New Mechanism of Generation New Mechanism of Generation of Large-Scale Magnetic Field of Large-Scale Magnetic Field in Turbulence with Large-Scale in Turbulence with Large-Scale

Velocity ShearVelocity Shear

I. ROGACHEVSKII, N. KLEEORIN, E. LIVERTS

Ben-Gurion University of the Negev, Beer Sheva, ISRAEL

OutlineOutline

IntroductionIntroduction

Physics of newPhysics of new “shear-current” effect “shear-current” effect and comparison and comparison

with alpha effect (hydrodynamic helicity)with alpha effect (hydrodynamic helicity)

Generation of large-scale magnetic fieldGeneration of large-scale magnetic field due to the due to the

“shear-current” effect“shear-current” effect (kinematic and nonlinear (kinematic and nonlinear

dynamos)dynamos)

Application to Astrophysics: magnetic fields in Application to Astrophysics: magnetic fields in

merging protostellar clouds, protogalactic clouds, etc.merging protostellar clouds, protogalactic clouds, etc.

Conclusions and future studiesConclusions and future studies

Mean-Field DynamoMean-Field Dynamo

Is it possible to generate a large-scale Is it possible to generate a large-scale

magnetic field in a magnetic field in a non-helicalnon-helical and and non-non-

rotatingrotating homogeneoushomogeneous turbulence ? turbulence ?

Alpha-Omega DynamoAlpha-Omega Dynamo(Mean-Field Approach)(Mean-Field Approach)

Induction equation for Induction equation for mean magnetic fieldmean magnetic field::

Electromotive forceElectromotive force::

Generation of the mean magnetic Generation of the mean magnetic field due to the dynamofield due to the dynamo

Dynamo number:

Mean magnetic field:

BpB

)(rΩ

Physics of the alpha-effectPhysics of the alpha-effect The -effectThe -effect is related to the is related to the

hydrodynamic helicityhydrodynamic helicity in an in an

inhomogeneous turbulenceinhomogeneous turbulence. .

The The deformations of the magnetic fielddeformations of the magnetic field

lines are caused by lines are caused by upwardupward and and

downwarddownward rotating turbulent eddies. rotating turbulent eddies.

The The inhomogeneity of turbulenceinhomogeneity of turbulence breaks breaks

a symmetry between the a symmetry between the upwardupward and and

downwarddownward eddies. eddies.

Therefore, the Therefore, the total effect of the upward total effect of the upward

and downwardand downward eddies on the mean eddies on the mean

magnetic field magnetic field does not vanishdoes not vanish and it and it

creates the creates the mean electric currentmean electric current parallel parallel

to the to the original mean magnetic fieldoriginal mean magnetic field..

J

B

Mean-Field DynamoMean-Field Dynamo

Do one need Do one need hydrodynamic helicityhydrodynamic helicity in in

order to generate a order to generate a large-scale magnetic large-scale magnetic

fieldfield in a homogeneous turbulent flow ? in a homogeneous turbulent flow ?

Mean-Field ApproachMean-Field Approach

Induction equation for Induction equation for mean magnetic fieldmean magnetic field::

Electromotive forceElectromotive force::

The ''shear-current" effectThe ''shear-current" effect The The large-scale shear motionslarge-scale shear motions implies a implies a

nonzero mean vorticitynonzero mean vorticity ::

The ''shear-current" effectThe ''shear-current" effect is related to is related to

the termthe term, ,

Therefore, Therefore, the termthe term determines determines

the ''shear-current" effectthe ''shear-current" effect..

Comparison of the alpha-effect Comparison of the alpha-effect with the ''shear-current" effectwith the ''shear-current" effect

The effectThe effect is caused by a is caused by a uniform rotationuniform rotation and and

inhomogeneity of turbulenceinhomogeneity of turbulence::

, where, where

The ''shear-current" effectThe ''shear-current" effect is related to is related to the termthe term and and

is caused by is caused by mean shearmean shear and and nonuniform mean nonuniform mean

magnetic fieldmagnetic field,,

, , wherewhere

Therefore,Therefore,

Physics of ''shear-current" effectPhysics of ''shear-current" effect In a turbulent flow with the mean In a turbulent flow with the mean

velocity shearvelocity shear, the , the inhomogeneity of inhomogeneity of

the original mean magnetic fieldthe original mean magnetic field breaks breaks

a symmetrya symmetry between the influence of between the influence of

the the upwardupward and and downwarddownward turbulent turbulent

eddies on the mean magnetic field.eddies on the mean magnetic field.

The deformations of the magnetic field The deformations of the magnetic field

lines lines in the ''shear-current"in the ''shear-current" dynamo are dynamo are

caused by the caused by the upwardupward and and downwarddownward

turbulent eddies which result in the turbulent eddies which result in the

mean electric currentmean electric current parallel to the parallel to the

mean magnetic field and mean magnetic field and produce the produce the

magnetic dynamomagnetic dynamo..

J

B

Generation of the mean magnetic Generation of the mean magnetic field due to the shear-current effectfield due to the shear-current effect

Mean velocity shear:

Necessary condition for Necessary condition for the shear-current dynamothe shear-current dynamo

The parameter :The growth rate of B:

The Kolmogorov Scaling (large Re and Rm):

Small Re and Rm (weak turbulence):

Rogachevskii and Kleeorin (2003): there is shear-current dynamo

In a good agreement with: Rädler and Stepanov (2006) there is no dynamo for: Rüdiger and Kitchatinov (2006) (SOCA)

Generation of the mean magnetic Generation of the mean magnetic field (kinematic dynamo)field (kinematic dynamo)

Solution for the symmetric mode:

The growth rate of B:

Critical dynamo number:

The magnetic scale at maximum :

Generation of the mean magnetic Generation of the mean magnetic field (kinematic dynamo)field (kinematic dynamo)

Solution for the antisymmetric mode:

The growth rate of B:

Critical dynamo number:

The magnetic scale at maximum :

Generation of the mean vorticity and Generation of the mean vorticity and magnetic field in sheared turbulencemagnetic field in sheared turbulence

Mean velocity shear:

The growth rate of

The mean vorticityThe mean magnetic field

The growth rate of B

Generation of the mean vorticity in Generation of the mean vorticity in turbulence with mean velocity shearturbulence with mean velocity shear

Mean velocity shear:

The growth rate of the mean vorticity

Elperin, Kleeorin and Rogachevskii, PRE, 68, 016311 (2003)

The shear-current nonlinear The shear-current nonlinear dynamo (algebraic nonlinearity)dynamo (algebraic nonlinearity)

Dynamo number:

Nonlinear shear-current effect:

Mean magnetic field:

Shear number:

Nonlinear shear-current effectNonlinear shear-current effect

Weak magnetic field:

Strong mean magnetic field:

There is no quenching of the nonlinear "shear-current" effect contrary to the quenching of the nonlinear alpha effect, the nonlinear turbulent magnetic diffusion, etc.

Method of DerivationMethod of Derivation

The spectral -approximation (the third-order closure procedure)

Equations for the correlation functions for:

The velocity fluctuations

The magnetic fluctuations

The cross-helicity tensor

The shear-current nonlinear The shear-current nonlinear dynamo (algebraic nonlinearity)dynamo (algebraic nonlinearity)

Dynamo number:

Nonlinear shear-current effect:

Mean magnetic field:

Shear number:

Nonlinear “shear-current” dynamoNonlinear “shear-current” dynamo(algebraic nonlinearity)(algebraic nonlinearity)

Nonlinear “shear-current” dynamoNonlinear “shear-current” dynamo(algebraic nonlinearity)(algebraic nonlinearity)

Magnetic HelicityMagnetic Helicity

Magnetic part of alpha effect:

Total magnetic helicityTotal magnetic helicity is conservedis conserved for very large for very large magnetic Reynolds numbersmagnetic Reynolds numbers

Dynamics of small-scale magnetic helicity:

The nonlinear function:

Dynamics of magnetic helicityDynamics of magnetic helicity

In the absence of the magnetic helicity flux,

In the presence of the flux of magnetic helicity:

i.e., catastrophic quenching (Vainshtein and Cattaneo, 1992)

Kleeorin and Ruzmaikin (1982); Gruzinov and Diamond (1994); Kleeorin and Rogachevskii (1999); Kleeorin, Moss, Rogachevskii and Sokoloff (2000); Blackman and Field (2000).

The shear-current nonlinear dynamo The shear-current nonlinear dynamo (algebraic and dynamic nonlinearities)(algebraic and dynamic nonlinearities)

Magnetic part of alpha effect:

Dynamical nonlinearity: magnetic helicity evolution

Mean magnetic field:

The nonlinear function:

The shear-current nonlinear dynamo The shear-current nonlinear dynamo (algebraic and dynamic nonlinearities)(algebraic and dynamic nonlinearities)

Mean magnetic field:

cr10 DD

cr8 DD

cr7 DD

Direct Numerical SimulationsDirect Numerical Simulations A. BrandenburgA. Brandenburg, , Astrophys. J. Astrophys. J. 625625, 539-547 (2005)., 539-547 (2005). A. Brandenburg, N.E.L. Haugen, P.J. Käpylä, C. SandinA. Brandenburg, N.E.L. Haugen, P.J. Käpylä, C. Sandin,,

Astron. Nachr. Astron. Nachr. 326326, 174-185 (2005)., 174-185 (2005).

1. 1. Non-helical forcingNon-helical forcing

2. 2. Imposed mean velocity Imposed mean velocity shearshear

3. 3. Open boundary conditionsOpen boundary conditions (non-zero flux of magnetic (non-zero flux of magnetic

helicity)helicity)

Astrophysical cloudsAstrophysical clouds We apply We apply the universal mechanismthe universal mechanism of generation of of generation of

large-scale magnetic fields due to shear-current effect to large-scale magnetic fields due to shear-current effect to

several astrophysical objects:several astrophysical objects:

merging protostellar cloudsmerging protostellar clouds

merging protogalactic cloudsmerging protogalactic clouds

colliding giant galaxy clusterscolliding giant galaxy clusters

Interactions of protostellar clouds, or colliding Interactions of protostellar clouds, or colliding

protogalactic clouds or giant galaxy clusters produce protogalactic clouds or giant galaxy clusters produce

large-scale shear motionslarge-scale shear motions which are superimposed on which are superimposed on

small-scale turbulence.small-scale turbulence.

ParametersParameters

ParametersParameters Protostellar Protostellar CloudsClouds

Protogalactic Protogalactic CloudsClouds

Giant Galaxy Giant Galaxy ClustersClusters

MassMass

R (pc)R (pc)

V (cm/s)V (cm/s)

Chernin (1993). Non-central collisionChernin (1993). Non-central collision

Different cloud sizes, Chernin (1993)Different cloud sizes, Chernin (1993)

ParametersParametersParametersParameters Protostellar Protostellar

CloudsCloudsProtogalactic Protogalactic

CloudsCloudsGiant Giant Galaxy Galaxy ClustersClusters

(cm/s)(cm/s)

(cm)(cm)

u (cm/s)u (cm/s)

(cm)(cm)

(years) (years)

ParametersParametersParametersParameters Protostellar Protostellar

CloudsCloudsProtogalactic Protogalactic

CloudsCloudsGiant Giant

Galaxy Galaxy ClustersClusters

(cm/s)(cm/s)

(cm)(cm)

(years)(years)

ReferencesReferences

I. Rogachevskii and N. KleeorinI. Rogachevskii and N. Kleeorin, , Phys. Rev. EPhys. Rev. E 6868, , 036301 (2003).036301 (2003).

I. Rogachevskii and N. KleeorinI. Rogachevskii and N. Kleeorin, Phys. Rev. E , Phys. Rev. E 7070, , 046310 (2004).046310 (2004).

I. Rogachevskii, N. Kleeorin, A. D. Chernin and I. Rogachevskii, N. Kleeorin, A. D. Chernin and E. LivertsE. Liverts, Astron. Nachr. , Astron. Nachr. 327, 327, 591-594 (2006).591-594 (2006).

I. RogachevskiiI. Rogachevskii, , N. Kleeorin and E. Liverts,N. Kleeorin and E. Liverts, to be submitted to to be submitted to GAFDGAFD (2006). (2006).

ConclusionsConclusions

Generation of large-scale magnetic fieldGeneration of large-scale magnetic field is caused is caused by a by a new ''shear-current" effectnew ''shear-current" effect which acts even in which acts even in a nonrotating and nonhelical homogeneous a nonrotating and nonhelical homogeneous turbulence. turbulence.

During the growth of the mean magnetic field, During the growth of the mean magnetic field, the the nonlinear nonlinear ''shear-current" effect''shear-current" effect is not quenched is not quenched and it only and it only changes its signchanges its sign at some value of the at some value of the mean magnetic field which can determine the mean magnetic field which can determine the level level of the saturated mean magnetic field.of the saturated mean magnetic field.

ConclusionsConclusions

We have taken into account the We have taken into account the transport of transport of magnetic helicitymagnetic helicity as dynamical nonlinearity. The as dynamical nonlinearity. The magnetic helicity fluxmagnetic helicity flux strongly affects the magnetic strongly affects the magnetic field dynamics during the field dynamics during the nonlinear shear-currentnonlinear shear-current dynamo. The dynamo. The level of the saturated mean level of the saturated mean magnetic fieldmagnetic field is of the order of the is of the order of the equipartition equipartition fieldfield..

The estimated saturated large-scale magnetic field for The estimated saturated large-scale magnetic field for merging protogalactic cloudsmerging protogalactic clouds and and colliding giant galaxy colliding giant galaxy clustersclusters is about is about several microgaussseveral microgauss, and for , and for merging merging protostellar cloudsprotostellar clouds is of the order of is of the order of several tenth of several tenth of microgaussmicrogauss..

THE ENDTHE END