Browsing by Author "Brandenburg, Axel"

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Astrophysical magnetic fields and nonlinear dynamo theory
(2006-01-10) Brandenburg, Axel; Subramanian, Kandaswamy
The current understanding of astrophysical magnetic ﬁelds is reviewed, focusing on their generation and maintenance by turbulence. In the astrophysical context this generation is usually explained by a self-excited dynamo, which involves ﬂows that can amplify a weak ‘seed’ magnetic ﬁeld exponentially fast. Particular emphasis is placed on the nonlinear saturation of the dynamo. Analytic and numerical results are discussed both for small scale dynamos, which are completely isotropic, and for large scale dynamos, where some form of parity breaking is crucial. Central to the discussion of large scale dynamos is the so-called alpha effect which explains the generation of a mean ﬁeld if the turbulence lacks mirror symmetry, i.e. if the ﬂow has kinetic helicity. Large scale dynamos produce small scale helical ﬁelds as a waste product that quench the large scale dynamo and hence the alpha effect. With this in mind, the microscopic theory of the alpha effect is revisited in full detail and recent results for the loss of helical magnetic ﬁelds are reviewed.
Dynamo Models: where do we stand?
(2014-12-09) Subramanian, Kandaswamy; Bhat, Pallavi; Brandenburg, Axel
Formation of intense bipolar regions in spherical dynamo
(2014-12-09) Jabbari, Sarah; Brandenburg, Axel; Kleeorin, Nathan; Mitra, Dhrubaditya; Rogachevskii, Igor
Hydraulic effects in a partially ionized radiative atmosphere
(2014-12-11) Bhat, Pallavi; Brandenburg, Axel; Subramanian, Kandaswamy (Advisor)
Kinematic alpha effect in isotropic turbulence simulations
(2008-01) Sur, Sharanya; Brandenburg, Axel; Subramanian, Kandaswamy
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 diffusivitywhose 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.
Kinetic and magnetic alpha effects in nonlinear dynamo theory
(2007-01-19) Sur, Sharanya; Subramanian, Kandaswamy; Brandenburg, Axel
The backreaction of the Lorentz force on the α-effect is studied in the limit of small magnetic and ﬂuid Reynolds numbers, using the ﬁrst order smoothing approximation (FOSA) to solve both the induction and momentum equations. Both steady and time dependent forcings are considered. In the low Reynolds number limit, the velocity and magnetic ﬁelds can be expressed explicitly in terms of the forcing function. The nonlinear α-effect is then shown to be expressible in several equivalent forms in agreement with formalisms that are used in various closure schemes. On the one hand, one can express α completely in terms of the helical properties of the velocity ﬁeld as in traditional FOSA, or, alternatively, as the sum of two terms, a so-called kinetic α-effect and an oppositely signed term proportional to the helical part of the small scale magnetic ﬁeld. These results hold for both steady and time dependent forcing at arbitrary strength of the mean ﬁeld. In addition, the τ-approximation is considered in the limit of small ﬂuid and magnetic Reynolds numbers. In this limit, the τ closure term is absent and the viscous and resistive terms must be fully included. The underlying equations are then identical to those used under FOSA, but they reveal interesting differences between the steady and time dependent forcing. For steady forcing, the correlation between the forcing function and the small-scale magnetic ﬁeld turns out to contribute in a crucial manner to determine the net α-effect. However for delta-correlated time-dependent forcing, this force–ﬁeld correlation vanishes, enabling one to write α exactly as the sum of kinetic and magnetic α-effects, similar to what one obtains also in the large Reynolds number regime in theτ-approximation closure hypothesis. In the limit of strong imposed ﬁelds, B0, we ﬁnd α ∝ B−2 0 for delta-correlated forcing, in contrast to the well-known α ∝ B−3 0 behaviour for the case of a steady forcing. The analysis presented here is also shown to be in agreement with numerical simulations of steady as well as random helical ﬂows.
Magnetic quenching of alpha and diffusity tensors in helical turbulence
(2011-07-06) Brandenburg, Axel; Biman, B.; Subramanian, Kandaswamy; et al.
We study the implications of primordial magnetic ﬁelds for the thermal and ionization history of the post-recombination era. In particular we compute the eﬀects of dissipation of primordial magnetic ﬁelds owing to ambipolar diﬀusion and decaying turbulence in the intergalactic medium (IGM) and the collapsing halos and compute the eﬀects of the altered thermal and ionization history on the formation of molecular hydrogen.We show that, for magnetic ﬁeld strengths in the range 2×10−10 G < ∼ B0 < ∼ 2× 10−9 G, the molecular hydrogen fraction in IGM and collapsing halo can increase by a factor 5 to 1000 over the case with no magnetic ﬁelds. We discuss the implication of the increased molecular hydrogen fraction on the radiative transfer of UV photons and the formation of ﬁrst structures in the universe
Magnetohydrodynamic simulations of stellar differential rotation and meridional circulation (submitted to A&A, arXiv:1407.0984)
(2014-12-09) Karak, Bidya Binay; Kaepyla, Petri J.; Kaepyla, Maarit J.; Brandenburg, Axel
Minimal tau approximation and simulations of the alpha effect
(2005-08-01) Brandenburg, Axel; Subramanian, Kandaswamy
The validity of a closure called the minimal tau approximation (MTA), is tested in the context of dynamo theory, wherein triple correlations are assumed to provide relaxation of the turbulent electromotive force. Under MTA, the alpha effect in mean ﬁeld dynamo theory becomes proportional to a relaxation time scale multiplied by the difference between kinetic and current helicities. It is shown that the value of the relaxation time is positive and, in units of the turnover time at the forcing wavenumber, it is of the order of unity. It is quenched by the magnetic ﬁeld – roughly independently of the magnetic Reynolds number. However, this independence becomes uncertain at large magnetic Reynolds number. Kinetic and current helicities are shown to be dominated by large scale properties of the ﬂow.
Nonlinear current helicity fluxes in turbulent dynamos and alpha quenching
(2011-07-06) Subramanian, Kandaswamy; Brandenburg, Axel
Large scale dynamos produce small scale current helicity as a waste product that quenches the large scale dynamo process (alpha effect). This quenching can be catastrophic (i.e. intensify with magnetic Reynolds number) unless one has ﬂuxes of small scale magnetic (or current) helicity out of the system. We derive the form of helicity ﬂuxes in turbulent dynamos, taking also into account the nonlinear effects of Lorentz forces due to ﬂuctuating ﬁelds. We conﬁrm the form of an earlier derived magnetic helicity ﬂux term, and also show that it is not renormalized by the small scale magnetic ﬁeld, just like turbulent diffusion. Additional nonlinear ﬂuxes are identiﬁed, which are driven by the anisotropic and antisymmetric parts of the magnetic correlations. These could provide further ways for turbulent dynamos to transport out small scale magnetic helicity, so as to avoid catastrophic quenching.
Role of the Yoshizawa effect in the Archontis dynamo
(2009-05-01) Sur, Sharanya; Brandenburg, Axel
The generation of mean magnetic ﬁelds is studied for a simple non-helical ﬂow where a net cross helicity of either sign can emerge. This ﬂow, which is also known as the Archontis ﬂow, is a generalization of the Arnold–Beltrami–Childress ﬂow, but with the cosine terms omitted. The presence of cross helicity leads to a mean-ﬁeld dynamo effect that is known as the Yoshizawa effect. Direct numerical simulations of such ﬂows demonstrate the presence of magnetic ﬁelds on scales larger than the scale of the ﬂow. Contrary to earlier expectations, the Yoshizawa effect is found to be proportional to the mean magnetic ﬁeld and can therefore lead to its exponential instead of just linear ampliﬁcation for magnetic Reynolds numbers that exceed a certain critical value. Unlike α effect dynamos, it is found that the Yoshizawa effect is not noticeably constrained by the presence of a conservation law. It is argued that this is due to the presence of a forcing term in the momentum equation which leads to a nonzero correlation with the magnetic ﬁeld. Finally, the application to energy convergence in solar wind turbulence is discussed.
Strong mean field dynamos require supercritical helicity fluxes
(2006-01-10) Brandenburg, Axel; Subramanian, Kandaswamy
Several one and two dimensional mean ﬁeld models are analyzed where the effects of current helicity ﬂuxes and boundaries are included within the framework of the dynamical quenching model. In contrast to the case with periodic boundary conditions, the ﬁnal saturation energy of the mean ﬁeld decreases inversely proportional to the magnetic Reynolds number. If a nondimensional scaling factor in the current helicity ﬂux exceeds a certain critical value, the dynamo can operate even without kinetic helicity, i.e. it is based only on shear and current helicity ﬂuxes, as ﬁrst suggested by Vishniac & Cho (2001, ApJ 550, 752). Only above this threshold is the current helicity ﬂux also able to alleviate catastrophic quenching. The fact that certain turbulence simulations have now shown apparently non-resistively limited mean ﬁeld saturation amplitudes may be suggestive of the current helicity ﬂux having exceeded this critical value. Even below this critical value the ﬁeld still reaches appreciable strength at the end of the kinematic phase, which is in qualitative agreement with dynamos in periodic domains. However, for large magnetic Reynolds numbers the ﬁeld undergoes subsequent variations on a resistive time scale when, for long periods, the ﬁeld can be extremely weak.