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Recent PIC simulations of relativistic electron-positron (electron-ion) jets injected into a stationary medium show that particle acceleration occurs in the shocked regions. Simulations show that the Weibel instability is responsible for generating and amplifying highly nonuniform, small-scale magnetic fields and for particle acceleration. These magnetic fields contribute to the electron’s transverse eflection behind the shock. The “jitter” radiation from deflected electrons in turbulent magnetic fields has properties different from synchrotron radiation calculated in a uniform magnetic field. This jitter radiation may be important for understanding the complex time evolution and/or spectral structure of gamma-ray bursts, relativistic jets in general, and supernova remnants. In order to calculate radiation from first principles and go beyond the standard synchrotron model, we have used PIC simulations. We present synthetic spectra to compare with the spectra obtained from Fermi observations., Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe, 600

In this study, we investigate the interaction of jets with their environment at a microscopic level, which is a key open question in the study of relativistic jets. Using small simulation systems during past research, we initially studied the evolution of both electron–proton and electron–positron relativistic jets containing helical magnetic fields, by focusing on their interactions with an ambient plasma. Here, using larger jet radii, we have performed simulations of global jets containing helical magnetic fields in order to examine how helical magnetic fields affect kinetic instabilities, such as the Weibel instability, the kinetic Kelvin–Helmholtz instability (kKHI) and the mushroom instability (MI). We found that the evolution of global jets strongly depends on the size of the jet radius. For example, phase bunching of jet electrons, in particular in the electron–proton jet, is mixed with a larger jet radius as a result of the more complicated structures of magnetic fields with excited kinetic instabilities. In our simulation, these kinetic instabilities led to new types of instabilities in global jets. In the electron–proton jet simulation, a modified recollimation occurred, and jet electrons were strongly perturbed. In the electron–positron jet simulation, mixed kinetic instabilities occurred early, followed by a turbulence-like structure. Simulations using much larger (and longer) systems are required in order to further thoroughly investigate the evolution of global jets containing helical magnetic fields., This work is supported by NSF AST-0908010, AST-0908040, NASA-NNX09AD16G, NNX12AH06G, NNX13AP-21G, and NNX13AP14G grants. The work of J.N. and O.K. has been supported by Narodowe Centrum Nauki through research project DEC-2013/10/E/ST9/00662. Y.M. is supported by the ERC Synergy Grant “BlackHoleCam—Imaging the Event Horizon of Black Holes” (Grant No. 610058). M.P. acknowledges support through grant PO 1508/1-2 of the Deutsche Forschungsgemeinschaft. Simulations were performed using Pleiades and Endeavor facilities at NASA Advanced Supercomputing (NAS), and using Gordon and Comet at The San Diego Supercomputer Center (SDSC), and Stampede at The Texas Advanced Computing Center, which are supported by the NSF. This research was started during the program “Chirps, Mergers and Explosions: The Final Moments of Coalescing Compact Binaries” at the Kavli Institute for Theoretical Physics, which is supported by the National Science Foundation under grant No. PHY05-51164. The first velocity shear results using an electron positron plasma were obtained during the Summer Aspen workshop “Astrophysical Mechanisms of Particle Acceleration and Escape from the Accelerators” held at the Aspen Center for Physics (1–15 September 2013)., We acknowledge support by the CSIC Open Access Publication Initiative through its Unit of Information Resources for Research (URICI)

Galaxies 4(4), 38 (2016). doi:10.3390/galaxies4040038, In the study of relativistic jets one of the key open questions is their interaction with the environment on the microscopic level. Here, we study the initial evolution of both electron–proton ( e$^−$ – p$^+$ ) and electron–positron ( e$^{±}$ ) relativistic jets containing helical magnetic fields, focusing on their interaction with an ambient plasma. We have performed simulations of “global” jets containing helical magnetic fields in order to examine how helical magnetic fields affect kinetic instabilities such as the Weibel instability, the kinetic Kelvin-Helmholtz instability (kKHI) and the Mushroom instability (MI). In our initial simulation study these kinetic instabilities are suppressed and new types of instabilities can grow. In the e$^−$ – p$^+$ jet simulation a recollimation-like instability occurs and jet electrons are strongly perturbed. In the e$^{±}$ jet simulation a recollimation-like instability occurs at early times followed by a kinetic instability and the general structure is similar to a simulation without helical magnetic field. Simulations using much larger systems are required in order to thoroughly follow the evolution of global jets containing helical magnetic fields., Published by MDPI, Basel

The compressibility of molecular cloud (MC) turbulence plays a crucial role in star formation models, because it controls the amplitude and distribution of density fluctuations. The relation between the compressive ratio (the ratio of powers in compressive and solenoidal motions) and the statistics of turbulence has been previously studied systematically only in idealized simulations with random external forces. In this work, we analyze a simulation of large-scale turbulence (250 pc) driven by supernova (SN) explosions that has been shown to yield realistic MC properties. We demonstrate that SN driving results in MC turbulence with a broad lognormal distribution of the compressive ratio, with a mean value $\approx 0.3$, lower than the equilibrium value of $\approx 0.5$ found in the inertial range of isothermal simulations with random solenoidal driving. We also find that the compressibility of the turbulence is not noticeably affected by gravity, nor are the mean cloud radial (expansion or contraction) and solid-body rotation velocities. Furthermore, the clouds follow a general relation between the rms density and the rms Mach number similar to that of supersonic isothermal turbulence, though with a large scatter, and their average gas density PDF is described well by a lognormal distribution, with the addition of a high-density power-law tail when self-gravity is included., Accepted by ApJ

The Padoan and Nordlund model of the stellar initial mass function (IMF) is derived from low order statistics of supersonic turbulence, neglecting gravity (e.g. gravitational fragmentation, accretion and merging). In this work the predictions of that model are tested using the largest numerical experiments of supersonic hydrodynamic (HD) and magneto-hydrodynamic (MHD) turbulence to date (~1000^3 computational zones) and three different codes (Enzo, Zeus and the Stagger Code). The model predicts a power law distribution for large masses, related to the turbulence energy power spectrum slope, and the shock jump conditions. This power law mass distribution is confirmed by the numerical experiments. The model also predicts a sharp difference between the HD and MHD regimes, which is recovered in the experiments as well, implying that the magnetic field, even below energy equipartition on the large scale, is a crucial component of the process of turbulent fragmentation. These results suggest that the stellar IMF of primordial stars may differ from that in later epochs of star formation, due to differences in both gas temperature and magnetic field strength. In particular, we find that the IMF of primordial stars born in turbulent clouds may be narrowly peaked around a mass of order 10 solar masses, as long as the column density of such clouds is not much in excess of 10^22 cm^-2.

The morphology and kinematics of molecular clouds (MCs) are best explained as the consequence of super--sonic turbulence. Super--sonic turbulence fragments MCs into dense sheets, filaments and cores and large low density ``voids'', via the action of highly radiative shocks. We refer to this process as "turbulent fragmentation". In this work we derive the mass distribution of gravitationally unstable cores generated by the process of turbulent fragmentation. The mass distribution above one solar mass depends primarily on the power spectrum of the turbulent flow and on the jump conditions for isothermal shocks in a magnetized gas. For a power spectrum index \beta=-1.74, consistent with Larson's velocity dispersion--size relation as well as with new numerical and analytic results on super--sonic turbulence, we obtain a power law mass distribution of dense cores with a slope equal to 3/(4-\beta) = 1.33, consistent with the slope of the stellar IMF. Below one solar mass, the mass distribution flattens and turns around at a fraction of a solar mass, as observed for the stellar IMF in a number of stellar clusters, because only the densest cores are gravitationally unstable. The mass distribution at low masses is determined by the probability distribution of the gas density, which is known to be approximately Log--Normal for an isothermal turbulent gas. The intermittent nature of the turbulent density distribution is thus responsible for the existence of a significant number of small collapsing cores, even of sub--stellar mass. Since turbulent fragmentation is unavoidable in super--sonically turbulent molecular clouds, and given the success of the present model in predicting the observed shape of the stellar IMF, we conclude that turbulent fragmentation is essential to the origin of the stellar IMF.

We present a direct numerical and analytical study of driven supersonic MHD turbulence that is believed to govern the dynamics of star-forming molecular clouds. We describe statistical properties of the turbulence by measuring the velocity difference structure functions up to the fifth order. In particular, the velocity power spectrum in the inertial range is found to be close to E(k) \~ k^{-1.74}, and the velocity difference scales as ~ L^{0.42}. The results agree well with the Kolmogorov--Burgers analytical model suggested for supersonic turbulence in [astro-ph/0108300]. We then generalize the model to more realistic, fractal structure of molecular clouds, and show that depending on the fractal dimension of a given molecular cloud, the theoretical value for the velocity spectrum spans the interval [-1.74 ... -1.89], while the corresponding window for the velocity difference scaling exponent is [0.42 ... 0.78]., Comment: 17 pages, 6 figures included

We report on realistic simulations of solar surface convection that are essentially parameter-free, but include detailed physics in the equation of state and radiative energy exchange. The simulation results are compared quantitatively with observations. Excellent agreement is obtained for the distribution of the emergent continuum intensity, the profiles of weak photospheric lines, the p-mode frequencies, the asymmetrical shape of the mode velocity and intensity spectra, the p-mode excitation rate, and the depth of the convection zone. We describe how solar convection is non-local. It is driven from a thin surface thermal boundary layer where radiative cooling produces low entropy gas which forms the cores of the downdrafts in which most of the buoyancy work occurs. Turbulence and vorticity are mostly confined to the intergranular lanes and underlying downdrafts. Finally, we present some preliminary results on magneto-convection.

Supersonic random motions are observed in dark clouds and are traditionally interpreted as Alfven waves, but the possibility that these motions are super-Alfvenic has not been ruled out. In this work we report the results of numerical experiments in two opposite regimes; M_a ~ 1 and M_a >> 1, where M_a is the initial Alfvenic Mach number --the ratio of the rms velocity to the Alfven speed. Our results show that models with M_a >> 1 are consistent with the observed properties of molecular clouds that we have tested --statistics of extinction measurements, Zeeman splitting measurements of magnetic field strength, line width versus integrated antenna temperature of molecular emission line spectra, statistical B-n relation, and scatter in that relation-- while models with M_a ~ 1 have properties that are in conflict with the observations. We find that both the density and the magnetic field in molecular clouds may be very intermittent. The statistical distributions of magnetic field and gas density are related by a power law, with an index that decreases with time in experiments with decaying turbulence. After about one dynamical time it stabilizes at B ~ n^{0.4}. Magnetically dominated cores form early in the evolution, while later on the intermittency in the density field wins out, and also cores with weak field can be generated, by mass accretion along magnetic field lines., 10 figures, 2 tables included

Lada et al. (1994) have described a method for studying the distribution of dust in dark clouds using infrared imaging surveys. In particular they show that the method provides some information about the structure of the gas (dust) on scales smaller than their resolution. In the present work we clarify the nature of the information provided by their method. We show that: 1) the 3D density field of the gas is well described by a Log-Normal distribution down to very small scales; 2) the power spectrum and the standard deviation of the 3D density field can be constrained; 3) the origin of such a structure of the density field is likely to be the supersonic turbulence in the gas. In fact we find a qualitative and quantitative agreement between the predictions based on recent numerical simulations of supersonic turbulence (Nordlund and Padoan 1996; Padoan, Nordlund and Jones 1996) and the constraints given by the infrared dust extinction measurements.

The short-lived $^{26}$Al and $^{60}$Fe radionuclides are synthesized and expelled in the interstellar medium by core-collapse supernova events. The solar system's first solids, calcium-aluminium refractory inclusions (CAIs), contain evidence for the former presence of the $^{26}$ Al nuclide defining the canonical $^{26}$Al/$^{27}$ Al ratio of $\sim5 \times10^{-5}$. A different class of objects temporally related to canonical CAIs are CAIs with fractionation and unidentified nuclear effects (FUN CAIs), which record a low initial $^{26}$Al/$^{27}$Al of $10^{-6}$. The contrasting level of $^{26}$Al between these objects is often interpreted as reflecting the admixing of the $^{26}$Al nuclide during the early formative phase of the Sun. We use giant molecular cloud (GMC) scale adaptive mesh-refinement numerical simulations to trace the abundance of $^{26}$Al and $^{60}$Fe in star-forming gas during the early stages of accretion of individual low mass protostars. We find that the $^{26}$Al/$^{27}$Al and $^{60}$Fe/$^{56}$Fe ratios of accreting gas within a vicinity of 1000 AU of the stars follow the predicted decay curves of the initial abundances at time of star formation without evidence of spatial or temporal heterogeneities for the first 100 kyr of star formation. Therefore, the observed differences in $^{26}$Al/$^{27}$Al ratios between FUN and canonical CAIs are likely not caused by admixing of supernova material during the early evolution of the proto-Sun. Selective thermal processing of dust grains is a more viable scenario to account for the heterogeneity in $^{26}$Al/$^{27}$Al ratios at the time of solar system formation., Comment: 15 pages, 13 figures accepted for publication in ApJ

Plasma instabilities excited in collisionless shocks are responsible for particle acceleration, generation of magnetic fields , and associated radiation. We have investigated the particle acceleration and shock structure associated with an unmagnetized relativistic jet propagating into an unmagnetized plasma. Cold jet electrons are thermalized and slowed while the ambient electrons are swept up to create a partially developed hydrodynamic-like shock structure. The shock structure depends on the composition of the jet and ambient plasma (electron-positron or electron-ions). Strong electromagnetic fields are generated in the reverse , jet shock and provide an emission site. These magnetic fields contribute to the electron's transverse deflection behind the shock. We have calculated, self-consistently, the radiation from electrons accelerated in the turbulent magnetic fields. We found that the synthetic spectra depend on the Lorentz factor of the jet, its thermal temperature and strength of the generated magnetic fields. The detailed properties of the radiation are important for understanding the complex time evolution and/or spectral structure in gamma-ray bursts, relativistic jet shocks, and supernova remnants

We employ simulations of supersonic super-Alfvenic turbulence decay as a benchmark test problem to assess and compare the performance of nine astrophysical MHD methods actively used to model star formation. The set of nine codes includes: ENZO, FLASH, KT-MHD, LL-MHD, PLUTO, PPML, RAMSES, STAGGER, and ZEUS. We present a comprehensive set of statistical measures designed to quantify the effects of numerical dissipation in these MHD solvers. We compare power spectra for basic fields to determine the effective spectral bandwidth of the methods and rank them based on their relative effective Reynolds numbers. We also compare numerical dissipation for solenoidal and dilatational velocity components to check for possible impacts of the numerics on small-scale density statistics. Finally, we discuss convergence of various characteristics for the turbulence decay test and impacts of various components of numerical schemes on the accuracy of solutions. We show that the best performing codes employ a consistently high order of accuracy for spatial reconstruction of the evolved fields, transverse gradient interpolation, conservation law update step, and Lorentz force computation. The best results are achieved with divergence-free evolution of the magnetic field using the constrained transport method, and using little to no explicit artificial viscosity. Codes which fall short in one or more of these areas are still useful, but they must compensate higher numerical dissipation with higher numerical resolution. This paper is the largest, most comprehensive MHD code comparison on an application-like test problem to date. We hope this work will help developers improve their numerical algorithms while helping users to make informed choices in picking optimal applications for their specific astrophysical problems., Comment: 17 pages, 5 color figures, revised version to appear in ApJ, 735, July 2011

Supersonic turbulence fragments the interstellar medium into dense sheets, filaments, cores and large low-density voids, thanks to a complex network of highly radiative shocks. The turbulence is driven on large scales, predominantly by supernovae. While on scales of the order of the galactic disk thickness the magnetic energy is in approximate equipartition with the kinetic energy of the turbulence, on scales of a few pc the turbulent kinetic energy significantly exceeds the magnetic energy.

Using a three dimensional relativistic particle-in-cell code we have performed numerical experiments of plasma shells colliding at relativistic velocities. Such scenarios are found in many astrophysical objects e.g. the relativistic outflow from gamma ray bursts, active galactic nuclei jets and supernova remnants. We show how a Weibel like two-stream instability is capable of generating small- scale magnetic filaments with strength up to percents of equipartition. Such field topology is ideal for the generation of jitter radiation as opposed to synchrotron radiation. We also explain how the field generating mechanism involves acceleration of electrons to power law distributions (N(γ) ∞ γ−p ) through a non-Fermi acceleration mechanism. The results add to our understanding of collisionless shocks.

Numerical simulations of the multi-phase interstellar medium have been carried out, using a 3D, nonlinear, magnetohydrodynamic, shearing-box model, with random motions driven by supernova explosions. These calculations incorporate the effects of magnetic fields and rotation in 3D; these play important dynamical roles in the galaxy, but are neglected in many other simulations. The supernovae driving the motions are not arbitrarily imposed, but occur where gas accumulates into cold, dense clouds; their implementation uses a physically motivated model for the evolution of such clouds. The process is self-regulating, and produces mean supernova rates as part of the solution. Simulations with differing mean density show a power law relation between the supernova rate and density, with exponent 1.7; this value is within the range suggested from observations (taking star formation rate as a proxy for supernova rate). The global structure of the supernova driven medium is strongly affected by the presence of magnetic fields; e.g. for one solution the filling factor of hot gas is found to vary from 0.19 (with no field) to 0.12 (with initial mid-plane field B_0=6 muG)., 6 pages, 4 figures, v2: minor revisions, now accepted for publication in: Magnetic fields and star formation: theory versus observations, eds: A. I. Gomez de Castro et al., Kluwer Acad. Publ., Dordrecht

Supersonic turbulent flows of magnetized gas are believed to play an important role in the dynamics of star-forming clouds in galaxies. Understanding statistical properties of such flows is crucial for developing a theory of star formation. In this letter we propose a unified approach for obtaining the velocity scaling in compressible and super--Alfv\'{e}nic turbulence, valid for arbitrary sonic Mach number, \ms. We demonstrate with numerical simulations that the scaling can be described with the She--L\'{e}v\^{e}que formalism, where only one parameter, interpreted as the Hausdorff dimension of the most intense dissipative structures, needs to be varied as a function of \ms. Our results thus provide a method for obtaining the velocity scaling in interstellar clouds once their Mach numbers have been inferred from observations., Comment: published in Physical Review Letters

Statistical parameters of the ISM driven by thermal energy injections from supernova explosions have been obtained from 3D, nonlinear, magnetohydrodynamic, shearing-box simulations for spiral arm and interarm regions. The density scale height obtained for the interarm regions is 50% larger than within the spiral arms because of the higher gas temperature. The filling factor of the hot gas is also significantly larger between the arms and depends sensitively on magnetic field strength., 6 pages, 4 figures, submitted to proceedings issue of Astrophysics & Space Science following the JENAM 2002 Workshop: "From observations to self-consistent modeling of the ISM in galaxies"

Hundreds of brown dwarfs (BDs) have been discovered in the last few years in stellar clusters and among field stars. BDs are almost as numerous as hydrogen burning stars and so a theory of star formation should also explain their origin. The ``mystery'' of the origin of BDs is that their mass is two orders of magnitude smaller than the average Jeans' mass in star--forming clouds, and yet they are so common. In this work we investigate the possibility that gravitationally unstable protostellar cores of BD mass are formed directly by the process of turbulent fragmentation. Supersonic turbulence in molecular clouds generates a complex density field with a very large density contrast. As a result, a fraction of BD mass cores formed by the turbulent flow are dense enough to be gravitationally unstable. We find that with density, temperature and rms Mach number typical of cluster--forming regions, turbulent fragmentation can account for the observed BD abundance., 11 pages, 3 figures, ApJ submitted Error in equation 1 has been corrected. Improved figures

Numerical simulations of kinematic dynamo action in steady and 3-d ABC flows are presented with special focus on growth rates and multiple periods of the prescribed velocity field. It is found that the difference in growth rate is due to differences in the recycling of the weakest part of the magnetic field. Differences in the topology in cases with and without stagnation points in the imposed velocity field are also investigated, and it is found that the cigar-like structures that develop in the classical A=B=C dynamos, are replaced by ribbon structures in cases where the flow is without stagnation points., 7 pages, 12 PS figures, submitted to A&A (+ slight changes from previous version)

We have investigated the generation of magnetic fields associated with velocity shear between an unmagnetized relativistic (core) jet and an unmagnetized sheath plasma by the kinetic Kelvin-Helmholtz instability for different mass ratios (m i /m e = 1, 20, and 1836) and different jet Lorentz factors. We found that electron-positron cases have alternating magnetic fields instead of the DC magnetic fields found in electron-ion cases. We have also investigated particle acceleration and shock structure associated with an unmagnetized relativistic jet propagating into an unmagnetized plasma for electron-positron and electron-ion plasmas. Strong magnetic fields generated in the trailing shock lead to transverse deflection and acceleration of the electrons. We have self-consistently calculated the radiation from the electrons accelerated in the turbulent magnetic fields for different jet Lorentz factors. We find that the synthetic spectra depend on the bulk Lorentz factor of the jet, the jet temperature, and the strength of the magnetic fields generated in the shock.

The observed similarities between the mass function of prestellar cores (CMF) and the stellar initial mass function (IMF) have led to the suggestion that the IMF is already largely determined in the gas phase. However, theoretical arguments show that the CMF may differ significantly from the IMF. In this Letter, we study the relation between the CMF and the IMF, as predicted by the IMF model of Padoan and Nordlund. We show that 1) the observed mass of prestellar cores is on average a few times smaller than that of the stellar systems they generate; 2) the CMF rises monotonically with decreasing mass, with a noticeable change in slope at approximately 3-5 solar masses, depending on mean density; 3) the selection of cores with masses larger than half their Bonnor-Ebert mass yields a CMF approximately consistent with the system IMF, rescaled in mass by the same factor as our model IMF, and therefore suitable to estimate the local efficiency of star formation, and to study the dependence of the IMF peak on cloud properties; 4) only one in five pre-brown-dwarf core candidates is a true progenitor to a brown dwarf.

The role of turbulence in various astrophysical settings is reviewed. Among the differences to laboratory and atmospheric turbulence we highlight the ubiquitous presence of magnetic fields that are generally produced and maintained by dynamo action. The extreme temperature and density contrasts and stratifications are emphasized in connection with turbulence in the interstellar medium and in stars with outer convection zones, respectively. In many cases turbulence plays an essential role in facilitating enhanced transport of mass, momentum, energy, and magnetic fields in terms of the corresponding coarse-grained mean fields. Those transport properties are usually strongly modified by anisotropies and often completely new effects emerge in such a description that have no correspondence in terms of the original (non coarse-grained) fields., Comment: 88 pages, 26 figures, published in Reports on Progress in Physics

This work presents a new physical model of the star formation rate (SFR), which is verified with an unprecedented set of large numerical simulations of driven, supersonic, self-gravitating, magneto-hydrodynamic (MHD) turbulence, where collapsing cores are captured with accreting sink particles. The model depends on the relative importance of gravitational, turbulent, magnetic, and thermal energies, expressed through the virial parameter, αvir, the rms sonic Mach number, , and the ratio of mean gas pressure to mean magnetic pressure, β0. The SFR is predicted to decrease with increasing αvir (stronger turbulence relative to gravity), to increase with increasing (for constant values of αvir), and to depend weakly on β0 for values typical of star forming regions (-20 and β0 1-20). In the unrealistic limit of β0 → ∞, that is, in the complete absence of a magnetic field, the SFR increases approximately by a factor of three, which shows the importance of magnetic fields in the star formation process, even when they are relatively weak (super-Alfvenic turbulence). The star-formation simulations used to test the model result in an approximately constant SFR, after an initial transient phase. The dependence of the SFR on the virial parameter is shown to agree very well with the theoretical predictions.

Recent PIC simulations of relativistic electron-positron (electron-ion) jets injected into a stationary medium show that particle acceleration occurs in the shocked regions. Simulations show that the Weibel instability is responsible for generating and amplifying highly nonuniform, small-scale magnetic fields and for particle acceleration. These magnetic fields contribute to the electron's transverse deflection behind the shock. The “jitter” radiation from deflected electrons in turbulent magnetic fields has different properties from synchrotron radiation calculated in a uniform magnetic field. This jitter radiation may be important for understanding the complex time evolution and/or spectral structure of gamma-ray bursts, relativistic jets in general, and supernova remnants. In order to calculate radiation from first principles and go beyond the standard synchrotron model, we have used PIC simulations. We will present detailed spectra for conditions relevant to various astrophysical sites of collisionless shock formation. In particular we will discuss application to GRBs and SNRs.

We present results from numerical simulations of nonlinear MHD dynamo action produced by three-dimensional flows that become turbulent for high values of the fluid Reynolds number. The magnitude of the forcing function driving the flow is allowed to evolve with time in such way as to maintain an approximately constant velocity amplitude (and average kinetic energy) when the flow becomes hydrodynamically unstable. It is found that the saturation level of the dynamo increases with the fluid Reynolds number (at constant magnetic Prandtl number), and that the average growth rate approaches an asymptotic value for high fluid Reynolds number. The generation and destruction of magnetic field is examined during the laminar and turbulent phase of the flow and it is found that in the neighborhood of strong magnetic "flux cigars" Joule dissipation is balanced by the work done against the Lorentz force, while the steady increase of magnetic energy occurs mainly through work done in the weak part of the magnetic field., Comment: 9 pages, 12 figures, accepted by A&A (frontpage illustration): Corrected typos