Magnetic Field Saturation in the Riga Dynamo Experiment

Gailitis, A.; Lielausis, O.; Platacis, E.; Dement'ev, Sergej; Cifersons, Arnis; Gerbeth, Günter; Gundrum, Thomas; Stefani, Frank; Christen, M.; Will, Gotthard

doi:10.1103/physrevlett.86.3024

Cited by 247 publications

(218 citation statements)

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“…The backreaction mechanism reduced this exponential growth, and the saturation regime is finally achieved. The simulations show the strongest amplification of the axial magnetic field component ( ÿ ÿ) in the middle part of the setup (MON2, B y ) as observed in [3], confirming a strong criticality dependence on the underlying fluid flow and turbulence conditions, Fig. 3-middle.…”

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Numerical Simulation of a Turbulent Magnetic Dynamo

Kenjereš

Hanjalić

2007

Phys. Rev. Lett.

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We present numerical simulations of a turbulent magnetic dynamo mimicking closely the Riga-dynamo experiment at Re 3:5 10 6 and 15 Re m 20. The Reynolds-averaged Navier-Stokes equations for the fluid flow and turbulence field are solved simultaneously with the direct numerical solution of the magnetic field equations. The fully integrated two-way-coupled simulations reproduced all features of the magnetic self-excitation detected by the Riga experiment, with frequencies and amplitudes of the selfgenerated magnetic field in good agreement with the experimental records, and provided full insight into the unsteady magnetic and velocity fields and the mechanisms of the dynamo action. DOI: 10.1103/PhysRevLett.98.104501 PACS numbers: 47.11.ÿj, 47.27.Eÿ, 47.65.ÿd, 91.25.Cw Complex interactions between turbulent flow of electrically conductive fluids and electromagnetic fields play the key role in many physical phenomena in nature and technology. Of particular interest is the conversion of the mechanical energy of a moving electrically conductive medium into the magnetic energy, known as the magnetic dynamo. It is believed that the magnetic dynamo effects are responsible for the creation of magnetic fields in spiral galaxies, stars, and planets (including Earth's magnetic field), e.g., [1]. In order to create the favorable conditions for possible self-excitation of a magnetic field, it is necessary to achieve regimes where stretching of the magnetic field will overcome its resistive damping. This condition is defined by the critical magnetic Reynolds number Re m UL= > 1 (where U and L are typical velocity and length scale, respectively, and is magnetic diffusivity). In order to reach such conditions, one needs relatively large length scales and high velocities -even for the best electrically conductive fluids (e.g., liquid sodium, 1= 0 0:1 m 2 =s), where 0 and are the magnetic permeability and electric conductivity. For such configurations, the hydrodynamical Reynolds number (Re UL= ) will be also very high (Re 10 5 -10 6 ), making the flow highly turbulent. Experimental studies of magnetic fluid dynamos face many practical problems associated with large dimensions of setups and potentially hazardous working fluids (sodium). This explains why it was not until late 1999 when two experimental groups in Riga ([2 -6]) and Karlsruhe ([7-9]) finally and independently succeeded in detecting the self-excitation and subsequent sustenance of a magnetic field for the very first time. Although this is an important step towards understanding and explaining the Earth's magnetic field from the magnetic dynamo effect, both experiments were not designed to actually mimic the Geo-Dynamo (Earth-like) conditions, but rather to provide experimental proof of the magnetic field self-amplification.Despite their remarkable success, the experimental studies provided only the time records of the magnetic field components at particular locations -so information addressing the detailed spatial distribution of the magnetic field and its dynamics...

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Numerical Simulation of a Turbulent Magnetic Dynamo

Kenjereš

Hanjalić

2007

Phys. Rev. Lett.

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“…for Rm > Rm crit a small seed magnetic field will grow exponentially in time. The dynamo onset conditions have been tested in helical pipe-flow experiments at Riga [7,8] and Karlsruhe [9,10]. Both experiments generated magnetic fields at a value of Rm crit consistent with predictions from the kinematic theory.…”

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Intermittent Magnetic Field Excitation by a Turbulent Flow of Liquid Sodium

et al. 2006

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The magnetic field measured in the Madison Dynamo Experiment shows intermittent periods of growth when an axial magnetic field is applied. The geometry of the intermittent field is consistent with the fastest growing magnetic eigenmode predicted by kinematic dynamo theory using a laminar model of the mean flow. Though the eigenmodes of the mean flow are decaying, it is postulated that turbulent fluctuations of the velocity field change the flow geometry such that the eigenmode growth rate is temporarily positive. Therefore, it is expected that a characteristic of the onset of a turbulent dynamo is magnetic intermittency. Determining the onset conditions for magnetic field growth in magnetohydrodynamics is fundamental to understanding how astrophysical dynamos such as the Earth, the Sun, and the galaxy self-generate magnetic fields. These onset conditions are now being studied in laboratory experiments using flows of liquid sodium [1]. The conditions required for generating a dynamo can be determined by solving the magnetic induction equationwhere B is the magnetic field, V is the velocity field scaled by a characteristic speed V 0 , and the time is scaled to the resistive diffusion time τ σ = µ 0 σL 2 . The magnetic Reynolds number is Rm = µ 0 σLV 0 , where σ is the conductivity of the fluid and L is a characteristic scale length [2]. In the kinematic approximation, the velocity field is assumed to be a prescribed flow (either the flow is stationary or its time dependence is specified) and Lorentz forces due to the magnetic field are neglected. Equation 1 is then linear in B and can be solved as an eigenvalue problem. Several different types of stationary, helical flows have been shown theoretically to be kinematic dynamos [3,4,5,6], which in turn has lead to the design of current dynamo experiments. For particular flows, the kinematic model predicts a critical value of the magnetic Reynolds number, Rm crit , above which the magnetic field becomes linearly unstable, i.e. for Rm > Rm crit a small seed magnetic field will grow exponentially in time. The dynamo onset conditions have been tested in helical pipe-flow experiments at Riga [7,8] and Karlsruhe [9,10]. Both experiments generated magnetic fields at a value of Rm crit consistent with predictions from the kinematic theory.Fluids and plasmas such as the Earth's liquid core, the solar convection zone, and liquid metals are turbulent under the conditions required for a dynamo. The

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“…This approximation is very useful when conducting optimization of experiments, so as to get the lowest threshold for dynamo action based only on the mean flow Rm MF c [4,5,6,7]. It led to very good estimate of the measured dynamo threshold in the case of experiments in constrained geometries [8], where the instantaneous velocity field is very close to its time-average.In contrast, unconstrained experiments [7,9] are characterized by large velocity fluctuations, allowing the exploration of the influence of turbulence onto the meanflow dynamo threshold. Theoretical predictions regarding this influence are scarce.…”

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Influence of Turbulence on the Dynamo Threshold

et al. 2006

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We use direct and stochastic numerical simulations of the magnetohydrodynamic equations to explore the influence of turbulence on the dynamo threshold. In the spirit of the Kraichnan-Kazantsev model, we model the turbulence by a noise, with given amplitude, injection scale and correlation time. The addition of a stochastic noise to the mean velocity significantly alters the dynamo threshold. When the noise is at small (resp. large) scale, the dynamo threshold is decreased (resp. increased). For a large scale noise, a finite noise correlation time reinforces this effect.PACS numbers: 47.27. Eq, 47.27.Sd, 47.65.+a, 91.25.Cw The process of magnetic field generation through the movement of an electrically conducting medium is called a dynamo. When this medium is a fluid, the instability results from a competition between magnetic field amplification via stretching and folding, and damping through magnetic diffusion. This is quantified by the magnetic Reynolds number Rm, which must exceed some critical value Rm c for the instability to operate. Despite their obvious relevance in natural objects, such as stars, planets or galaxies, dynamos are not so easy to study or model. Computer resources limit the numerical study of dynamos to a range of either small Reynolds numbers Re (laminar dynamo), modest Rm and Re [1] or small P m = Rm/Re using Large Eddy Simulation [2]. These difficulties explain the recent development of experiments involving liquid metals, as a way to study the dynamo problem at large Reynolds number. In this case, the flow has a non-zero mean component and is fully turbulent. There is, in general, no exact analytical or numerical predictions regarding the dynamo threshold. However, prediction for the mean flow action can be obtained in the so-called "kinematic regime" where the magnetic field back reaction onto the flow is neglected (see e.g. [3]). This approximation is very useful when conducting optimization of experiments, so as to get the lowest threshold for dynamo action based only on the mean flow Rm MF c [4,5,6,7]. It led to very good estimate of the measured dynamo threshold in the case of experiments in constrained geometries [8], where the instantaneous velocity field is very close to its time-average.In contrast, unconstrained experiments [7,9] are characterized by large velocity fluctuations, allowing the exploration of the influence of turbulence onto the meanflow dynamo threshold. Theoretical predictions regarding this influence are scarce. Small velocity fluctuations produce little impact on the dynamo threshold [10]. Predictions for arbitrary fluctuation amplitudes can be reached by considering the turbulent dynamo as an instability (driven by the mean flow) in the presence of a multiplicative noise (turbulent fluctuations) [11]. In this context, fluctuations favor or impede the magnetic field growth depending on their intensity or correlation time. This observation is confirmed by recent numerical simulations of simple periodic flows with non-zero mean flow [12,13] showing that tur...

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Magnetic Field Saturation in the Riga Dynamo Experiment

Cited by 247 publications

References 4 publications

Numerical Simulation of a Turbulent Magnetic Dynamo

Numerical Simulation of a Turbulent Magnetic Dynamo

Intermittent Magnetic Field Excitation by a Turbulent Flow of Liquid Sodium

Influence of Turbulence on the Dynamo Threshold

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