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At least 91 records · Page 5

Opacity of shock-heated boron plasmas

Standard measures of opacity, the imaginary part of the atomic scattering factor f 2 and the x-ray mass attenuation coefficient μ/ρ, are assessed in shock-heated boron, boron carbide and boron nitride plasmas. The Hugoniot equation, relating the temperature T behind a shock wave to the compression ratio ρ/ρ 0 across the shock front, is used in connection with the plasma equation of state to determine the pressure p, effective plasma charge Z* and the K-shell occupation in terms of ρ/ρ 0 . Solutions of the Hugoniot equation (determined within the framework of the generalized Thomas–Fermi theory) show that the K-shell occupation in low-Z ions decreases rapidly from 2 to 0.1 as the temperature increases from 20 eV to 500 eV; a temperature range in which the shock compression ratio is near 4. The average-atom model (a quantum mechanical version of the generalized Thomas–Fermi theory) is used to determine K-shell and continuum wave functions and the photoionization cross section for x-rays in the energy range ω = 1 eV to 10 keV, where the opacity is dominated by the atomic photoionization process. For an uncompressed boron plasma at T = 10 eV, where the K-shell is filled, the average-atom cross section, the atomic scattering factor and the mass attenuation coefficient are all shown to agree closely with previous (cold matter) tabulations [1, 2, 3]. For shock-compressed plasmas, the dependence of μ/ρ on temperature can be approximated by scaling previously tabulated cold-matter values by the relative K-shell occupation; yet, there is a relatively small residual dependence arising from the photoionization cross section. Attenuation coefficients μ for a 9 keV x-ray are given as functions of T along the Hugoniot for B, C, B 4 C and BN plasmas.

52.25.Os: Emission↗

High Compression in Palladium Alloy Metal Foil Pumps

Metal foil pumps (MFPs) are key components in the direct internal recycling inner fuel cycle loop for the recovery of hydrogen isotopes from deuterium-tritium fusion exhaust. Operating under vacuum conditions, they utilize superthermal hydrogen as the feed gas in a process called superpermeation. A notable feature of MFPs is their ability to pump against a pressure gradient. This study examines the compression capabilities of PdAg and PdCu MFPs at low temperatures with a constant feed pressure of 10 Pa. At 75°C, compression ratios exceeding 200 were readily achieved, with downstream pressures exceeding 4500 Pa using PdCu. For both alloys, net fluxes decreased by only ~15% at downstream pressures of 1000 Pa, which offers potential simplifications for the downstream pump train. Performance declined markedly when the temperature was elevated to 200°C. Pump curves were constructed and advocated as the most appropriate manner to assess MFP performance. Separate pressure-driven-permeation experiments at relevant conditions were conducted, providing a direct measurement of the hydrogen dissociation constant $k$ d , which was found to be in good agreement with the previous literature. Further, these measurements were used to predict pump curves and maximum compression ratios by balancing superpermeation with pressure-driven permeation, achieving excellent agreement with experiment. Last, experiments using asymmetric MFPs revealed the detrimental impact that surface impurities have on performance in this system.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Evaluating Chemical Kinetics Predictions for Propane Using 3-D and 0-D Models in a Boosted Spark-Ignited Engine

Propane has been shown to be a promising alternative fuel to reduce emissions while simultaneously achieving high efficiencies in medium- and heavy-duty engines. These high-power density applications require boosted engines which, combined with high compression ratio, can lead to auto-ignition and knock. While three-dimensional (3-D) computational fluid dynamics (CFD) models are often used for resolving the complex fluid flow in engines, these models can become computationally expensive when simulating detailed chemical kinetics. Likewise, zero-dimensional (0-D) models are computationally concise enough for kinetics development, but lack any flow-field information which governs the flame propagation processes in spark ignition (SI) engines. This work presents a comprehensive comparison between 3-D and 0-D closed cycle simulations at knocking conditions in a high compression ratio high stroke-to-bore ratio propane engine. In order to initialize the flow-field for the 3-D closed cycle (intake valve closing, (IVC) to exhaust valve opening, (EVO)) simulation, a motored multi-cycle 3-D model was run using Converge to create a map at IVC, reducing the computational time. The map allowed a non-homogeneous 3-D closed cycle simulation to be satisfactorily validated against experiments, while a homogeneous case using only the turbulence field mapping was also simulated, mimicking 0-D modeling. The 3-D simulations were used to prescribe the initial conditions (e.g., IVC thermodynamics, speciation, burn-rate profile) for a 2-zone 0-D SI engine model in Chemkin Pro for both cases. It was found that 2-zone 0-D modeling underpredicted the knock onset timing, likely due to the lack of thermal stratification in the unburned gas region. Future work will carry multi-zone 0-D modeling to capture the fuel auto-ignition in the unburned region.

Douvry-Rabjeau, Julien [Oakland University, Roches↗

Optimizing the fuel efficiency of an opposed piston engine for electric power generation

This paper investigates the optimal crankshaft motion for an opposed piston (OP) engine in a novel hybrid architecture to maximize fuel efficiency. The OP engine was selected for this work due to its inherent thermodynamic benefits and the balanced nature of the engine which can achieve downsizing through reducing the number of cylinders rather than the individual cylinder volume. The typical geartrain required on an OP engine was exchanged for two electric motors, reducing friction loss and decoupling the crankshafts. Using the motors to control the crankshaft motion profiles, this architecture introduces capabilities to dynamically vary compression ratio, combustion volume, and scavenging dynamics. To leverage these opportunities, an optimization scheme was developed utilizing nonlinear optimization of a 0-D model to compute the crankshaft motion profile that maximizes the work generated by the system. This optimization was then iteratively coupled with a high fidelity model which supplies the cylinder flow boundary conditions. This iterative approach reduces the model complexity used in the optimal control problem (OCP) while capturing the gas exchange dynamics critical to the 2-stroke cycle of the OP engine. By using the rate of change of motor torque as the input to the OCP, the torque fluctuation in a single cycle can be limited to ensure tracking feasibility. The results show crankshaft velocity slows during the compression stroke and conversely accelerates during the expansion stroke, reducing the peak motor torque required for control and thus reducing the motor losses. The extended residence time at top dead center, however, leads to an increase in heat transfer, illustrating the trade-off between the work extraction efficiency and the indicated engine efficiency.

Engineering↗

MULTI-SPACECRAFT ANALYSIS OF ENERGETIC HEAVY ION AND INTERPLANETARY SHOCK PROPERTIES IN ENERGETIC STORM PARTICLE EVENTS NEAR 1 au

We examine the longitude distribution of and relationship between interplanetary (IP) shock properties and ∼0.1–20 MeV nucleon{sup -1} O and Fe ions during seven multi-spacecraft energetic storm particle (ESP) events at 1 au. These ESP events were observed at two spacecraft and were primarily associated with low Mach number, quasi-perpendicular shocks. Key observations include the following: (i) the Alfvén Mach number increased from east to west of the coronal mass ejection source longitude, while the shock speed, compression ratios, and obliquity showed no clear dependence; (ii) the O and Fe time intensity profiles and peak intensities varied significantly between longitudinally separated spacecraft observing the same event, the peak intensities being larger near the nose and smaller along the flank of the IP shock; (iii) the O and Fe peak intensities had weak to no correlations with the shock parameters; (iv) the Fe/O time profiles showed intra-event variations upstream of the shock that disappeared downstream of the shock, where values plateaued to those comparable to the mean Fe/O of solar cycle 23; (v) the O and Fe spectral index ranged from ∼1.0 to 3.4, the Fe spectra being softer in most events; and (vi) the observed spectral index was softer than the value predicted from the shock compression ratio in most events. We conclude that while the variations in IP shock properties may account for some variations in O and Fe properties within these multi-spacecraft events, detailed examination of the upstream seed population and IP turbulence, along with modeling, are required to fully characterize these observations.

79 ASTRONOMY AND ASTROPHYSICS↗

Chemically-bonded brick production based on burned clay by means of semidry pressing

We presented a study on the possibility of using the burnt rocks of the Krasnoyarsk Territory for production of chemically-bonded materials in the form of bricks which are so widely used in multistory housing and private house construction. The radiographic analysis of the composition of burnt rock was conducted and a modifier to adjust the composition uniformity was identified. The mixing moisture content was identified and optimal amount at 13-15% was determined. The method of semidry pressing has been chosen. The process of obtaining moldings has been theoretically proved; the advantages of chemically-bonded wall materials compared to ceramic brick were shown. The production of efficient artificial stone based on material burnt rocks, which is comparable with conventionally effective ceramic materials or effective with cell tile was proved, the density of the burned clay-based cell tile makes up to 1630-1785 kg \ m{sup 3}, with compressive strength of 13.6-20.0 MPa depending on the compression ratio and cement consumption, frost resistance index is F50, and the thermal conductivity in the masonry is λ = 0,459-0,546 W \ m {sup *} °C. The clear geometric dimensions of pressed products allow the use of the chemically-bonded brick based on burnt clay as a facing brick.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Capturing the Impact of Fuel Octane Number on Modern Gasoline Vehicles with Octane Indices

The need for high efficiency automotive engines has led to more complex air handling and fuel injection systems, higher compression ratios, more advanced combustion and aftertreatment systems, and the use of fuels with higher octane ratings. Higher octane number fuels have a lower propensity to knock. This work studies the influence of changing fuel octane rating on two modern production gasoline vehicles, one with a naturally aspirated, port injected engine and the other with a turbocharged, direct injected engine, using fuels with four different octane number grades (with 85, 87, 91, and 93 anti-knock indices) and operated over a variety of driving cycles and temperature conditions. Unlike previous studies, this effort develops and demonstrates a methodology that isolates fuel effects on fuel consumption and provides a clear view of the octane impact on existing vehicles. While fuel octane rating can also impact factors such as the allowable compression ratio and gear shifting strategies, this study examines fuel consumption changes that are solely attributable to octane rating on production vehicles. The developed approach uses results from drive cycle as well as steady-state tests along with response surface modeling to predict the engine combustion phasing and changes in efficiency for each fuel relative to the baseline 87 anti-knock index (AKI) fuel. The methodology is then used to capture the role of fuel octane rating on powertrain efficiency over Environmental Protection Agency (EPA) certification drive cycles and demonstrate the variation of that impact as a function of powertrain output power. Based on the vehicles and fuels tested in this study, the metrics indicate that the effects of octane on efficiency are limited to a portion of the operating modes represented in the driving cycles used for vehicle certification. In addition, an octane potential benefit index (OPBI) suggests that the vehicle with the turbocharged, direct injected engine has a greater potential to benefit from higher octane number fuel compared to the naturally aspirated, port injected engine and proposes a way to quantify this impact for production vehicles.

Jehlik, Forrest↗

Evaluation of Knock Behavior for Natural Gas - Gasoline Blends in a Light Duty Spark Ignited Engine

The compression ratio is a strong lever to increase the efficiency of an internal combustion engine. However, among others, it is limited by the knock resistance of the fuel used. Natural gas shows a higher knock resistance compared to gasoline, which makes it very attractive for use in internal combustion engines. The current paper describes the knock behavior of two gasoline fuels, and specific incylinder blend ratios with one of the gasoline fuels and natural gas. The engine used for these investigations is a single cylinder research engine for light duty application which is equipped with two separate fuel systems. Both fuels can be used simultaneously which allows for gasoline to be injected into the intake port and natural gas to be injected directly into the cylinder to overcome the power density loss usually connected with port fuel injection of natural gas. Adding natural gas at wide open throttle helps to reduce knock mitigating measures and increases the efficiency and power density compared to the other gasoline type fuels with lower knock resistance. The used methods, knock intensity and number of pressure waves, do not show significant differences in knock behavior for the natural gas - gasoline blends compared to the gasoline type fuels. A knock integral was used to describe the knock onset location of the fuels tested. Two different approaches were used to determine the experimental knock onset and were compared to the knock onset delivered by the knock integral (chemical knock onset). The gasoline type fuels show good agreement between chemical and experimental knock onset. However, the natural gas -gasoline blends show higher discrepancies comparing chemical and experimental knock onset.

Advanced Combustion Concept↗

Gasoline Engine and Fuels Offering Reduced Fuel Consumption and Emissions: Vehicle Modeling Final Report

The Gasoline Engine and Fuels Offering Reduced Fuel Consumption and Emissions (GEFORCE) project was proposed in response to the U.S. Department of Energy’s Funding Opportunity Announcement 0991 by a team made up of the members of the Coordinating Research Council (CRC) and the research staff at Oak Ridge National Laboratory (ORNL.) The project focused on investigating the potential benefits that might be attained through synergistic use of specific engine technology together with fuels formulated to represent potential directions that high-octane fuels of the future might progress. A stated objective in the DOE FOA was to demonstrate a 25% reduction in petroleum consumption through optimization of the engine technologies together with a suitable fuel. An advanced engine was constructed and used with a matrix of research fuels to investigate potential avenues for efficiency improvement. The engine incorporated technologies expected to become mainstream for boosted engines in the next 10 to 20 years. These included increased compression ratio, a two-stage turbocharger, and cooled external exhaust gas recirculation (EGR). The fuel matrix was designed to investigate impacts from research octane number (RON), volumetric ethanol content, and the final boiling point of the fuel. The engine calibration was optimized for each fuel individually and data collected to enable vehicle system modelling that projected energy consumption, fuel economy, tailpipe CO₂ emissions, and impact on petroleum consumption for an industry-average mid-size sedan. The engine calibration and data collection were carried out at IAV in Michigan and is the subject of a separate report. IAV provided the engine data to Oak Ridge National Laboratory to support the vehicle modelling portion of the project. The vehicle modelling results show the following trends: Ethanol content does have a consistently strong influence on the fuel economy results for all cycles and all fuels. Among the fuels of a nominal RON level, increasing ethanol content consistently lowers fuel economy, with the 30% ethanol fuels always providing the lowest fuel economy for a given RON level. However, in some cases the energy consumption improvement allows the 30% ethanol fuels to match the fuel economy of the ethanol-free fuel P. These observations underscore the importance of both engine efficiency and fuel volumetric energy content on vehicle fuel economy.; There was no consistent trend in the projected energy consumption results for differences in fuel T90 for all fuels and cycles. Fuel economy projections did show a consistent trend, with the higher T90 fuel providing slightly greater fuel economy when compared to the low T90 fuel of the same ethanol content. The observed trends were consistent with differences in the heating value of the fuels.; The 102-RON fuels provided reduced energy consumption and greater fuel economy for the advanced engine on all drive cycles. The engine compression ratio of 11.5 was higher than would typically be used in a turbocharged engine when 92-RON fuel use is expected. Hence, the engine experiences more efficiency degradation from knock avoidance when using the 92-RON fuels. This degradation causes the fuel economy results for the 92-RON fuels to be lower than those for the 102-RON fuels.; Fuels E and F (92-RON, 30% ethanol) are projected to achieve 10% or greater reduction in petroleum consumption, with fuels K (102-RON, 30% ethanol) and O (97 RON, 30% ethanol) achieving greater than a 20% reduction. Fuel L (102-RON, 30% ethanol) achieves greater than 25% reduction, meeting the petroleum reduction target of the project. All of the fuels that achieve 10% or greater reduction in petroleum consumption are 30% ethanol blends.; Increasing final boiling point increased fuel economy at fixed ethanol content when the 102-RON fuels were used. This trend is a result of differences in the volumetric energy content of the fuels and the projected energy consumption values for the fuels. In the case of the 102-RON fuels, increasing final boiling point also resulted in an increase in the energy content of the fuel. There was not a consistent trend between the energy content and final boiling point for the 92-RON fuels at fixed ethanol content.

33 ADVANCED PROPULSION SYSTEMS↗

Piston geometry and stroke optimization for high efficiency propane spark ignition engines

Propane has unique properties and offers interesting characteristics for high-efficiency spark ignition engines. Its high volatility reduces or completely eliminates fuel-wall wetting and facilitates fuel air mixing. Furthermore, propane has a research octane number of 112 and a high octane sensitivity of 15. Finally, its laminar flame speed is on the same order as that of conventional gasoline, and it exhibits high dilution tolerance. Modern spark ignition internal combustion engines rely on fast combustion rates and high dilution to achieve high brake thermal efficiencies. To accomplish this, high stroke-to-bore ratios and high geometric compression ratios have been used in new engine designs. Therefore, propane’s relatively high laminar flame speeds, high knock resistance, and dilution tolerance make it an excellent candidate fuel for modern spark ignition engines. The objective of this work is to co-optimize the piston geometry and the engine stroke to maximize the efficiency of a spark-ignition engine fueled with propane. 3D computational fluid dynamics (CFD) simulations employing the extended coherent flamelet model were used to study the parametric effects of piston shape and stroke length. A piston geometry based on high performing pistons was parameterized using four controlling parameters. The piston geometry and engine stroke design space was explored using deterministic and quasi-random sampling techniques. In conclusion, a Gaussian process regression model was built using the simulation data to explain the results observed.

33 ADVANCED PROPULSION SYSTEMS↗

DuoModel: Leveraging Reduced Model for Data Reduction and Re-Computation on HPC Storage

High-performance computing (HPC) applications generate large amounts of floating-point data that need to be stored and analyzed efficiently to extract the insights and advance knowledge discovery. With the growing disparities between compute and I/O, optimizing the storage stack alone may not suffice to cure the I/O problem. There has been a strong push in the HPC communities to perform data reduction before data is transmitted to storage in order to lower the I/O cost. However, as of now, neither lossless nor lossy compressors can achieve the adequate reduction ratio that is desired by applications. This paper proposes DuoModel, a new approach that leverages the similarity between the full and reduced application models, and further improve the data reduction ratio. DouModel further improves the compression ratio of state-of-the-art compressors via compressing the differences (termed as delta) between the data products of the two models. For data analytics, the high fidelity data can be re-computed by launching the reduced model and applying the compressed delta. Our evaluations confirm that DuoModel can further push the limit of data reduction while the high fidelity of data is maintained.

Luo, Huizhang (ORCID:0000000323920267)↗

Unsupervised classification-based hyperspectral data processing: lossy compression

The existing lossy compression algorithms play an important role in reducing the cost of storage equipment and bandwidth for hyperspectral (HS) application. However, none of the lossy compression algorithms considers the real-time classification of HS data. In this paper, we present a new lossy compression method for HS data that aims to optimally compress in both spatial and spectral domains and simultaneously maximize classification performance. For this target, Harsanyi–Farrand–Chang (HFC) and k-means++ algorithms are applied to achieve a spectral library and an index matrix for HS image. Spectral angle mapping and Euclidean distance are used to update the spectral library and the index matrix. The experiment results indicate that the proposed method has a good classification performance. The results also reveal that the proposed method works well in real-time classification and compression of HS data with a large volume and achieves a high compression ratio. It is noteworthy to mention that the superiority of our method in compression becomes more apparent as the volume of HS data grows. Consequently, the proposed method has a strong advantage in HS applications that require both compression and classification.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

waveSZ: A Hardware-Algorithm Co-Design of Efficient Lossy Compression for Scientific Data

Error-bounded lossy compression is critical to the success of extreme-scale scientific research because of ever-increasing volumes of data produced by today's high-performance computing (HPC) applications. Not only can error-controlled lossy compressors significantly reduce the I/O and storage burden but they can retain high data fidelity for post analysis. Existing state-of-the-art lossy compressors, however, generally suffer from relatively low compression and decompression throughput (up to hundreds of megabytes per second on a single CPU core), which considerably restrict the adoption of lossy compression by many HPC applications especially those with a fairly high data production rate. In this paper, we propose a highly efficient lossy compression approach based on field programmable gate arrays (FPGAs) under the state-of-the-art lossy compression model SZ. Our contributions are fourfold. (1) We adopt a wavefront memory layout to alleviate the data dependency during the prediction for higher-dimensional predictors, such as the Lorenzo predictor. (2) We propose a co-design framework named WAVESZ based on the wavefront memory layout and the characteristics of SZ algorithm and carefully implement it by using high-level synthesis. (3) We propose a hardware-algorithm co-optimization method to improve the performance. (4) We evaluate our proposed WAVESZ on three real-world HPC simulation datasets from the Scientific Data Reduction Benchmarks and compare it with other state-of-the-art methods on both CPUs and FPGAs. Experiments show that our WAVESZ can improve SZ's compression throughput by 6.9x similar to 8.7x over the production version running on a state-of-the-art CPU and improve the compression ratio and throughput by 2.1x and 5.8x on average, respectively, respectively, compared with the state-of-the-art FPGA design.

Compression Ratio↗

THE FLOW AROUND A COSMIC STRING. I. HYDRODYNAMIC SOLUTION

Cosmic strings are linear topological defects which are hypothesized to be produced during inflation. Most searches for strings have relied on the string’s lensing of background galaxies or the cosmic microwave background. In this paper, I obtained a solution for the supersonic flow of collisional gas past the cosmic string which has two planar shocks with a shock compression ratio that depends on the angle defect of the string and its speed. The shocks result in the compression and heating of the gas and, given favorable conditions, particle acceleration. Gas heating and over-density in an unusual wedge shape can be detected by observing the Hi line at high redshifts. Particle acceleration can occur in the present-day universe when the string crosses the hot gas contained in galaxy clusters and, since the consequences of such a collision persist for cosmological timescales, could be located by looking at unusual large-scale radio sources situated on a single spatial plane.

79 ASTRONOMY AND ASTROPHYSICS↗

Design of bunch compressing system with suppression of coherent synchrotron radiation for ATF upgrade

One of the operation modes for Accelerator Test Facility (ATF) upgrade is to provide high peak current, high quality electron beam for users. Such operation requires a bunch compressing system with a very large compression ratio. The CSR originating from the strong compressors generally could greatly degrade the quality of the electron beam. In this paper, we present our design for the entire bunch compressing system that will limit the effect of CSR on the e-beam’s quality. We discuss and detail the performance from the start to end simulation of such a compressor for ATF.

43 PARTICLE ACCELERATORS↗

HTTR-GT/H2 test plant - design study on helium gas turbine for the heat utilization system connected to JAEA's HTTR - 18674

In JAEA (Japan Atomic Energy Agency), the program of verification of combined system with helium gas turbine power generation and hydrogen production using nuclear heat which becomes the first in the world, is proceeding. From 2014 to 2015 Japanese Fiscal Year, the design study of the heat utilization system which is arranged in cascade to the heat supply system to supply the hydrogen production system and helium gas turbine system which are installed in the secondary helium-cooling system of High Temperature Engineering Test Reactor (HTTR) was performed and measure technologies of the system have been verified. MHI participated in the design study work of main equipment of this system. This paper reports the result of the design study of a helium gas turbine among those results. Self-sustaining condition (a power generation output is attained) is required for the gas turbine system in three modes of operation such as a) gas turbine individual operation, b) gas turbine + hydrogen production system combined operation, and c) hydrogen production system load loss and gas turbine independent shift operation]. By adopting a multi-stage centrifugal type impeller as a gas turbine and a compressor as a result of design study, it confirmed that all the mode-of-operation self-sustaining can be attained, and can attain a maximum of approx. 1 MWe power generation output on condition of the turbine inlet temperature of 560 deg. C, the turbine flow of 9.8 kg/sec, the compressor inlet temperature of 30 deg. C, and the compression ratio 1.3. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Plasma physical parameters along coronal-mass-ejection-driven shocks. I. Ultraviolet and white-light observations

In this work, UV and white-light (WL) coronagraphic data are combined to derive the full set of plasma physical parameters along the front of a shock driven by a coronal mass ejection. Pre-shock plasma density, shock compression ratio, speed, and inclination angle are estimated from WL data, while pre-shock plasma temperature and outflow velocity are derived from UV data. The Rankine-Hugoniot (RH) equations for the general case of an oblique shock are then applied at three points along the front located between 2.2 and 2.6 R {sub ☉} at the shock nose and at the two flanks. Stronger field deflection (by ∼46°), plasma compression (factor ∼2.7), and heating (factor ∼12) occur at the nose, while heating at the flanks is more moderate (factor 1.5-3.0). Starting from a pre-shock corona where protons and electrons have about the same temperature (T{sub p} ∼ T{sub e} ∼ 1.5 × 10{sup 6} K), temperature increases derived with RH equations could better represent the proton heating (by dissipation across the shock), while the temperature increase implied by adiabatic compression (factor ∼2 at the nose, ∼1.2-1.5 at the flanks) could be more representative of electron heating: the transit of the shock causes a decoupling between electron and proton temperatures. Derived magnetic field vector rotations imply a draping of field lines around the expanding flux rope. The shock turns out to be super-critical (sub-critical) at the nose (at the flanks), where derived post-shock plasma parameters can be very well approximated with those derived by assuming a parallel (perpendicular) shock.

79 ASTRONOMY AND ASTROPHYSICS↗