Emneord:
Astronomi og astrofysikk,
Solfysikk
Publikasjoner
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Pecseli, Hans Laszlo; Trulsen, Jan Karsten; Yan, Ning; Nielsen, Anders H.; Rasmussen, Jens Juul & Zhang, Yufei
(2026).
Small scale turbulence and plasma transport in the EAST tokamak.
Plasma Physics and Controlled Fusion.
ISSN 0741-3335.
68(3).
doi:
10.1088/1361-6587/ae4f20.
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A movable multi-pin probe in deuterium discharges in the superconducting EAST tokamak was used to recover local plasma parameters and electrostatic fluctuation characteristics along prescribed radial traverses. Several spatial regions are distinguished during the radial probe motion. The present analysis is restricted to a region inside the last closed magnetic flux surface, where locally homogeneous conditions can be argued. The data are analyzed with particular attention to the presence of cm-scale electrostatic plasma fluctuations. The detailed characteristics of the observed structures are described and quantified. Their contribution to anomalous plasma transport across magnetic field lines is demonstrated. Supported by correlation analyses, the primary analysis tool is conditional averaging, where the results are here presented with conditional variances included. Detailed information on properties of plasma blobs propagating across magnetic field lines is recovered. Alternative diagnostic methods are described and given analytic support. These tools can be applied when partial or reduced results suffice, offering also means of cross-checking basic fluctuation parameters. The agreement is good for the present plasma conditions.
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Omang, Marianne Gjestvold; Hauge, K.O. & Trulsen, Jan Karsten
(2023).
Combustion models for shock-induced cloud ignition of aluminium particles using smoothed particle hydrodynamics.
Shock Waves.
ISSN 0938-1287.
doi:
10.1007/s00193-023-01148-z.
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Abstract The present work is a numerical follow-up on our published experimental paper on shock ignition of aluminium particle clouds in the low-temperature regime. The in-house multi-phase regularized smoothed particle hydrodynamics (MP-RSPH) code is used to perform numerical simulations with an increasing degree of complexity, looking at single-phase, inert, and reactive particles in separate simulations. The first part of the paper gives a short description of the additional physics added to the code. Based on the experimental results, the numerical code is then used to estimate the particle temperature at the time of ignition. Results from simulations with three different numerical descriptions, the diffusive, kinetic, and total burn rates, are then compared to the experimental results. The two diffusive burn rate simulations (K &H and O &H) show the best fit to the experimental results. The burn rate formula based on our experimental data (O &H) is preferred, since it has the gas temperature dependency included and does not require additional parameter adjustments. The results from the numerical simulations support the theory that the observed aluminium particle cloud burning process is diffusive, as indicated in the experimental paper.
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Sato, Hiroatsu; Pecseli, Hans Laszlo; Trulsen, Jan Karsten; Sandholt, Per Even & Farrugia, Charles J.
(2022).
Impulse-driven oscillations of the near-Earth's magnetosphere.
Annales Geophysicae.
ISSN 0992-7689.
40(6),
s. 641–663.
doi:
10.5194/angeo-40-641-2022.
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It is argued that a simple model based on magnetic image arguments suffices to give a convincing insight into both the basic static as well as some transient dynamic properties of the near-Earth's magnetosphere, particularly accounting for damped oscillations being excited in response to impulsive perturbations. The parameter variations of the frequency are given. Qualitative results can also be obtained for heating due to the compression of the radiation belts. The properties of this simple dynamic model for the solar wind–magnetosphere interaction are discussed and compared to observations. In spite of its simplicity, the model gives convincing results concerning the magnitudes of the near-Earth's magnetic and electric fields. The database contains ground-based results for magnetic field variation in response to shocks in the solar wind. Here, the observations also include data from the two Van Allen satellites.
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Pécseli, Hans L & Trulsen, Jan Karsten
(2021).
On the applicability of Taylor's hypothesis, including small sampling velocities.
Journal of Fluid Mechanics.
ISSN 0022-1120.
932.
doi:
10.1017/jfm.2021.969.
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Taylor's hypothesis, or the frozen turbulence approximation, can be used to estimate also the specific energy dissipation rate ϵ by comparing experimental results with the Kolmogorov–Obukhov expression. The hypothesis assumes that a frequency detected by an instrument moving with a constant large velocity <i><b>V</i></b> can be related to a wavenumber by <i><b>ω=kV</i></b>. It is, however, not obvious how large the translational velocity has to be in order to make the hypothesis valid, or at least applicable with some acceptable uncertainty. Using the space–time-varying structure function for homogeneous and isotropic conditions, this question is addressed in the present study with emphasis on small velocities <i><b>V</i></b>. The structure function is obtained using results from numerical solutions of the Navier–Stokes equation. Particular attention is given to the <i><b>V</i></b> variation of the estimated specific energy dissipation, <i><b>ϵ<sub>est</sub></i></b>, compared with the actual value, <i><b>ϵ</i></b>, used in the numerical calculations. In contrast to previous studies, the results emphasize velocities <i><b>V</i></b> less than or comparable to the one-component root-mean-square velocity, <i><b>u<sub>rms</sub></i></b>. We find that <i><b>ϵ</i></b> can be determined to an acceptable accuracy for <i><b>V</i></b>≥<b>0.3</b><i><b>u<sub>rms</sub></i></b>. A simple analytical model is suggested to explain the main features of the observations, both Eulerian and Lagrangian. The model assumes that the observed time variations are solely due to eddies moving past the observer, thus ignoring eddy deformation and intermittency effects. In spite of these simplifications, the analysis accounts for most of the numerical results when also eddy-size-dependent velocities are accounted for.
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Fredriksen, Åshild; Pécseli, Hans L & Trulsen, Jan Karsten
(2020).
Anomalous transport due to large coherent structures in a magnetized toroidal plasma.
Plasma Physics and Controlled Fusion.
ISSN 0741-3335.
63(1).
doi:
10.1088/1361-6587/abc518.
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Anomalous transport due to large coherent structures, or coherent events, is studied experimentally in a magnetized toroidal discharge plasma. The present analysis emphasizes anomalous plasma losses as well as transport of electron thermal energy density across magnetic field lines. The experiment was carried out in the Blaamann device at the University of Tromsø. The diagnostics are based on data for potential, density and electron temperature variations as detected by Langmuir probes. Most of the data analysis uses conditional sampling. The flux of thermal energy density can be broken down into several components which are analyzed separately. Experimental means for obtaining the space-time variation of the complete polarization drifts are demonstrated, and the results compared with the fluctuating E × B<sub>0</sub>/<i>B</i><sup>2</sup><sub>0</sub>-velocities. For the present conditions these polarization drifts contribute only little to the plasma losses, but for other discharge parameters in heavier gases they can be important. Our results show that while the density, the potential and the electric field variations are dominated by large scales, the vorticity of the E × B<sub>0</sub>/<i>B</i><sup>2</sup><sub>0</sub>-flow as well as the ion polarization drifts are strongly intermittent.
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Pécseli, Hans L; Trulsen, Jan Karsten; Stiansen, Jan Erik & Sundby, Svein
(2020).
Feeding of plankton in a turbulent environment: A comparison of analytical and observational results covering also strong turbulence.
Fluids.
5(1).
doi:
10.3390/fluids5010037.
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The present studies address feeding of plankton in turbulent environments, discussed by a comparison of analytical results and field data. Various models for predator-prey encounters and capture probabilities are reviewed. Generalized forms for encounter rates and capture probabilities in turbulent environments are proposed. The analysis emphasizes ambush predators, exemplified by cod larvae Gadus morhua L. in the start-feeding phase (stage 7 larvae) collected in shallow waters near Lofoten, Norway. During this campaign, data were obtained at four sites with strongly turbulent conditions induced by tidal currents and long-wave swells, and one site where the turbulence had a lower level in comparison. The guts of the selected cod larvae were examined in order to determine the number of nauplii ingested. Analytically obtained probability densities for the gut content were compared with observations and the results used for estimating the rate of capture of the nauplii. This capture rate was then compared with analytical results using also data for the surroundings, such as measured prey densities and turbulence conditions, as quantified by the specific energy dissipation rate. Different from earlier studies, the presented data include conditions where the turbulence exceeds the level for optimal larval encounter-capture rates.
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Pécseli, Hans L; Trulsen, Jan Karsten; Stiansen, Jan Erik; Sundby, Svein & Fossum, Petter
(2019).
Feeding of plankton in turbulent oceans and lakes.
Limnology and Oceanography.
ISSN 0024-3590.
64(3),
s. 1034–1046.
doi:
10.1002/lno.11094.
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Analytical models for the statistical distribution of the gut content of fish larvae in a turbulent ocean environment are compared to data obtained in a field experiment. The proposed model allows the nutrition state and thereby the survival probability of plankton populations to be estimated for given conditions and parameters characterizing their environment, i.e., prey concentrations and turbulence levels. These parameters are all available in the field data. Other parameters such as the capture range and fields of view together with a characteristic time for digesting prey are assumed to be known. The analysis allows an estimate for the probability density of the gut content of plankton in terms of the number of nauplii in the gut. In particular, the analytical results give a basis for evaluating the average gut content of a given plankton population on the basis of basic information concerning the prey concentration and the turbulence intensity. Also analytical models for the prey capture rates are compared with results based on the field data. The analysis emphasizes the effects of turbulence.
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Omang, Marianne Gjestvold; Hauge, Knut Ove & Trulsen, Jan Karsten
(2019).
Exploring the Capability of a New Shock Tube Facility to Investigate Shock Interaction with Inert Particle Columns.
I Sasoh, Akihiro; Aoki, Toshiyuki & Katayama, Masahide (Red.),
31st International Symposium on Shock Waves 2: Applications.
Springer Nature.
ISSN 9783319910161.
s. 705–709.
doi:
10.1007/978-3-319-91017-8_88.
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Fredriksen, Åshild; Pecseli, Hans & Trulsen, Jan Karsten
(2018).
A solvable model for the basic properties of a simple magnetized plasma torus.
Plasma Physics and Controlled Fusion.
ISSN 0741-3335.
60:085021(8).
doi:
10.1088/1361-6587/aacd2a.
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A simple magnetized plasma torus is modeled by using a 'top-hat' density variation. The benefit of this simplification is an exactly solvable model, allowing for a few additions, such as an externally maintained parabolic steady state potential variation imposed on the plasma. The combined effects of the resulting plasma rotation and the plasma polarization due to magnetic field gradient particle drifts can be described. The stabilizing and confining effects of plasma rotation are explicitly demonstrated. In a special high plasma density limit the results are confirmed by a more general model, indicating that the results of the top-hat model can be used with confidence in more general cases. A small vertical magnetic field component can be included for a plasma with neutral collisions and its influence on the electron dynamics studied. The effects of ion–neutral collisions are also included. The rotation and polarization of the plasma has different effects on the time variations of the plasma density and potential. As a reference we use data from the Blaamann device at the University of Tromsø obtained by a movable multi-probe, measuring variations in density, floating potential and an electric field component. The fluctuations in the plasma are characterized by auto-correlations and by cross-correlations between the signal from a fixed reference probe and data. The model accounts adequately for the phase variations of the signals for varying spatial multi-probe positions.
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Bergsaker, Anne Schad; Fredriksen, Åshild; Pecseli, Hans & Trulsen, Jan Karsten
(2015).
Models for the probability densities of the turbulent plasma flux in magnetized plasmas.
Physica Scripta.
ISSN 0031-8949.
90(10).
doi:
10.1088/0031-8949/90/10/108005.
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Garcia, Odd Erik; Leer, Egil; Pecseli, Hans & Trulsen, Jan Karsten
(2015).
Magnetic field-aligned plasma currents in gravitational fields.
Annales Geophysicae.
ISSN 0992-7689.
33(3),
s. 257–266.
doi:
10.5194/angeo-33-257-2015.
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Analytical models are presented for currents along vertical magnetic field lines due to slow bulk electron motion in plasmas subject to a gravitational force. It is demonstrated that a general feature of this problem is a singularity in the plasma pressure force that develops at some finite altitude when a plasma that is initially in static equilibrium is set into slow motion. Classical fluid models thus do not allow general steady-state solutions for field-aligned currents. General solutions have to be non-stationary, varying on time scales of many periods of a plasma equivalent to the Brunt–Väisälä frequency. Except for very special choices of parameters, a steady-state solution exists only in an average sense. The conditions at large altitudes turn out to be extremely sensitive to even small changes in parameters at low altitudes. Low frequency fluctuations detected at large altitudes in the polar regions need not be caused by local low frequency instabilities, but merely reflect small fluctuations in conditions at low altitudes.
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Bergsaker, Anne Schad; Fredriksen, Åshild; Pecseli, Hans & Trulsen, Jan Karsten
(2014).
Analytical models for skewness-kurtosis relations in turbulent transport,
41st EPS Conference on Plasma Physics.
European Physical Society.
ISSN 9782914771900.
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Pecseli, Hans; Trulsen, Jan Karsten & Fiksen, Øyvind
(2014).
Predator-prey encounter and capture rates in turbulent environments.
Limnology and Oceanography.
ISSN 0024-3590.
4,
s. 85–105.
doi:
10.1215/21573689-2768717.
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Miloch, Wojciech Jacek; Pecseli, Hans & Trulsen, Jan Karsten
(2013).
Unstable ring-shaped ion distribution functions induced by charge–exchange collisions.
Plasma Physics and Controlled Fusion.
ISSN 0741-3335.
55(12).
doi:
10.1088/0741-3335/55/12/124006.
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Rekaa, Vegard Lundby; Pecseli, Hans & Trulsen, Jan Karsten
(2013).
Self-similar space-time evolution of an initial density discontinuity.
Physics of Plasmas.
ISSN 1070-664X.
20(7).
doi:
10.1063/1.4816953.
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The space-time evolution of an initial step-like plasma density variation is studied. We give particular attention to formulate the problem in a way that opens for the possibility of realizing the conditions experimentally. After a short transient time interval of the order of the electron plasma period, the solution is self-similar as illustrated by a video where the space-time evolution is reduced to be a function of the ratio x/t. Solutions of this form are usually found for problems without characteristic length and time scales, in our case the quasi-neutral limit. By introducing ion collisions with neutrals into the numerical analysis, we introduce a length scale, the collisional mean free path. We study the breakdown of the self-similarity of the solution as the mean free path is made shorter than the system length. Analytical results are presented for charge exchange collisions, demonstrating a short time collisionless evolution with an ensuing long time diffusive relaxation of the initial perturbation. For large times, we find a diffusion equation as the limiting analytical form for a charge-exchange collisional plasma, with a diffusion coefficient defined as the square of the ion sound speed divided by the (constant) ion collision frequency. The ion-neutral collision frequency acts as a parameter that allows a collisionless result to be obtained in one limit, while the solution of a diffusion equation is recovered in the opposite limit of large collision frequencies. © 2013 AIP Publishing LLC.
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Miloch, Wojciech Jacek; Yaroshenko, V.; Vladimirov, Sergei V.; Pecseli, Hans & Trulsen, Jan Karsten
(2012).
Spacecraft charging in flowing plasmas; numerical simulations.
Journal of Physics: Conference Series (JPCS).
ISSN 1742-6588.
370.
doi:
10.1088/1742-6596/370/1/012004.
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Sato, Hiroatsu; Pecseli, Hans & Trulsen, Jan Karsten
(2012).
Fluctuations in the direction of propagation of intermittent low-frequency ionospheric waves.
Journal of Geophysical Research (JGR): Space Physics.
ISSN 2169-9380.
117.
doi:
10.1029/2011JA017242.
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Pecseli, Hans; Trulsen, Jan Karsten & Fiksen, Øyvind
(2012).
Predator-prey encounter and capture rates for plankton in turbulent environments.
Progress in Oceanography.
ISSN 0079-6611.
101(1),
s. 14–32.
doi:
10.1016/j.pocean.2011.12.001.
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Fattorini, L.; Fredriksen, Åshild; Pecseli, Hans; Riccardi, C. & Trulsen, Jan Karsten
(2012).
Turbulent transport in a toroidal magnetized plasma.
Plasma Physics and Controlled Fusion.
ISSN 0741-3335.
54(8).
doi:
10.1088/0741-3335/54/8/085017.
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Rekaa, Vegard Lundby; Pecseli, Hans & Trulsen, Jan Karsten
(2012).
Numerical studies of a plasma diode with external forcing.
Physics of Plasmas.
ISSN 1070-664X.
19(8).
doi:
10.1063/1.4747620.
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With reference to laboratory Q-machine studies we analyze the dynamics of a plasma diode under external forcing. Assuming a strong axial magnetic field, the problem is analyzed in one spatial dimension by a particle-in-cell code. The cathode is assumed to be operated in electron rich conditions, supplying an abundance of electrons. We compare different forcing schemes with the results obtained by solving the van der Pol equation. In one method of forcing we apply an oscillation in addition to the DC end plate bias and consider both amplitude and frequency variations. An alternative method of perturbation consists of modelling an absorbing grid at some internal position. Also in this case we can have a constant frequency with varying amplitude or alternatively an oscillation with chirped frequency but constant amplitude. We find that the overall features of the forced van der Pol equation are recovered, but the details in the plasma response need more attention to the harmonic responses, requiring extensions of the model equation. The analysis is extended by introducing collisional effects, where we emphasize charge exchange collisions of ions, since these processes usually have the largest cross sections and give significant modifications of the diode performance. In particular we find a reduction in oscillator frequency, although a linear scaling of the oscillation time with the system length remains also in this case. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing.
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Daldorff, Lars Kristen Selberg; Pecseli, Hans; Trulsen, Jan Karsten; Ulriksen, Margit Iren; Eliasson, B. & Stenflo, Lennart
(2011).
Nonlinear beam generated plasma waves as a source for enhanced plasma and ion acoustic lines.
Physics of Plasmas.
ISSN 1070-664X.
18(5).
doi:
10.1063/1.3582084.
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Sato, Hiroatsu; Pecseli, Hans & Trulsen, Jan Karsten
(2011).
Fluctuations in the Direction of Propagation of Low Frequency Ionospheric Waves.
I Ouwehand, L (Red.),
Proceedings of the 20th ESA Symposium on European Rocket and Balloon Programmes and Related Research.
ESA Communications.
ISSN 9789290922643.
s. 625–628.
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Børve, Steinar; Sato, Hiroatsu; Pecseli, Hans & Trulsen, Jan Karsten
(2011).
Minute-scale period oscillations of the magnetosphere.
Annales Geophysicae.
ISSN 0992-7689.
doi:
10.5194/angeo-29-663-2011.
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Oscillations with periods on the order of 5–10 min have been observed by instrumented spacecrafts in the Earth's magnetosphere. These oscillations often follow sudden impacts related to coronal mass ejections. It is demonstrated that a simple model is capable of explaining these oscillations and give a scaling law for their basic characteristics in terms of the basic parameters of the problem. The period of the oscillations and their anharmonic nature, in particular, are accounted for. The model has no free adjustable numerical parameters. The results agree well with observations. The analysis is supported by numerical simulations solving the Magneto-Hydro-Dynamic (MHD) equations in two spatial dimensions, where we let a solar wind interact with a magnetic dipole representing a magnetized Earth. We consider two tilt-angles of the magnetic dipole axis. We find the formation of a magnetosheath with the magnetopause at a distance corresponding well to the analytical results. Sudden pulses in the model solar wind sets the model magnetosphere into damped oscillatory motions and quantitatively good agreement with the analytical results is achieved.
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Pecseli, Hans; Trulsen, Jan Karsten & Fiksen, Øyvind
(2010).
Predator-prey encounter rates in turbulent water: Analytical models and numerical tests.
Progress in Oceanography.
ISSN 0079-6611.
85(3-4),
s. 171–179.
doi:
10.1016/j.pocean.2010.01.002.
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Miloch, Wojciech Jacek; Rekaa, Vegard Lundby; Pecseli, Hans & Trulsen, Jan Karsten
(2010).
Ion acoustic double layers forming behind irradiated solid objects in streaming plasmas.
Journal of Plasma Physics.
ISSN 0022-3778.
76,
s. 429–439.
doi:
10.1017/S002237780999064X.
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Krane, Bård; Pecseli, Hans; Sato, Hiroatsu; Trulsen, Jan Karsten & Wernik, A. W.
(2010).
Low-frequency electrostatic waves in the ionospheric E region.
Plasma Sources Science & Technology.
ISSN 0963-0252.
19(3).
doi:
10.1088/0963-0252/19/3/034007.
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Miloch, Wojciech Jacek; Vladimirov, Sergei V.; Pecseli, Hans & Trulsen, Jan Karsten
(2009).
Charging of insulating and conducting dust grains by flowing plasma and photoemission.
New Journal of Physics.
11.
doi:
10.1088/1367-2630/11/4/043005.
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Miloch, Wojciech Jacek; Vladimirov, Sergei V.; Pecseli, Hans & Trulsen, Jan Karsten
(2009).
Charging of Dust in the Presence of a Directed Photon Flux: Numerical Simulations.
Journal of Plasma and Fusion Research Series.
8,
s. 265–268.
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Børve, Steinar; Speith, Roland & Trulsen, Jan Karsten
(2009).
Numerical dissipation in RSPH simulations of astrophysical flows with applications to protoplanetary disks.
The Astrophysical Journal (ApJ).
ISSN 0004-637X.
701(2),
s. 1269–1282.
doi:
10.1088/0004-637X/701/2/1269.
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Pecseli, Hans & Trulsen, Jan Karsten
(2009).
Predator-prey Encounter Rates in Turbulent Environments: Consequences of Inertia Effects and Finite Sizes.
AIP Conference Proceedings.
ISSN 0094-243X.
1177,
s. 85–95.
doi:
10.1063/1.3253968.
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Omang, Marianne Gjestvold; Christensen, S. O.; Børve, Steinar & Trulsen, Jan Karsten
(2009).
Height of burst explosions: a comparative study of numerical and experimental results.
Shock Waves.
ISSN 0938-1287.
19(2),
s. 135–143.
doi:
10.1007/s00193-009-0196-8.
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Miloch, Wojciech Jacek; Vladimirov, Sergei V.; Pecseli, Hans & Trulsen, Jan Karsten
(2009).
Interaction of two elongated dust grains in flowing plasmas studied by numerical simulations.
Physics of Plasmas.
ISSN 1070-664X.
16(2).
doi:
10.1063/1.3077667.
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Miloch, Wojciech Jacek; Trulsen, Jan Karsten & Pecseli, Hans
(2008).
Numerical studies of ion focusing behind macroscopic obstacles in a supersonic plasma flow.
Physical Review E. Statistical, Nonlinear, and Soft Matter Physics.
ISSN 1539-3755.
77.
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Miloch, Wojciech Jacek; Pecseli, Hans; Trulsen, Jan Karsten & Vladimirov, Sergei V.
(2008).
Ion focusing and interaction potential for spherical and rodlike obstacles in a supersonic plasma flow: numerical simulations.
AIP Conference Proceedings.
ISSN 0094-243X.
1041,
s. 287–288.
doi:
10.1063/1.2997133.
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Guio, Patrick; Miloch, Wojciech Jacek; Pecseli, Hans & Trulsen, Jan Karsten
(2008).
Sound Radiation from Moving Point-Like Charged Particles in Plasmas.
AIP Conference Proceedings.
ISSN 0094-243X.
1061,
s. 142–151.
doi:
10.1063/1.3013762.
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Dyrud, Lars; Krane, B.; Oppenheim, Meers; Pecseli, Hans; Trulsen, Jan Karsten & Wernik, Andrzej
(2008).
Structure functions and intermittency in ionospheric plasma turbulence.
Nonlinear processes in geophysics.
ISSN 1023-5809.
15(6),
s. 847–862.
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Dyrud, Lars; Wilson, Derek; Børve, Steinar; Trulsen, Jan Karsten; Pecseli, Hans & Close, Sigrid
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(2008).
Plasma and electromagnetic wave simulations of meteors.
Advances in Space Research.
ISSN 0273-1177.
42,
s. 136–142.
doi:
10.1016/j.asr.2007.03.048.
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Every day billions of meteoroids impact and disintegrate in the Earth’s atmosphere. Current estimates for this global meteor flux vary from 2000-200,000 tons per year, and estimates for the average velocity range between 10 km/s to 70 km/s. The basic properties of this global meteor flux, such as the average mass, velocity, and chemical composition remain poorly constrained. We believe much of the mystery
surrounding the basic parameters of the interplanetary meteor flux exists for the following reason, the unknown sampling characteristics of different radar meteor observation techniques, which are used to derive or constrain most models. We believe this arises due to poorly understood radio scattering characteristics of the meteor plasma, especially in light of recent work showing that plasma turbulence and instability greatly influences meteor trail properties at every stage of evolution. We present our results on meteor plasmas simulations of head echoes using particle in cell (PIC) ions, which show that electric fields
strongly influence early stage meteor plasma evolution, by accelerating ions away from the meteoroid body. We also present the results of finite difference time domain electromagnetic simulations (FDTD), which can calculate the radar cross section of the simulated meteor plasmas. These simulations have shown that the radar cross section depends in a complex manner on a number of parameters. These include the angle between radar and meteor entry, a large dependence on radar frequency, which shows that for a given meteor plasma size and density, the reflectivity as a function of probing radar frequency varies, but typically peaks below 100 MHz.
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Dyrud, Lars; Wilson, Derek; Børve, Steinar; Trulsen, Jan Karsten; Pecseli, Hans & Close, Sigrid
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(2008).
Plasma and Electromagnetic Simulations of Meteor Head Echo Radar Reflections.
Earth, Moon, and Planets.
ISSN 0167-9295.
102.
doi:
10.1007/s11038-007-9189-8.
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Recently, meteor head echo detections from high powered large aperture radars (HPLA) have brought new measurements to bear on the study of sporadic interplanetary meteors. These same observations have demonstrated an ability to observe smaller meteoroids without some of the geometrical restrictions of specular radar techniques. Yet incorporating data from various radar reflection types and from different radars into a single consistent model has proven challenging. We believe this arises due to poorly understood radio scattering characteristics of the meteor plasma, especially in light of recent work showing that plasma turbulence and instability greatly influences meteor trail
properties at every stage of evolution. In order to overcome some of the unknown relationships between meteoroid characteristics (such as mass and velocity) and the resulting
head echo radar cross-sections (RCS), we present our results on meteor plasma simulations of head echo plasmas using particle in cell (PIC) ions, which show that electric fields
strongly influence early stage meteor plasma evolution, by accelerating ions away from the meteoroid body at speeds as large as several kilometers per second. We also present the
results of finite difference time domain electromagnetic simulations (FDTD), which can calculate the radar cross-section of the simulated meteor plasma electron distributions. These simulations have shown that the radar cross-section depends in a complex manner on a number of parameters. In this paper we demonstrate that for a given head echo plasma the RCS as a function of radar frequency peaks at sqrt (2*peak plasma frequency) and then decays linearly on a dB scale with increasing radar frequency. We also demonstrate that for a fixed radar frequency, the RCS increases linearly on a dB scale with increasing head echo plasma frequency. These simulations and resulting characterization of the head echo radar cross-section will both help relate HPLA radar observations to meteoroid properties and aid in determining a particular radar facility’s ability to observe various meteoroid populations.
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Miloch, Wojciech Jacek; Vladimirov, Sergei V.; Pecseli, Hans & Trulsen, Jan Karsten
(2008).
Numerical simulations of potential distribution for elongated insulating dust being charged by drifting plasmas.
Physical Review E. Statistical, Nonlinear, and Soft Matter Physics.
ISSN 1539-3755.
78.
doi:
10.1103/PhysRevE.78.036411.
Fulltekst i vitenarkiv
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Guio, Patrick; Miloch, Wojciech Jacek; Pecseli, Hans & Trulsen, Jan Karsten
(2008).
Patterns of sound radiation behind pointlike charged obstacles in plasma flows.
Physical Review E. Statistical, Nonlinear, and Soft Matter Physics.
ISSN 1539-3755.
78.
doi:
10.1103/PhysRevE.78.016401.
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Fredriksen, Åshild; Fredriksen, A.A.; Pecseli, Hans L. & Trulsen, Jan
(2008).
Crash and recovery of the potential in a toroidal plasma column, as observed by generalized conditional sampling.
New Journal of Physics.
10(033030).
doi:
10.1088/1367-2630/10/3/033030.
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Vis sammendrag
Conditional sampling methods are generalized by applying a matched-filter on the reference signal. This generalized method is illustrated by data obtained in a magnetized toroidal plasma without rotational transform. By proper choice of the filter characteristics we can observe a rapid ‘crash’ in the electrostatic plasma potential in the entire plasma column. The crash is then followed by a slower recovery phase. The results are noticeably different from those found by using a more traditional conditional analysis of the same data. The significant differences between the two results indicate that generalizations of the conditional sampling method can give new insights. Conditionally obtained local power spectra demonstrate an enhancement in the amplitude of the fluctuations preceding the potential crash. The analysis is also illustrated by using a synthetic dataset.
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Miloch, Wojciech Jacek; Vladimirov, SV; Pecseli, Hans & Trulsen, Jan Karsten
(2008).
Wake behind dust grains in flowing plasmas with a directed photon flux.
Physical Review E. Statistical, Nonlinear, and Soft Matter Physics.
ISSN 1539-3755.
77.
doi:
10.1103/PhysRevE.77.065401.
Fulltekst i vitenarkiv
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Daldorff, Lars K Selberg; Pecseli, Hans & Trulsen, Jan Karsten
(2007).
Nonlinearly generated plasma waves as a model for enhanced ion acoustic lines in the ionosphere.
Geophysical Research Letters.
ISSN 0094-8276.
34.
doi:
10.1029/2007/2007GL031513.
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Børve, Steinar; Speith, Roland; Omang, Marianne Gjestvold & Trulsen, Jan Karsten
(2007).
Challenges related to particle regularization in SPH.
I Crespo, Alejandro J.C.; Gómez-Gesteira, Moncho; Souto-Iglesias, Antonio; Delorme, Louis & Grassa, José María (Red.),
SPHERIC – Smoothed Particle Hydrodynamics European Research Interest Community: SECOND INTERNATIONAL WORKSHOP.
Aica Ediciones.
ISSN 9788469061596.
s. 67–70.
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Omang, Marianne Gjestvold; Børve, Steinar; Christensen, S. O. & Trulsen, Jan Karsten
(2007).
Symmetry assumptions in SPH.
I Crespo, Alejandro J.C.; Gómez-Gesteira, Moncho; Souto-Iglesias, Antonio; Delorme, Louis & Grassa, José María (Red.),
SPHERIC – Smoothed Particle Hydrodynamics European Research Interest Community: SECOND INTERNATIONAL WORKSHOP.
Aica Ediciones.
ISSN 9788469061596.
s. 103–106.
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Pecseli, Hans & Trulsen, Jan Karsten
(2007).
Numerical studies of viscous effects for particle fluxes to perfectly absorbing spherical surfaces in turbulent environments: biological applications.
I Geurts, B. J.; Clercx, H & Uijttewaal, W (Red.),
Particle-Laden Flows. From Geophysical to Kolmogorov Scales.
Springer.
ISSN 9781402062179.
s. 229–241.
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Omang, Marianne Gjestvold; Børve, Steinar & Trulsen, Jan Karsten
(2007).
Shock collisions in 3D using an axi-symmetric regularized smoothed particle hydrodynamics code.
Shock Waves.
ISSN 0938-1287.
16,
s. 467–475.
doi:
10.1007/s00193-007-0083-0.
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Miloch, Wojciech Jacek; Pecseli, Hans & Trulsen, Jan Karsten
(2007).
Numerical simulations of the charging of dust particles by contact with hot plasmas.
Nonlinear processes in geophysics.
ISSN 1023-5809.
14,
s. 575–586.
Fulltekst i vitenarkiv
Se alle arbeider i NVA
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Sato, Hiroatsu; Pecseli, Hans Laszlo; Trulsen, Jan Karsten; Sandholt, Per Even & Farrugia, C
(2023).
Impulse-driven oscillations of near-Earth magnetosphere.
Fulltekst i vitenarkiv
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Pecseli, Hans & Trulsen, Jan Karsten
(2015).
Excess statistics with applications to turbulence in marine environments.
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Børve, Steinar; Sato, Hiroatsu; Pecseli, Hans & Trulsen, Jan Karsten
(2014).
LOW FREQUENCY OSCILLATIONS OF THE MAGNETOSPHERE.
Fulltekst i vitenarkiv
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Bergsaker, Anne Schad; Fredriksen, Åshild; Pecseli, Hans & Trulsen, Jan Karsten
(2014).
Analytical models for skewness-kurtosis relations in turbulent transport.
Fulltekst i vitenarkiv
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Miloch, Wojciech Jacek; Pecseli, Hans & Trulsen, Jan Karsten
(2013).
Kinetic plasma instabilities due to charge exchange collisions.
Fulltekst i vitenarkiv
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Miloch, Wojciech Jacek; Pecseli, Hans & Trulsen, Jan Karsten
(2013).
Numerical simulations of kinetic plasma instabilities induced by charge exchange collisions.
Fulltekst i vitenarkiv
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Pecseli, Hans; Trulsen, Jan Karsten & Fiksen, Øyvind
(2013).
Predator-prey encounter and capture rates in turbulent environments.
Fulltekst i vitenarkiv
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Pecseli, Hans; Miloch, Wojciech Jacek & Trulsen, Jan Karsten
(2013).
Kinetically unstable velocity distributions formed by charge exchange collisions with drifting ions.
Fulltekst i vitenarkiv
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Sato, Hiroatsu; Pecseli, Hans; Børve, Steinar & Trulsen, Jan Karsten
(2012).
Dynamic models for magnetospheric oscillations on the minute scale.
Fulltekst i vitenarkiv
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Miloch, Wojciech Jacek; Pecseli, Hans & Trulsen, Jan Karsten
(2012).
Numerical simulations of collisional partially ionized plasmas.
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Vis sammendrag
The stability of plasma can be related to the shape of its velocity distributions [1]. For instance, for ionospheric plasmas it is argued that ion velocity distributions can deviate from Maxwellian giving rise to plasma instabilities [2, 3]. In order to study the possibility for losscone instabilities in collisional plasmas with Hall currents, we have modified our particle-in-cell code to include collisional effects in a magentized plasma. We have the option of adding a DCelectric field in the direction perpendicular to the magnetic field. We present the results from the self-consistent three dimensional simulations of the plasma velocity distributions under such conditions. In this study we investigate the role of collisions with the neutral component for the evolution and stability of the velocity distributions. In the most general case, we include elastic electron-neutral collisions, as well as charge exchange and elastic ion-neutral collisions. The results will be important for a detailed understanding of low frequency ionospheric plasmas, for instance in the E-region.
References
[1] O. Penrose, Phys. Fluids 3, 258 (1960).
[2] J.-P. St.-Maurice, E. Winkler, and A. M. Hamza, J. Geophys. Res. 99, 19527 (1994)
[3] J.-P. St.-Maurice and R. W. Schunk, Planet. Space Sci. 25, 243 (1977
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Rekaa, Vegard Lundby; Pecseli, Hans & Trulsen, Jan Karsten
(2012).
Numerical studies of a plasma diode with external forcings.
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With reference to laboratory studies we analyze the dynamics of a plasma diode under external forcing. Assuming a strong axial magnetic field, the problem is analyzed in
one spatial dimension by a Particle in Cell code. The cathode is assumed to be operated in electron rich conditions, supplying an abundance of electrons. We compare different forcing schemes with the results obtained by solving the van der Pol equation. In one method of forcing we apply an oscillation in addition to the DC end plate bias, and consider both amplitude and frequency variations. An alternative method of perturbation consists of modelling an absorbing grid at some internal position. Also in this case we can have a constant frequency with varying amplitude, or alternatively an oscillation with chirped frequency but constant amplitude. We find that the overall features of the forced van der Pol equation are recovered, but the details in the plasma response require more attention to the harmonic responses, requiring extensions of the model equation. The analysis is extended by introducing collisional effects, where we emphasize
charge exchange collisions of ions, since these processes usually have the largest cross sections. Charge exchange collisions give significant modifications of the diode performance when the effects are compared with the influence of elastic electron-neutral and ion-neutral collisions with the same collisional mean free paths.
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Sato, Hiroatsu; Børve, Steinar; Pécseli, Hans & Trulsen, Jan Karsten
(2012).
Minute-scale period oscillations of the magnetosphere.
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Oscillations with periods on the order of 5–10 min have been observed by instrumented spacecrafts in the Earth’s magnetosphere. These oscillations often follow sudden impacts related to coronal mass ejections. It is demonstrated that a simple model is capable of explaining the basic properties of these oscillations and give scaling laws for their basic characteristics in terms of the basic parameters of the problem. The period of the oscillations and their anharmonic nature, in particular, are accounted for. The model has no free adjustable numerical parameters. We use measurable quantities as inputs (such as Solar wind momentum density), and our results can be seen as an effort to predict some dynamic properties of magnetospheres on the basis of measurable steady state characteristics. A simple test of the model is found by comparing its prediction of the Earth-Magnetopause distance with observed values. The general results agree with observations. The analysis is supported by numerical simulations solving the Magneto-Hydro-Dynamic (MHD) equations in two spatial dimensions, where we let a solar wind interact with a magnetic dipole representing a magnetized Earth. Two tilt-angles of the magnetic dipole axis were considered. We observed the formation of a magnetosheath, with the magnetopause at a distance corresponding well to the analytical results. Sudden pulses in the model solar wind sets the model magnetosphere into damped oscillatory motions and quantitatively good agreement with the analytical results is found. The models seem to be robust, and give good qualitative agreement with the numerical simulations for a range of parameters.
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Trulsen, Jan Karsten & Omang, Marianne Gjestvold
(2012).
Shock propagation through bounded dust clouds.
Fulltekst i vitenarkiv
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Omang, Marianne Gjestvold; Christensen, Svein Olav; Hauge, Knut Ove & Trulsen, Jan Karsten
(2011).
A numerical and experimental study on charge geometries.
Fulltekst i vitenarkiv
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Miloch, Wojciech Jacek; Yaroshenko, V.; Vladimirov, Sergei V.; Pecseli, Hans & Trulsen, Jan Karsten
(2011).
Spacecraft charging in space and ionospheric plasma; numerical simulations.
Fulltekst i vitenarkiv
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Rekaa, Vegard Lundby; Pecseli, Hans & Trulsen, Jan Karsten
(2011).
Numerical simulations of anomalous resistivity in the ion acoustic and Buneman regime.
Fulltekst i vitenarkiv
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Pecseli, Hans & Trulsen, Jan Karsten
(2011).
Encounter rates and transit time distributions for surfacesmoving in turbulent flows.
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Reaction rates as relevant for many chemical processes as well as a number of biological applications depend on encounter rates of reacting elements and the probability of a reaction occurring given an encounter. Turbulent mixing can enhance the encounter rate, but it can also have adverse effects by reducing the reaction probability. We model the probability for a reaction by letting it depend on the time available, i.e. the time spent by of reacting particles within some given interaction volume. We study the problems by numerical simulations where we analyze the statistics of the motion of passively convected point particles in turbulent flows. The database used is obtained by direct numerical solution of the Navier-Stokes equation. We estimate the encounter rates and also the probability distribution of the transit times of particles through reference volumes with given forms and sizes. A selected position within the reference volume is moving self consistently with the local flow velocity, thus determining the motion of the entire surface. The transit time is defined as the interval between entrance and exit times of surrounding particles convected through the volume by the turbulent motions. Scale sizes in the inertial as well as in the viscous subranges of the turbulence are considered. Simple, and seemingly universal, scaling laws are obtained for the encounter rate as well as the probability density of the transit times in terms of the basic properties of the turbulent flow and the geometry. In the present formulation, the results of the analysis are relevant for chemical reactions, but also for understanding details of the feeding rate of micro-organisms in turbulent waters, for instance.
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Omang, Marianne Gjestvold; Christensen, S. O.; Børve, Steinar & Trulsen, Jan Karsten
(2010).
Blast wave generation and propagation.
Fulltekst i vitenarkiv
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Miloch, Wojciech Jacek; Pecseli, Hans & Trulsen, Jan Karsten
(2009).
Interactions of two objects in flowing plasmas studied by numerical simulations.
Fulltekst i vitenarkiv
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Miloch, Wojciech Jacek; Pecseli, Hans & Trulsen, Jan Karsten
(2009).
Numerical studies of ion focusing in streaming plasmas; two and three dimensions.
Fulltekst i vitenarkiv
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Pecseli, Hans; Trulsen, Jan Karsten & Fiksen, Øyvind
(2009).
Predators in turbulent waters: an analytical model and a numerical test.
Fulltekst i vitenarkiv
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Miloch, Wojciech Jacek; Pecseli, Hans & Trulsen, Jan Karsten
(2009).
Ion focusing behind finite size objects in flowing plasmas; numerical studies in two and three dimensions.
Fulltekst i vitenarkiv
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Børve, Steinar; Omang, Marianne; Trulsen, Jan Karsten & Bjerke, Audun
(2008).
A Comparative Study of ANSYS AUTODYN and RSPH Simulations of Blast Waves.
Fulltekst i vitenarkiv
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Omang, Marianne; Børve, Steinar & Trulsen, Jan Karsten
(2008).
Numerical Simulations of Blast Wave Propagation in Underground Facilities.
Fulltekst i vitenarkiv
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Omang, Marianne; Christensen, S. O.; Børve, Steinar & Trulsen, Jan Karsten
(2008).
Numerical Simulations of Blast Waves from Spherical and Cylindrical Charges.
Fulltekst i vitenarkiv
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Miloch, Wojciech Jacek; Vladimirov, Sergei V.; Pecseli, Hans & Trulsen, Jan Karsten
(2008).
Charging of dust in the presence of a directed photon flux: numerical simulations.
Fulltekst i vitenarkiv
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Miloch, Wojciech Jacek; Vladimirov, Sergei V.; Pecseli, Hans & Trulsen, Jan Karsten
(2008).
Wake formation behind elongated insulating dust grains in drifting plasmas: numerical simulations.
Fulltekst i vitenarkiv
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Miloch, Wojciech Jacek; Vladimirov, Sergei V.; Pecseli, Hans & Trulsen, Jan Karsten
(2008).
Charging of insulating grains in flowing plasmas with a directed photon flux.
Fulltekst i vitenarkiv
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Miloch, Wojciech Jacek; Vladimirov, Sergei V.; Pecseli, Hans & Trulsen, Jan Karsten
(2008).
Charging of dust grains in flowing plasmas with a directed photon flux: numerical simulations.
Fulltekst i vitenarkiv
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Miloch, Wojciech Jacek; Pecseli, Hans & Trulsen, Jan Karsten
(2008).
Wake formation behind elongated insulating object in drifting plasmas: numerical simulations.
Fulltekst i vitenarkiv
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Guio, Patrick; Miloch, Wojciech Jacek; Pecseli, Hans & Trulsen, Jan Karsten
(2008).
Sound radiation from moving point-like charged particles in plasmas.
Fulltekst i vitenarkiv
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Fredriksen, Åshild; Pecseli, Hans & Trulsen, Jan Karsten
(2008).
Crash and recovery of the potential in a toroidal plasma column, as observed by generalized conditional sampling.
Fulltekst i vitenarkiv
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Miloch, Wojciech Jacek; Vladimirov, Sergei V.; Pecseli, Hans & Trulsen, Jan Karsten
(2008).
Charge and potential distributions on and around elongated dust grains in flowing plasmas: numerical simulations.
Fulltekst i vitenarkiv
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Miloch, Wojciech Jacek; Vladimirov, Sergei V.; Pecseli, Hans & Trulsen, Jan Karsten
(2008).
Interaction potential between two elongated dust grains in flowing plasmas: numerical simulations.
Fulltekst i vitenarkiv
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Miloch, Wojciech Jacek; Vladimirov, Sergei V.; Pecseli, Hans & Trulsen, Jan Karsten
(2008).
The charging of dust grains and the wake formation studied by numerical simulations.
Fulltekst i vitenarkiv
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Miloch, Wojciech Jacek; Vladimirov, Sergei V.; Pecseli, Hans & Trulsen, Jan Karsten
(2008).
Charging and wake of dust grains in supersonic plasma flows: numerical simulations.
Fulltekst i vitenarkiv
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Miloch, Wojciech Jacek; Pecseli, Hans; Trulsen, Jan Karsten & Vladimirov, Sergei V.
(2008).
Numerical simulations of interactions between solid surfaces (dust grains) and plasmas.
Fulltekst i vitenarkiv
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Miloch, Wojciech Jacek; Vladimirov, Sergei V.; Pecseli, Hans & Trulsen, Jan Karsten
(2008).
Numerical simulations of the charging and wake of dust grains in flowing plasmas.
Fulltekst i vitenarkiv
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Miloch, Wojciech Jacek; Pecseli, Hans; Trulsen, Jan Karsten & Vladimirov, Sergei V.
(2008).
Ion focusing and interaction potential for sphericaland rodlike obstacles in a supersonic plasma flow: numerical simulations.
Fulltekst i vitenarkiv
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Pecseli, Hans & Trulsen, Jan Karsten
(2008).
Planktonic contact and capture rates in turbulent environments.
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The motion of plankton in turbulent environments is studied by numerical simulations, where point particles are moving in a flow described by Navier-Stokes equation. Parts of the results are supported also by observations from a controlled laboratory experiment, where approximately homogeneous and isotropic turbulence can be generated by two moving grids. We find that the contact rates of passively moving prey and predators with a spherical capture volume follow seemingly universal scaling laws in terms of the specific turbulent dissipation rate and the radius in the capture volume. For radii smaller than or comparable to the Kolmogorov-scale, also the viscosity enters the scaling laws. The models are extended to cover also non-spherical capture volumes. The average capture rate of prey is modelled by a product of the encounter rate and a capture probability, where the basic parameter for the capture is identified as the time duration of the encounter. Also the transit time of passively moving prey through the volume of interception is measured, and universal scaling laws for its probability density are estimated. Parameterizing the capture probability for given transit times, we obtain an estimate of the average capture rate of prey, indicating that small or moderate levels of turbulence are advantageous for the capture by increasing the contact rate, while strong turbulence is a disadvantage by reducing the capture probability due to the short transit times. We demonstrate how self induced cruising motions of predators can be included in the models, and obtain a parameterized expression for the average capture rate that includes also this effect.
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Dyrud, Lars; Krane, Bård; Oppenheim, Mers; Pecseli, Hans; Trulsen, Jan Karsten & Wernik, A. W.
(2008).
Structure functions and intermittency in ionospheric plasma turbulence.
Fulltekst i vitenarkiv
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Guio, Patrick; Miloch, Wojciech Jacek; Pecseli, Hans & Trulsen, Jan Karsten
(2008).
Ion-sound from charged obstacles in a plasma flow.
Fulltekst i vitenarkiv
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Pecseli, Hans; Dyrud, Lars; Oppenheim, Meers; Wernik, Andrzej & Trulsen, Jan Karsten
(2007).
Low-frequency electrostatic waves in the ionospheric E region: a comparison of rocket observations and numerical simulations.
Fulltekst i vitenarkiv
Vis sammendrag
Low frequency electrostatic waves in the lower parts of the ionosphere are studied by a comparison of observations by instrumented rockets and of results from numerical simulations [1,2]. Particular attention is given to the spectral properties of the waves [1]. On the basis of a good agreement between the observations and the simulations, it can be argued that the most important nonlinear dynamics can be accounted for in a two-dimensional numerical model, referring to a plane perpendicular to a locally homogeneous magnetic field. It does not seem necessary to take into account turbulent fluctuations or motions in the neutral gas component. The numerical simulations explain the observed strongly intermittent nature of the fluctuations: secondary instabilities develop on the large scale gradients of the largest amplitude waves, and the small scale dynamics is strongly influenced by these secondary instabilities. We compare potential variations obtained at a single position in the numerical simulations with two point potential-difference signals, where the latter is the adequate representation for the data obtained by instrumented rockets. We can demonstrate a significant reduction in the amount of information concerning the plasma turbulence when the latter signal is used for analysis [2]. In particular we show that the bicoherence estimate is strongly affected. The conclusions have implications for studies of low frequency ionospheric fluctuations in the E and F regions by instrumented rockets, and also for other methods relying on difference measurements, using two probes with large separation. The analysis also resolves a long standing controversy concerning the supersonic phase velocities of these cross-field instabilities being observed in laboratory experiments. In a general context we might argue that our results illustrate the necessity of being particularly careful when comparing analytical and experimental results when the latter are obtained by instrumented space-crafts.
[1] B. Krane, H.L. Pécseli, J. Trulsen and F. Primdahl, Spectral properties of low-frequency electrostatic waves in the ionospheric E-region. J. Geophys. Res. 105, 10,585-10,602, 2000
[2] L. Dyrud, B. Krane, M. Oppenheim, H.L. Pécseli, K. Schlegel, J. Trulsen and A.W. Wernik, Low-frequency electrostatic waves in the ionospheric E region: a comparison of rocket observations and numerical simulations. Ann. Geophysicae, 24, 2959-2979, 2006
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Miloch, Wojciech Jacek; Pecseli, Hans & Trulsen, Jan Karsten
(2007).
Numerical simulations of the charging of dust particles by contact with warm plasmas.
Fulltekst i vitenarkiv
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Miloch, Wojciech Jacek; Pecseli, Hans & Trulsen, Jan Karsten
(2007).
Numerical simulations of interactions of warm plasmas and a dust-grain.
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Vis sammendrag
Results from numerical simulations of the interaction between a warm plasma and individual dust
particles are reported. The analysis is carried out in two spatial dimensions, using a particle-in-cell
(PIC) numerical code, considering conducting as well as insulating materials for the dust. For
macroscopic dust particles in streaming plasmas, we observe the development of an electric dipole
moment associated with the particles. The strength of this dipole moment is very different for
conducting and insulating materials, and its direction is opposite for the two cases. For supersonic
flows we note the formation of a Mach-cone, with properties in agreement with analytical results,
in particular also concerning the effects of Landau damping.
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Publisert
3. nov. 2010 15:21
- Sist endret
13. sep. 2021 14:10