Chemie und Prozesstechnik
Filtern
Erscheinungsjahr
- 2018 (155) (entfernen)
Dokumenttyp
- Posterpräsentation (155) (entfernen)
Referierte Publikation
- nein (155)
Schlagworte
- Nanoparticles (14)
- LIBS (11)
- Nanoparticle (10)
- Bioimaging (6)
- Concrete (6)
- Copper (5)
- Dosimetry (5)
- Geant4 (5)
- LA-ICP-MS (5)
- Mechanochemistry (5)
- PCA (5)
- Radiation damage (5)
- Small-angle scattering (5)
- Soil (5)
- Thermography (5)
- XPS (5)
- Biofilms (4)
- DNA (4)
- Data analysis (4)
- ICP-MS (4)
- Laser ablation (4)
- Low energy electrons (4)
- Microdosimetry (4)
- PLSR (4)
- Reference material (4)
- ATCUN (3)
- E. coli (3)
- Electron microscopy (3)
- Hydroxyl radical (3)
- Immunoassay (3)
- In situ (3)
- Isotope dilution mass spectrometry (3)
- LET (3)
- Labeling (3)
- Lanthanide (3)
- Metal phosphonates (3)
- Metalloproteins (3)
- Mycotoxins (3)
- NAP-XPS (3)
- NMR (3)
- Nickel (3)
- PXRD (3)
- Peptides (3)
- Plasmonic enhancement (3)
- Raman spectroscopy (3)
- SAXS (3)
- SEM (3)
- Silica coating (3)
- Silver nanoparticles (3)
- Simulation (3)
- ToF-SIMS (3)
- Upconversion nanoparticles (3)
- Alginate (2)
- CRM (2)
- Cell (2)
- Certification (2)
- Chloride (2)
- Computed tomography (2)
- Corrosion (2)
- ESI-MS (2)
- Eisenbahn (2)
- Electron irradiation (2)
- Electron probe microanalysis (EPMA) (2)
- FEM (2)
- Feuchte (2)
- Fluorescence (2)
- Fusion protein (2)
- GD-OES (2)
- Graphite (2)
- Immuno-assay (2)
- Ink (2)
- Instrumentation (2)
- Ionizing radiation (2)
- Iron disorders (2)
- KorroPad (2)
- LEE (2)
- Laser thermography (2)
- Linear energy transfer (2)
- MAUS (2)
- MCS (2)
- Manuscript (2)
- Mass cytometry (2)
- Measurement uncertainty (2)
- Monitoring (2)
- Monte-Carlo simulations (2)
- Mycotoxin Biomarker (2)
- NDT (2)
- Nanomaterial (2)
- PS (2)
- Quantification (2)
- RP-HPLC (2)
- Radiation therapy (2)
- SAM (2)
- SI traceability (2)
- SUMO (2)
- Single cell (2)
- Spectroscopic ellipsometry (2)
- Standardization (2)
- Tandem MS (2)
- Thin polymeric films (2)
- Trace elements (2)
- Trichodiene (2)
- Ultraschall (2)
- Ultrasound (2)
- XRF (2)
- Zinc (2)
- 1d laser (1)
- 2D model (1)
- 3D imaging (1)
- 5-hydroxynicotinic acid (1)
- ALCOREF (1)
- ALD-Beschichtung (1)
- Additive manufacturing (1)
- Air traffic (1)
- Airborne ultrasonic testing (1)
- Alignment (1)
- Amplification (1)
- Analytical standards (1)
- Analytik (1)
- Antikörper (1)
- Antimicrobials (1)
- Aqueous solution (1)
- Archival format (1)
- Arzneimittel (1)
- BAMline (1)
- BET (1)
- BFR (1)
- Bacteria (1)
- Beton (1)
- Bioconjugates (1)
- Bioconjugation (1)
- Biomarkers (1)
- Biotechnology (1)
- Biotransformation (1)
- Bivalves (1)
- Bodenstruktur (1)
- Bonse Hart (1)
- Breath alcohol control (1)
- Broadband (1)
- C-C coupling (1)
- CF-LIBS (1)
- CODA wave interferometry (1)
- Calibration (1)
- Carbon dynamics (1)
- Cement (1)
- Certified Reference Material (1)
- Certified reference material (1)
- Certified reference materials (1)
- Characterization methods (1)
- Chlorid (1)
- Chlorride (1)
- Chromatography (1)
- Cleavable probes (1)
- Cleavable reporter (1)
- Climate Changes (1)
- Clinical samples (1)
- Coda wave interferometry (1)
- Combinatorial library (1)
- Compatible solute (1)
- Computertomographie (1)
- Condition assesment (1)
- Conventional dyes (1)
- Coptic (1)
- Core-shell nanoparticles (1)
- Corrosion resistance (1)
- Corrosion testing (1)
- Coulometric sensors (1)
- Crack Detection (1)
- Crack detection (1)
- Cracks (1)
- Crystal Engineering (1)
- Cyanide detection (1)
- Cyanide in soil (1)
- DAWN (1)
- DGT (1)
- DNA damage (1)
- DNA radiation damage (1)
- Damage processes (1)
- Data correction (1)
- Data reconstruction (1)
- Data standard (1)
- Delivery system (1)
- Dielectric spectroscopy (1)
- Drugs (1)
- DySEM (1)
- Dynamic light scattering (1)
- EC/LC/MS (1)
- EDS (1)
- EDS Spectrometer Test (1)
- EDS-TM001 (1)
- EDS-TM002 (1)
- ELISA (1)
- EU definition (1)
- Ectoin (1)
- Ectoine (1)
- Ectoine radiation protection (1)
- Ectoine radical scavenger (1)
- Electric discharge (1)
- Electro catalyst (1)
- Electrochemical oxidation (1)
- Electrochemistry (1)
- Electron Microscope (1)
- Electron scattering (1)
- Electrospray (1)
- Electrospray deposition (1)
- Elektrochemie (1)
- Elektrolyseverfahren (1)
- Ellipsometric metrology (1)
- Embedded ultrasonic sensor (1)
- Estrich (1)
- Fe-Ni (1)
- Ferroelectret (1)
- Flat bottom holes (1)
- Fluorescence standards (1)
- Food safety (1)
- Functional group (1)
- Fußboden (1)
- GC-MS (1)
- Gas Source Localisation (1)
- Gas Spectroscopy (1)
- Gas pressure influence (1)
- Gaschromatographie-Massenspektrometrie (1)
- Gaschromatography-Mass Spectrometry (1)
- Geopolymer (1)
- Glasmalfarben (1)
- Glue (1)
- Grain size (1)
- Grazing incidence (1)
- HAXPES (1)
- HR-CS-MAS (1)
- High purity material (1)
- High-power laser (1)
- Hydroxyectoine (1)
- Hydroxyl radicals (1)
- Illumina (1)
- Imaging (1)
- Imaging condition (1)
- Imaging mass cytometry (1)
- Iodine (1)
- Ionische Flüssigkeiten (1)
- Ionophore Antibiotics (1)
- Ionophore Antibiotika (1)
- Iridium oxide (1)
- Iridium oxide films (1)
- Isotope (1)
- Isotope dilution (1)
- Joint sparsity (1)
- Knoevenagel (1)
- LC-MS/MS peptide quantification (1)
- LIPS (1)
- Laminography (1)
- Large Aperture Ultrasound System (LAUS) (1)
- Laser Thermography (1)
- Laser ablation in liquid (1)
- Laser array (1)
- Laser induced plasma (1)
- Lock-in Thermography (1)
- Lock-in thermography (1)
- Long-term stability (1)
- MC-LIBS (1)
- MOF (1)
- Mass Spectrometry (1)
- Mercury intrusion porosimetry (1)
- Mesoporous materials (1)
- Metal organic frameworks (1)
- Metal-Tag (1)
- Metformin (1)
- Methodology (1)
- Metrology institute (1)
- Microplastics (1)
- Microwave synthesis (1)
- Mobile Robot Olfaction (1)
- Mobile-LIBS (1)
- Modern painting (1)
- Molecular Conformation (1)
- Mono-hydride (1)
- Monte-Carlo simulation (1)
- Multi-sample analysis (1)
- Multimodal (1)
- Multimodal reporters (1)
- Mykotoxin-Biomarker (1)
- NEXAFS (1)
- NMR relaxometry (1)
- Nano graphene (1)
- Nanocrystal (1)
- Nanodefine (1)
- Nanofiber (1)
- Nanogenotoxicity (1)
- Nanoparticle size (1)
- NeXus (1)
- Neutronensonde (1)
- NoStep Standards (1)
- Non invasive analysis (1)
- Non-invasive analysis (1)
- Notches (1)
- Numerical modelling (1)
- OER (1)
- OH radicals (1)
- OH-radical (1)
- Oberflächenenergie (1)
- On-site analysis (1)
- Opaque materials (1)
- Optical assays (1)
- Optical sensing (1)
- Optical spectroscopy (1)
- Osmolyte (1)
- PEG (1)
- PP (1)
- PTFE (1)
- Particle size distribution (1)
- Passivity (1)
- Pesticide (1)
- Pharmaceutical Drugs (1)
- Pharmaceuticals (1)
- Photocatalysis (1)
- Pitting corrosion (1)
- Plasma (1)
- Plasma diagnostics (1)
- Plasma modeling (1)
- Plasma reheating (1)
- Pollen (1)
- Polyamide (1)
- Polymer (1)
- Polymer testing (1)
- Polymers (1)
- Pore size (1)
- Pore size distribution (1)
- Porengrößen (1)
- Porous thin films (1)
- Primary standard (1)
- Protein (1)
- Pulse thermography (1)
- Purity determination (1)
- Pyrethroids (1)
- Qdots (1)
- Quality (1)
- Quantum dots (1)
- Radar (1)
- Radiation protection (1)
- Radical scavenger (1)
- Raid test (1)
- Reconstruction algorithm (1)
- Reference materials (1)
- Reference procedure (1)
- Reference procedures (1)
- Reference samples (1)
- Reinforced concrete (1)
- Relaxometrie (1)
- Resistance (1)
- Resonance (1)
- Reverse painting on glass (1)
- Reverse time migration (1)
- Rigidity (1)
- Risse (1)
- Rough surface (1)
- SALSA (1)
- SANS (1)
- SEM/EDX (1)
- STXM (1)
- Sampling (1)
- Sampling techniques (1)
- Sanger sequencing (1)
- Screening (1)
- SealWasteSafe (1)
- Sem (1)
- Sensor (1)
- Sensorbeschichtung (1)
- Shape (1)
- Short chained phthalates (1)
- Si-Ge (1)
- Size (1)
- Small angle scattering (1)
- Soil P species (1)
- Spatial resolution (1)
- Spectral induced polarzation (1)
- Spectrometry (1)
- Spectroscopy (1)
- Spurenfeuchtemessung (1)
- Stable-Isotope-Dilution-Analysis (1)
- Stainless Steel (1)
- Stainless steel (1)
- Stratagem (1)
- Sulfur (1)
- Sulfur species conversion (1)
- Sulfur-copper-sepration (1)
- Sulfur-matrix separation (1)
- Super resolution (1)
- Surface chemistry (1)
- Surface finish (1)
- Surface functionalization (1)
- Surface functions (1)
- Surface groups (1)
- Synchrotron (1)
- Synchrotron-XPS (1)
- Synthesis (1)
- Synthetic and building materials (1)
- TDLAS (1)
- TXRF (1)
- Target volume (1)
- Test material (1)
- Test strip (1)
- Thermoacoustic (1)
- Thermoacoustics (1)
- Thin film metrology (1)
- Titania (1)
- Titanium oxide (1)
- Tomography (1)
- Total cyanide (1)
- Trace humidity measurement (1)
- Traceability (1)
- Traceable size (1)
- Transcriptomic (1)
- Transducers (1)
- Transformation Product (1)
- Transformation product (1)
- Transformationsprodukte (1)
- Trichodien (1)
- UAV (1)
- USAXS (1)
- Ultrasonic Borehole Array (1)
- Ultrasonic Testing (1)
- Ultrasound Emission (1)
- Umweltsimulation (1)
- Uncertainty (1)
- VCSEL array (1)
- VSSA (1)
- Vacuum Ultraviolet (1)
- Validation (1)
- Verbundfestigkeit (1)
- Vergleichskörper (1)
- Virtual wave (1)
- Wasserproben (1)
- Water (1)
- Weathering (1)
- X-ray (1)
- X-ray Photoelectron Spectroscopy (XPS) (1)
- X-ray computed tomography (1)
- X-ray spectroscopy (1)
- X-rays (1)
- XANES (1)
- XRD (1)
- XRF Analysis (1)
- Zerstörungsfreie Prüfung von Stahlbeton (1)
- ZfP (1)
- aRTist (1)
- thin film analysis (1)
- µ-CT (1)
Organisationseinheit der BAM
- 1 Analytische Chemie; Referenzmaterialien (65)
- 6 Materialchemie (52)
- 8 Zerstörungsfreie Prüfung (35)
- 6.1 Oberflächen- und Dünnschichtanalyse (22)
- 1.1 Anorganische Spurenanalytik (17)
- 8.2 Zerstörungsfreie Prüfmethoden für das Bauwesen (16)
- 4 Material und Umwelt (12)
- 6.3 Strukturanalytik (12)
- 1.2 Biophotonik (10)
- 1.7 Organische Spuren- und Lebensmittelanalytik (10)
Optical lock-in thermography is a completely contactless and very sensitive NDT technique. As an optical source of energy, incandescent (i.e. halogen) lamps are most commonly used because they are relatively inexpensive and offer high irradiances at the test site. However, they are strongly restricted by their low modulation bandwidth with a maximum modulation frequency of only about 1 Hz. The use of high-power kilowatt-class laser sources, e.g. diode laser arrays, pushes this constraint beyond 100 Hz, see Fig.1. This allows for the exploration of the near-surface region of metals and layer systems with better and more accurate penetration depth and depth resolution. Moreover, these lasers are virtually free of any additional thermal radiation that could interfere with the “true” thermal response emitted from the heated sample. In turn, they can be easily used in a one-sided test configuration.
Using the one-dimensional solution to the thermal heat diffusion equation together with the absorptance of the material which is illuminated with a harmonically modulated light source, we can calculate the temperature oscillation at the surface of a solid. As a second step, we calculate the corresponding oscillation of the total thermal emission using Stefan-Boltzmann law as a first order approximation and taking into account the emissivity of the material. Within this framework we can calculate the minimal irradiance of a light source necessary to provoke a measurable signal within a thermographic camera at a noise equivalent temperature difference (NETD) of 30 mK. In Fig. 2 this relationship is displayed for a wide spectrum of modulation frequencies and for a number of different light sources scaled to the same electrical input power and illumination area. Using this figure, it is now easily possible to analyze the range of materials to be tested using lock-in thermography, since only the materials (dotted lines) below the irradiance-vs-frequency curves (solid lines) are heated in excess of the camera’s NETD. This figure clearly shows that laser sources considerably increase the application range of lock-in thermography, since especially for metals with a high reflectance and high thermal diffusivity a high irradiance is vitally important to allow for lock-in texting.
We present current activities with kilowatt-class high-power laser sources for advanced lock-in thermography and focus on the application of laser arrays that offer a very high irradiation strength over a large sample area beyond the mentioned advantages.
Optical lock-in thermography is a completely contactless and very sensitive NDE technique. As an optical source of energy, incandescent (i.e. halogen) lamps are most commonly used because they are relatively inexpensive, do not need any work safety measures and offer high irradiances at the test site. However, they are strongly restricted by their low modulation bandwidth with a maximum modulation frequency of only about 1 Hz. The use of high-power kilowatt-class laser sources, e.g. diode laser arrays, pushes this constraint beyond 100 Hz. This allows for the exploration of the near-surface region of metals and layer systems with better and more accurate penetration depth and depth resolution. Moreover, these lasers are virtually free of any additional thermal radiation that could interfere with the “true” thermal response emitted from the heated sample. In turn, they can be easily used in a one-sided test configuration. Altogether using lasers considerably increases the application range of lock-in thermography, since especially for metals with a high reflectance and high thermal diffusivity a high irradiance is vitally important to allow for lock-in testing [1, 2]. We report on the mentioned benefits of using such high-power lasers and analyze the range of materials to be tested using lock-in thermography in dependence on the laser irradiance, the modulation frequency, the infrared camera as well as the optical and thermal material parameters. In this context, we also address a number of systematic errors caused by the use of ideal and non-ideal heat sources. For example, the measured phase angle in lock-in thermography depends on the irradiance and the modulation bandwidth of the source. This in turn has a decisive influence on the uncertainty in the quantification of, e.g. layer thicknesses.
Die Laserinduzierte Plasmaspektroskopie (engl.: Laser-induced Breakdown Spectroscopy, kurz: LIBS) ist eine Kombination aus Laserablation mittels eines energiereichen Laser-Pulses, der Erzeugung eines Plasmas auf der zu untersuchenden Oberfläche und dem quantitativen Nachweis der Elementzusammensetzung durch spektroskopische Untersuchung der vom Plasma emittierten Strahlung. Ein LIBS-Gerät liefert dem sachkundigen Planer Daten für die Bewertung des Ist-Zustandes von Bauwerken unserer Infrastruktur durch die zweidimensionale Erfassung von Elementverteilungen. Typische Anwendungen sind die Erfassung von Chlor, Schwefel, Kohlenstoff, Natrium, Kalium und Lithium in Beton oder als – Qualitätssicherung – der Nachweis der mit einem Marker versehenen Tiefenhydrophobierung.
In Zusammenarbeit zwischen Industriepartnern und der BAM wurden ein Labor und ein mobiles LIBS-System für die Vor-Ort-Messungen entwickelt. Die Analyse erfolgt vollautomatisch. Die Ortsauflösung beträgt bis zu 0,1 mm x 0,1 mm. Es können Messflächen von 140 mm x 170 mm gescannt werden. Die Erstellung von 2D-Elementverteilungen im Beispiel unten benötigt weniger als 10 Minuten.
Detection of ion ingress by LIBS for Evaluation of the remaining lifetime of a concrete structure
(2018)
The majority of the built infrastructure is made of concrete, which is a multiphase system made of cement, aggregates, water and pores. Concrete is often used in combination with steel as reinforced concrete. Environmental influences, especially the ingress of harmful ions in combination with the ingress of water, trigger different damage processes which reduce the designed lifetime of a structure. The ingress of chlorides from de-icing salt or sea water leads to corrosion of the reinforcement. Also the carbonation of the concrete may trigger the corrosion of the reinforcement. The ingress of alkalis from de-icing salts may cause the expansion of the amorphous silica aggregates (alkali-silica reaction) through formation of a swelling gel of calcium silicate hydrate if water is present. The ingress of sulfates may cause spalling of the concrete surface due to ettringite formation.
For the standard procedure in civil engineering cores are taken, cut in slices, grinded and the obtained homogenized powder is solved in acid and investigated by standard procedures.
BAM has developed the LIBS technique for the 2D evaluation of the chemical composition of concrete [1-11]. The technique is established for automated laboratory use with high numbers of samples to investigate transport processes of harmful species (Cl-, CO2, SO42- and alkalis) in concrete. Information about ingress depth and the quantitative values are important to estimate the remaining lifetime of the infrastructure. LIBS is a surface technique. To get information about the ingress depth, a core has to be taken and cut in the middle. The measurements are carried out at the cross section. The main advantages of LIBS are the direct measurement on the surface of the concrete, fast analysis (sample rate 100 Hz) with a spatial resolution of up to 100 µm, the consideration of the heterogeneity of the concrete and the possibility of automated measurements which save a lot of manpower and time. As an example the investigation of ingress profiles for standard diffusion and migration tests in civil engineering takes hours in comparison to just a few minutes using LIBS. At the same time a 2D-evaluation provides information about hot spots of elemental concentration which may not be found by standard methods.
Ingress of chlorides due to a crack in a repair mortar. Left: Photo of the cross section of a concrete core and the surface investigated by LIBS (area 70 mm x 70 mm). Right: Color coded chlorine intensity on the cross section of a concrete core, dark red represents high chlorine content.
The state of the art of LIBS technique for applications in civil engineering will be presented, including typical results of 2D investigation of concrete in laboratory. The performance is also demonstrated by examples for onsite applications using a mobile LIBS system. The road map to standardization is presented as well.
Main aim is to improve ultrasonic sensor networks to monitor concrete structures under dynamic loads. Novel algorithms have to be developed and tested to separate the influence of various effects for field data. Ways to quantify the interpretation of ultrasonic data e.g. in terms of degree of damage or capacity, have to be found. Improve and simplify imaging techniques, extend them to arbitrary structures, to foster field applications.
Die Simulation von Ultraschallausbreitung ist ein wesentliches Hilfsmittel zur Optimierung von Prüfanordnungen und wird zunehmend in der Prüfvorbereitung eingesetzt. Eisenbahnschienen sind Bauteile mit komplexer Geometrie und im eingebauten Zustand eingeschränkter Zugänglichkeit. Bei der Prüfung im Feld entstehen aus der Schienengeometrie komplexe Echosignale mit Formanzeigen, die schwer zu interpretieren sind.
Für das bessere Verständnis der Schallausbreitung in der Eisenbahnschiene wird diese in einem ersten Schritt mit Hilfe verschiedener Ansätze modelliert. Hierbei werden Finite Elemente Methoden und semi-analytischen Modelle verwendet. In einem zweiten Schritt werden die Ergebnisse der Simulationsmodelle einander gegenübergestellt und mit Messungen an realen Schienen verglichen.
Ziel dieser Untersuchungen ist die Validierung von Simulationsverfahren mit Hilfe von Messdatensätzen und Überprüfung der Anwendbarkeit bei der Bewertung von Ergebnissen der Schienenprüfung.
Die Simulation von Ultraschallausbreitung ist ein wesentliches Hilfsmittel zur Optimierung von Prüfanordnungen und wird zunehmend in der Prüfvorbereitung eingesetzt.
Eisenbahnschienen sind Bauteile mit komplexer Geometrie und im eingebauten Zustand eingeschränkter Zugänglichkeit. Bei der Prüfung im Feld entstehen aus der Schienengeometrie komplexe Echosignale mit Formanzeigen, die schwer zu interpretieren sind.
Für das bessere Verständnis der Schallausbreitung in der Eisenbahnschiene wird diese in einem ersten Schritt mit Hilfe verschiedener Ansätze modelliert. Hierbei werden Finite Elemente Methoden und semi-analytischen Modelle verwendet. In einem zweiten Schritt werden die Ergebnisse der Simulationsmodelle einander gegenübergestellt und mit Messungen an realen Schienen verglichen.
Ziel dieser Untersuchungen ist die Validierung von Simulationsverfahren mit Hilfe von Messdatensätzen und Überprüfung der Anwendbarkeit bei der Bewertung von Ergebnissen der Schienenprüfung.
Two calibration-free (CF) LIBS approaches are used for the quantitative analysis of cement samples: the CF-LIBS based on the Boltzmann plot method and the Monte Carlo (MC) LIBS based on the iterative spectrum fitting. In CF-LIBS, the inverse problem is solved, i.e. the elemental concentrations are determined by the reconstruction of plasma parameters from spectra. The MC-LIBS technique solves the direct problem by finding the highest correlation between the model-generated and experimental spectrum. The accuracy of both calibration-free LIBS methods suffers from factors such as inaccurately determined instrumental function, the deviation of experimental plasma from the mathematical model used, not taking into account the collection geometry, and from the uncertainty of spectroscopic data. The both calibration-free LIBS approaches are first applied to synthetic spectra which perfectly suit the mathematical model of the method, i.e. the model of the uniform, isothermal, and stationary plasma. This test yields the accuracy of both the approaches for the ideal case. In addition, the accuracy of both the methods is investigated for non-uniform and non-isothermal plasma, because real laser-induced plasma often has high gradients in temperature and particle number densities. Finally, both calibration-free LIBS approaches are applied to experimental spectra obtained from cement samples. The figures of merits of two approaches are compared when working with both synthetic and experimental spectra.
Two calibration-free LIBS techniques are used for the quantitative analysis of synthetic cement samples: the CF-LIBS based on the Boltzmann plot method and the Monte Carlo (MC) LIBS based on the iterative spectrum fitting. In CF-LIBS, the inverse problem is solved, i.e. the elemental concentrations are determined by the reconstruction of plasma parameters from spectra. The MC-LIBS technique solves the direct problem by finding the highest correlation between the model-generated and experimental spectrum. The accuracy of both calibration-free LIBS methods suffers from factors such as inaccurately determined instrumental function, the deviation of experimental plasma from the mathematical model used, not taking into account the collection geometry and from the uncertainty of spectroscopic data. Therefore, the both calibration-free LIBS approaches are applied to synthetic spectra which perfectly suit the mathematical model of the method. This test yields the accuracy of both the approaches for the ideal case. In addition, the accuracy of both methods is investigated for non-isothermal plasma, because real laser-induced plasma often has high gradients in temperature. Both methods assume an isothermal plasma.