Kinematic alpha effect in isotropic turbulence simulations

Using numerical simulations at moderate magnetic Reynolds numbers up to 220 it is shown that in the kinematic regime, isotropic helical turbulence leads to an alpha effect and a turbulent diffusivity whose values are independent of the magnetic Reynolds number, \Rm, provided \Rm exceeds unity. These turbulent coefficients are also consistent with expectations from the first order smoothing approximation. For small values of \Rm, alpha and turbulent diffusivity are proportional to \Rm. Over finite time intervals meaningful values of alpha and turbulent diffusivity can be obtained even when there is small-scale dynamo action that produces strong magnetic fluctuations. This suggests that small-scale dynamo-generated fields do not make a correlated contribution to the mean electromotive force.Comment: Accepted for publication in MNRAS Letter

Properties of pp- and ff-modes in hydromagnetic turbulence

With the ultimate aim of using the fundamental or $f$-mode to study helioseismic aspects of turbulence-generated magnetic flux concentrations, we use randomly forced hydromagnetic simulations of a piecewise isothermal layer in two dimensions with reflecting boundaries at top and bottom. We compute numerically diagnostic wavenumber-frequency diagrams of the vertical velocity at the interface between the denser gas below and the less dense gas above. For an Alfv\'en-to-sound speed ratio of about 0.1, a 5% frequency increase of the $f$-mode can be measured when $k_xH_{\rm p}=3$-$4$, where $k_x$ is the horizontal wavenumber and $H_{\rm p}$ is the pressure scale height at the surface. Since the solar radius is about 2000 times larger than $H_{\rm p}$, the corresponding spherical harmonic degree would be 6000-8000. For weaker fields, a $k_x$-dependent frequency decrease by the turbulent motions becomes dominant. For vertical magnetic fields, the frequency is enhanced for $k_xH_{\rm p}\approx4$, but decreased relative to its nonmagnetic value for $k_xH_{\rm p}\approx9$.Comment: 17 pages, 22 figures, Version accepted in MNRA

The inverse cascade and nonlinear alpha-effect in simulations of isotropic helical hydromagnetic turbulence

A numerical model of isotropic homogeneous turbulence with helical forcing is investigated. The resulting flow, which is essentially the prototype of the alpha^2 dynamo of mean-field dynamo theory, produces strong dynamo action with an additional large scale field on the scale of the box (at wavenumber k=1; forcing is at k=5). This large scale field is nearly force-free and exceeds the equipartition value. As the magnetic Reynolds number R_m increases, the saturation field strength and the growth rate of the dynamo increase. However, the time it takes to built up the large scale field from equipartition to its final super-equipartition value increases with magnetic Reynolds number. The large scale field generation can be identified as being due to nonlocal interactions originating from the forcing scale, which is characteristic of the alpha-effect. Both alpha and turbulent magnetic diffusivity eta_t are determined simultaneously using numerical experiments where the mean-field is modified artificially. Both quantities are quenched in a R_m-dependent fashion. The evolution of the energy of the mean field matches that predicted by an alpha^2 dynamo model with similar alpha and eta_t quenchings. For this model an analytic solution is given which matches the results of the simulations. The simulations are numerically robust in that the shape of the spectrum at large scales is unchanged when changing the resolution from 30^3 to 120^3 meshpoints, or when increasing the magnetic Prandtl number (viscosity/magnetic diffusivity) from 1 to 100. Increasing the forcing wavenumber to 30 (i.e. increasing the scale separation) makes the inverse cascade effect more pronounced, although it remains otherwise qualitatively unchanged.Comment: 21 pages, 26 figures, ApJ (accepted

Mean-field diffusivities in passive scalar and magnetic transport in irrotational flows

Certain aspects of the mean-field theory of turbulent passive scalar transport and of mean-field electrodynamics are considered with particular emphasis on aspects of compressible fluids. It is demonstrated that the total mean-field diffusivity for passive scalar transport in a compressible flow may well be smaller than the molecular diffusivity. This is in full analogy to an old finding regarding the magnetic mean-field diffusivity in an electrically conducting turbulently moving compressible fluid. These phenomena occur if the irrotational part of the motion dominates the vortical part, the P\`eclet or magnetic Reynolds number is not too large, and, in addition, the variation of the flow pattern is slow. For both the passive scalar and the magnetic cases several further analytical results on mean-field diffusivities and related quantities found within the second-order correlation approximation are presented, as well as numerical results obtained by the test-field method, which applies independently of this approximation. Particular attention is paid to non-local and non-instantaneous connections between the turbulence-caused terms and the mean fields. Two examples of irrotational flows, in which interesting phenomena in the above sense occur, are investigated in detail. In particular, it is demonstrated that the decay of a mean scalar in a compressible fluid under the influence of these flows can be much slower than without any flow, and can be strongly influenced by the so-called memory effect, that is, the fact that the relevant mean-field coefficients depend on the decay rates themselves.Comment: 13 pages, 10 figures, published on PR

Turbulent transport in hydromagnetic flows

The predictive power of mean-field theory is emphasized by comparing theory with simulations under controlled conditions. The recently developed test-field method is used to extract turbulent transport coefficients both in kinematic as well as nonlinear and quasi-kinematic cases. A striking example of the quasi-kinematic method is provided by magnetic buoyancy-driven flows that produce an alpha effect and turbulent diffusion.Comment: 17 pages, 6 figures, topical issue of Physica Scripta on turbulent mixing and beyon

Simulations of galactic dynamos

We review our current understanding of galactic dynamo theory, paying particular attention to numerical simulations both of the mean-field equations and the original three-dimensional equations relevant to describing the magnetic field evolution for a turbulent flow. We emphasize the theoretical difficulties in explaining non-axisymmetric magnetic fields in galaxies and discuss the observational basis for such results in terms of rotation measure analysis. Next, we discuss nonlinear theory, the role of magnetic helicity conservation and magnetic helicity fluxes. This leads to the possibility that galactic magnetic fields may be bi-helical, with opposite signs of helicity and large and small length scales. We discuss their observational signatures and close by discussing the possibilities of explaining the origin of primordial magnetic fields.Comment: 28 pages, 15 figure, to appear in Lecture Notes in Physics "Magnetic fields in diffuse media", Eds. E. de Gouveia Dal Pino and A. Lazaria

Magnetic diffusivity tensor and dynamo effects in rotating and shearing turbulence

The turbulent magnetic diffusivity tensor is determined in the presence of rotation or shear. The question is addressed whether dynamo action from the shear-current effect can explain large-scale magnetic field generation found in simulations with shear. For this purpose a set of evolution equations for the response to imposed test fields is solved with turbulent and mean motions calculated from the momentum and continuity equations. The corresponding results for the electromotive force are used to calculate turbulent transport coefficients. The diagonal components of the turbulent magnetic diffusivity tensor are found to be very close together, but their values increase slightly with increasing shear and decrease with increasing rotation rate. In the presence of shear, the sign of the two off-diagonal components of the turbulent magnetic diffusion tensor is the same and opposite to the sign of the shear. This implies that dynamo action from the shear--current effect is impossible, except perhaps for high magnetic Reynolds numbers. However, even though there is no alpha effect on the average, the components of the alpha tensor display Gaussian fluctuations around zero. These fluctuations are strong enough to drive an incoherent alpha--shear dynamo. The incoherent shear--current effect, on the other hand, is found to be subdominant.Comment: 12 pages, 13 figures, improved version, accepted by Ap

Proton radiography to improve proton radiotherapy: Simulation study at different proton beam energies

To improve the quality of cancer treatment with protons, a translation of X-ray Computed Tomography (CT) images into a map of the proton stopping powers needs to be more accurate. Proton stopping powers determined from CT images have systematic uncertainties in the calculated proton range in a patient of typically 3-4\% and even up to 10\% in region containing bone~\cite{USchneider1995,USchneider1996,WSchneider2000,GCirrone2007,HPaganetti2012,TPlautz2014,GLandry2013,JSchuemann2014}. As a consequence, part of a tumor may receive no dose, or a very high dose can be delivered in healthy ti\-ssues and organs at risks~(e.g. brain stem)~\cite{ACKnopf2013}. A transmission radiograph of high-energy protons measuring proton stopping powers directly will allow to reduce these uncertainties, and thus improve the quality of treatment. The best way to obtain a sufficiently accurate radiograph is by tracking individual protons traversing the phantom (patient)~\cite{GCirrone2007,TPlautz2014,VSipala2013}. In our simulations we have used an ideal position sensitive detectors measuring a single proton before and after a phantom, while the residual energy of a proton was detected by a BaF$_{2}$ crystal. To obtain transmission radiographs, diffe\-rent phantom materials have been irradiated with a 3x3~cm$^{2}$ scattered proton beam, with various beam energies. The simulations were done using the Geant4 simulation package~\cite{SAgostinelli2003}. In this study we focus on the simulations of the energy loss radiographs for various proton beam energies that are clinically available in proton radiotherapy.Comment: 6 pages, 6 figures, Presented at Jagiellonian Symposium on Fundamental and Applied Subatomic Physics, 7-12 June, 2015, Krak\'ow, Polan

Current status of turbulent dynamo theory: From large-scale to small-scale dynamos

Several recent advances in turbulent dynamo theory are reviewed. High resolution simulations of small-scale and large-scale dynamo action in periodic domains are compared with each other and contrasted with similar results at low magnetic Prandtl numbers. It is argued that all the different cases show similarities at intermediate length scales. On the other hand, in the presence of helicity of the turbulence, power develops on large scales, which is not present in non-helical small-scale turbulent dynamos. At small length scales, differences occur in connection with the dissipation cutoff scales associated with the respective value of the magnetic Prandtl number. These differences are found to be independent of whether or not there is large-scale dynamo action. However, large-scale dynamos in homogeneous systems are shown to suffer from resistive slow-down even at intermediate length scales. The results from simulations are connected to mean field theory and its applications. Recent work on helicity fluxes to alleviate large-scale dynamo quenching, shear dynamos, nonlocal effects and magnetic structures from strong density stratification are highlighted. Several insights which arise from analytic considerations of small-scale dynamos are discussed.Comment: 36 pages, 11 figures, Spa. Sci. Rev., submitted to the special issue "Magnetism in the Universe" (ed. A. Balogh

Cosmological Magnetic Fields from Primordial Helicity

Primordial magnetic fields may account for all or part of the fields observed in galaxies. We consider the evolution of the magnetic fields created by pseudoscalar effects in the early universe. Such processes can create force-free fields of maximal helicity; we show that for such a field magnetic energy inverse cascades to larger scales than it would have solely by flux freezing and cosmic expansion. For fields generated at the electroweak phase transition, we find that the predicted wavelength today can in principle be as large as 10 kpc, and the field strength can be as large as 10^{-10} G.Comment: 13 page