Growth Of Large-scale Magnetic Field Research Articles

Magnetic Helicity Fluxes from Triple Correlators

Fluxes of the magnetic helicity density play an important role in large-scale turbulent dynamos, allowing the growth of large-scale magnetic fields while overcoming catastrophic quenching. We show here, analytically, how several important types of magnetic helicity fluxes can arise from terms involving triple correlators of fluctuating fields in the helicity density evolution equation. For this, we assume incompressibility and weak inhomogeneity, and use a quasi-normal closure approximation: fourth-order correlators are replaced by products of second-order ones, and the effect of the fourth-order cumulants on the evolution of the third moments is modeled by a strong damping term. First, we show how a diffusive helicity flux, until now only measured in simulations, arises from the triple correlation term. This is accompanied by what we refer to as a random advective flux, which predominantly transports magnetic helicity along the gradients of the random fields. We also find that a new helicity flux contribution, in some aspects similar to that first proposed by Vishniac, can arise from the triple correlator. This contribution depends on the gradients of the random magnetic and kinetic energies along the large-scale vorticity, and thus arises in any rotating, stratified system, even if the turbulence is predominantly non-helical. It can source a large-scale dynamo by itself while spatially transporting magnetic helicity within the system.

Generation of large-scale magnetic fields due to fluctuating in shearing systems

We explore the growth of large-scale magnetic fields in a shear flow, due to helicity fluctuations with a finite correlation time, through a study of the Kraichnan–Moffatt model of zero-mean stochastic fluctuations of the$\unicode[STIX]{x1D6FC}$parameter of dynamo theory. We derive a linear integro-differential equation for the evolution of the large-scale magnetic field, using the first-order smoothing approximation and the Galilean invariance of the$\unicode[STIX]{x1D6FC}$-statistics. This enables construction of a model that is non-perturbative in the shearing rate$S$and the$\unicode[STIX]{x1D6FC}$-correlation time$\unicode[STIX]{x1D70F}_{\unicode[STIX]{x1D6FC}}$. After a brief review of the salient features of the exactly solvable white-noise limit, we consider the case of small but non-zero$\unicode[STIX]{x1D70F}_{\unicode[STIX]{x1D6FC}}$. When the large-scale magnetic field varies slowly, the evolution is governed by a partial differential equation. We present modal solutions and conditions for the exponential growth rate of the large-scale magnetic field, whose drivers are the Kraichnan diffusivity, Moffatt drift, shear and a non-zero correlation time. Of particular interest is dynamo action when the$\unicode[STIX]{x1D6FC}$-fluctuations are weak; i.e. when the Kraichnan diffusivity is positive. We show that in the absence of Moffatt drift, shear does not give rise to growing solutions. But shear and Moffatt drift acting together can drive large-scale dynamo action with growth rate$\unicode[STIX]{x1D6FE}\propto |S|$.

Calculating turbulent transport tensors by averaging single-plume dynamics and application to dynamos

ABSTRACT Transport coefficients in turbulence are comprised of correlation functions between turbulent fluctuations and efficient methods to calculate them are desirable. For example, in mean-field dynamo theories used to model the growth of large-scale magnetic fields of stars and galaxies, the turbulent electromotive force is commonly approximated by a series of tensor products of turbulent transport coefficients with successively higher order spatial derivatives of the mean magnetic field. One ingredient of standard models is the kinematic coefficient of the zeroth-order term, namely the averaged kinetic pseudo-tensor $\boldsymbol \alpha$, that converts toroidal to poloidal fields. Here we demonstrate an efficient way to calculate this quantity for rotating stratified turbulence, whereby the pre-averaged quantity is calculated for the motion of a single plume, and the average is then taken over an ensemble of plumes of different orientations. We calculate the plume dynamics in the most convenient frame, before transforming back to the lab frame and averaging. Our concise configuration space calculation gives essentially identical results to previous lengthier approaches. The present application exemplifies what is a broadly applicable method.

Influence of small-scale EM and HM on the growth of large-scale magnetic field

We investigated the influence of small scale magnetic energy ($E_M$) and magnetic helicity ($H_M$) on the growth rate ($\gamma$) of large scale magnetic field ($\overline{{\bf B}}$). $H_M$ that plays a key role in MHD dynamo is a topological concept describing the structural properties of magnetic fields. So, it is not possible to differentiate the intrinsic properties of $H_M$ from the influence of $E_M$, and vice versa. However, to understand MHD dynamo the features of helical and nonhelical magnetic field should be made clear. For this, we made a detour: we gave each simulation set its own initial condition ($IC$, same $E_M$(0) and specific $H_M$(0) at $k_f=5$), and then drove the system with positive helical kinetic energy($k_f=5$). According to the simulation results, $E_M$(0), whether or not helical, increases the growth rate of $\overline{{\bf B}}$. The positive $H_M$(0) boosts the increased growth rate, but the negative $H_M$(0) decreases it. To explain these results two coupled equations of $H_M$ and $E_M$ were derived and solved using a simple approximate method. The equations imply that helical magnetic field generates the whole (helical and nonhelical) magnetic field but quenches itself. Nonhelical magnetic field also generates the whole magnetic field but quenches itself. The initially given $E_M$(0) modifies the electromotive force ($\langle {\bf v}{\bf \times} {\bf b}\rangle$, $EMF$) and generates new terms. The effects of these terms depend on the magnetic diffusivity $\eta$, position of initial conditions $k_f$, and time. But the influence disappears as time passes ($\sim e^{-\eta k_f^2 t}$), so the saturated magnetic fields are independent of the initial conditions.

Bihelical magnetic relaxation and large scale magnetic field growth

A unified, three-scale system of equations accommodating nonlinear velocity driven helical dynamos, as well as time-dependent relaxation of magnetically dominated unihelical or bihelical systems is derived and solved herein. When opposite magnetic helicities of equal magnitude are injected on the intermediate and small scales, the large scale magnetic helicity grows kinematically (independent of the magnetic Reynolds number) to equal that on the intermediate scale. For both free and driven relaxation large scale fields are rapidly produced. Subsequently, a dissipation-limited dynamo, driven by growth of small scale kinetic helicity, further amplifies the large scale field. The results are important for astrophysical coronae fed with bihelical structures by dynamos in their host rotators. The large scale for the rotator corresponds to the intermediate scale for the corona. That bihelical magnetic relaxation can produce global scale fields may help to explain the formation of astrophysical coronal holes and magnetohydrodynamic outflows.

Direct Simulations of Helical Hall‐MHD Turbulence and Dynamo Action

Direct numerical simulations of turbulent Hall dynamos are presented. The evolution of an initially weak and small-scale magnetic field in a system maintained in a stationary turbulent regime by a stirring force at a macroscopic scale is studied to explore the conditions for exponential growth of the magnetic energy. Scaling of the dynamo efficiency with Reynolds numbers is studied, and the resulting total energy spectra are found to be compatible with a Kolmogorov-type law. A faster growth of large-scale magnetic fields is observed at intermediate intensities of the Hall effect.

Effect of small-scale temperature modulation on magnetic field generation in laser plasmas

The generation of d.c. magnetic fields in electron time scale in the presence of small-scale temperature modulation is considered. It is shown that (i) the modulation leads to the growth of large-scale magnetic field, and (ii) the amplitude of this field as a function of the modulation amplitude M reaches its maximum at M ~ (kL)−1, where k is the modulation wavenumber and L is the spatial scale of the average temperature profile.