stable at the metamorphic conditions (∼600–650°C at ∼ 4.5 kbar) prevalent during metasomatism, Mg-rich tourmaline is absent in the biotite zone, suggesting that either the pH or composition (e.g. the (Al + Si)/(Ca + Mg + Fe) ratio) of the aqueous fluid phase was inappropriate for the preservation of this mineral.

The spinel peridotite inclusions in basalts from Sardinia are upper-mantle residues affected by metasomatism which led to an enrichment particularly of U and light REE. The metasomatism took place prior to the recrystallization which produced the primary mineral assemblage of the inclusions. The compositional variations imply that the xenoliths are residual after at least two melting events.

The upper 35 m of a thick (≤175 m) Early Jurassic North Mountain Basalt flow at KcKay Head contains 25 cm thick differentiated layers that are separated by 130 cm sections of basalt. The lower layers are mafic, pegmatitic, and contain thin (2 cm), fine-grained 'rhyolite' bands. Evidence that the rhyolite represents a Si-rich immiscible liquid includes: (1) textures such as fiine-grained globules of Ferich pyroxene (once Fe-rich liquid) bordering pegmatite feldspar grains; (2) structureless, microcrystalline, interstitial, polygonal patches of Si-rich minerals and similar areas of Fe-rich stilpnomelane surrounding skeletal Fe-Ti oxide grains, with bulk chemical compositions (to a first approximation), relative proportions and total modat percentages suggesting they were once Si-rich and Fe-rich glasses respectively; (3) basalt and pegmatite compositions (particularly their Fe, and Ti contents) similar to rocks known to contain immiscible liquids; (4) rhyolite major element compositions generally consistent with formation from an immiscible Si-rich liquid; (5) mineral compositions and temperature of pegmatite formation compatible with immiscibility; (6) the inability of mass balance calculations (crystal fractionation) to explain rhyolite formation unless mesostasis stilpnomelane (representing the Fe-rich liquid) is included in the caculations. If, as we suggest, these rocks are the result of immiscibility, they shed light on the incipient formation of granophyres in mafic intrusions and support liquid immiscibility as an important rock-forming process.

The experimental study of the plasma projectile acceleration in the laser-induced cavity pressure acceleration (LICPA) scheme is reported. In the experiment performed at the kilojoule PALS laser facility, the parameters of the projectile were measured using interferometry, a streak camera and ion diagnostics, and the measurements were supported by two-dimensional hydrodynamic simulations. It is shown that in the LICPA accelerator with a 200-J laser driver, a 4-μg gold plasma projectile is accelerated to the velocity of 140 km/s with the energetic acceleration efficiency of 15–19% which is significantly higher than those achieved with the commonly used ablative acceleration and the highest among the ones measured so far for any projectiles accelerated to the velocities ≥100 km/s. This achievement opens the possibility of creation and investigation of high-energy-density matter states with the use of moderate-energy lasers and may also have an impact on the development of the impact ignition approach to inertial confinement fusion.

The paper is a continuation of research carried out at Prague Asterix Laser System (PALS) related to the shock ignition (SI) approach in inertial fusion, which was carried out with use of 1ω main laser beam as the main beam generating a shock wave. Two-layer targets were used, consisting of Cu massive planar target coated with a thin polyethylene layer, which, in the case of two-beam irradiation geometry, simulate conditions related to the SI scenario. The investigations presented in this paper are related to the use of 3ω to create ablation pressure for high-power shock wave generation. The interferometric studies of the ablative plasma expansion, complemented by measurements of crater volumes and Kα emission, clearly demonstrate the effect of changing the incident laser intensity due to changing the focal radius on efficiency of laser energy transfer to a shock wave and fast electron emission. The efficiency of the energy transfer increases with the radius of the focused laser beam. The pre-plasma does not significantly change the character of this effect. However, it unambiguously results in the increasing temperature of fast electrons, the total energy of which remains very small (<0.1% of the laser energy). This study shows that the optimal radius from the point of view of 3ω radiation energy transfer to the shock wave is the maximal one used in these experiments and equal to 200 µm that corresponds to the minimal effect of two-dimensional (2D)-expansion. Such a result is typical for the ablation process determined by electron conductivity energy transfer under the conditions of one-dimensional or 2D matter expansion without any appreciable effect due to energy transfer by fast electrons. The 2D simulations based on application of the ALANT-HE code and an analytical model that includes generation and transport of hot electrons has been used to support of experimental data.

This paper reports on properties of a plasma formed by sequential action of two laser beams on a flat target, simulating the conditions of shock-ignited inertial confinement fusion target exposure. The experiments were performed using planar targets consisting of a massive copper (Cu) plate coated with a thin plastic (CH) layer, which was irradiated by the 1ω PALS laser beam (λ = 1.315 μm) at the energy of 250 J. The intensity of the fixed-energy laser beam was scaled by varying the focal spot radius. To imitate shock ignition conditions, the lower-intensity auxiliary 1ω beam created CH-pre-plasma which was irradiated by the main beam with a delay of 1.2 ns, thus generating a shock wave in the massive part of the target. To study the parameters of the plasma treated by the two-beam irradiation of the targets, a set of various diagnostics was applied, namely: (i) Two-channel polaro-interferometric system irradiated by the femtosecond laser (~40 fs), (ii) spectroscopic measurements in the X-ray range, (iii) two-dimensional (2D)-resolved imaging of the Kα line emission from Cu, (iv) measurements of the ion emission by means of ion collectors, and (v) measurements of the volume of craters produced in a massive target providing information on the efficiency of the laser energy transfer to the shock wave. The 2D numerical simulations have been used to support the interpretation of experimental data. The general conclusion is that the fraction of the main laser beam energy deposited into the massive copper at two-beam irradiation decreases in comparison with the case of pre-plasma. The reason is that the pre-formed and expanding plasma deteriorates the efficiency of the energy transfer from the main laser pulse to a solid part of the targets by means of the fast electrons and the wave of an electron thermal conductivity.

Extended abstract of a paper presented at Microscopy and Microanalysis 2012 in Phoenix, Arizona, USA, July 29 – August 2, 2012.

The Late Devonian South Mountain Batholith (SMB) of southwestern Nova Scotia is the largest batholith in the Appalachian Orogen of Eastern North America and contains economic deposits of U and Sn. The SMB comprises at least 11 individual plutons, which range in composition from granodiorite to biotite monzogranite, leucomonzogranite and leucogranite. Previous studies have suggested that a combination of fractional crystallization, assimilation of Meguma Supergroup country rocks and an influx of magmatic fluids contributed to the chemical evolution of the SMB. The amount of crustal assimilation is estimated to be as high as 33%. MELTS modelling assuming a starting composition of granodiorite with H2O = 4 wt%, pressure = 4 kbar (~12 km) and fO2 = FMQ can reproduce the chemical evolution observed in the SMB. However, some leucogranites likely require an additional component (e.g. hydrothermal fluids) to explain their alkali metal enrichment (e.g. Na, K, Rb). Zircon saturation thermometry estimates indicate the Salmontail Lake and Scrag Lake granodiorite plutons had high minimum initial temperatures of 823 ± 6°C and 832 ± 2°C, respectively, which are similar to low zircon-inheritance granitoids. The TiO2/Al2O3 and alkali-lime ratios of the surrounding country rocks and the leucogranites indicate the amount of crustal assimilation is likely to be between 10% and 20%. Our findings suggest the granodiorites of the SMB were likely produced by partial melting of the sub-Meguma Supergroup (e.g. Avalon terrane) lower crust caused by the contemporaneous injection of high temperature mafic to ultramafic magmas.