The Interplanetary Medium and The Solar Wind

The Interplanetary Medium and

The Solar Wind

Giuseppe Consolini

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INAF-Institute for Space Astrophysics and Planetology Email: [email protected]

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The eruption of a looped solar filament that is rooted in a magnetically-active region near the apparent edge, or limb, of the Sun. The image, from the TRACE spacecraft, was made in the light of the (invisible) extreme ultraviolet spectrum, emitted from regions of the solar atmosphere where temperatures exceed more than two million degrees Fahrenheit.

Coronal Mass Ejections

If sunspot magnetic fields are the gunpowder, flares the muskets and prominences the horse-drawn cannons in the venerable solar armory, coronal mass ejections or CMEs—which came to be recognized but thirty years ago— are truly the heavy artillery. Indeed, interplanetary CMEs are the primary

Introduction and some historical hints

• The first indirect evidence of solar wind dates back to about a hundred years

ago, when it was observed that a perturbation of the Earth’s magnetic field often follows the occurrence of large solar flares.

• The time delay between the occurrence of a solar flare and a jiggling of the

Earth’s magnetic field suggested that typical Sun-Earth transit time of solar wind should be of the order of 103 _km/s.

• However, we have to wait until the early 40s to see the beginning of the physics of solar wind (Gotrian, 1939; Lyot, 1939; Edlen, 1942; Chapman, 1954).

• One of the first evidences of solar wind, i.e. of a corpuscular outcome radially

Introduction and some historical hints

• The Solar Wind is a flow of a tenuous ionized solar plasma and a remnant of the solar magnetic field, pervading the interplanetary space.

• The origin of solar wind is due to the huge difference in gas pressure between the solar corona and interstellar space.

• The importance of studying solar wind stands in two major points

• the role that solar wind plays in the field known an solar-terrestrial relations, i.e. the impact that it has on magnetospheric environments;

• the basic physical processes concerning its formation, expansion and complex nature (turbulent features).

A survey of solar wind properties

• Our knowledge of the solar wind properties is based on in-situ spacecraft

observations covering a wide range of distances (from 0.3 AU on) and a wide interval of heliospheric latitude range.

• It consists largely of protons and electrons in nearly equal numbers (approx. 95%) and quasi-thermal equilibrium (?) with a small amount (5%) of alpha particles and other heavier ions.

Proton density 6.6 cm Electron density 7.1 cm

He 0.25 cm

Mean flow speed 450 km/s Proton kinetic temperature 1.2 x 10 Electron kinetic temperature 1.4 x 10 Magnetic field 7 x 10

Solar Wind features at 1AU

• Embedded in the SW plasma there is a

weak magnetic field that a 1AU is oriented in a direction parallel to the ecliptic plane with a 45° angle in respect to the Sun radial direction.

Introduction and some historical hints

In the 50s Ludwig Biermann studying the phenomenon of the anti-solar acceleration of comet tails noticed that the standard explanation for the anti-solar orientation of comet tails (based on light radiation pressure) is inadequate to explain the observed outward acceleration of small inhomogeneities in comet tails. !

This provided the evidence that solar wind is made of a corpuscular radiation

Comet Hale-Bopp. Credit: Dimai & Ghirardo - Col. Druscie Obs., AAC

Type I: gases origin affected by solar wind

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A survey of solar wind properties

from Bame et al., Phys. Rev. Lett., 1968

• Apart from the principal ion species, it is possible to find several other secondary elements in the SW:

A survey of solar wind properties

from Huba., NRL Plasma Formulary, 2007

• SW plasma in comparison with other typical astrophysical and laboratory plasmas

A survey of solar wind properties

from Asbridge et al., Solar Phys., 1974

Unnormalized energy per charge spectrum

• P1 and P2 = proton beams • 1 and 2 = alpha beams

• Bulk velocity >> thermal velocity (peak width)

cs = ⇢ p ⇤ 1 2 = ⇢ ⇥B mp + me (Tp + Te) 1 2 c_{s ⇠} 60km/s

A survey of solar wind properties

• Another feature of SW at 1AU is the super-Alfvénic nature of proton flow,

cA =

s

B2

4 ⇥ [CGS] cA ⇠ 30km/s ⌧ vbulk ⇠ 450km/s

1AU

They moves also faster than the fast magnetosonic wave velocity

c_{f ast ⇠} c_s + c_A

• Proton/ions distribution functions shows also a very complex angular velocity

distribution with different shapes parallel and perpendicular to the magnetic field.

A survey of solar wind properties

2D velocity distribution by Helios spacecraft

from Marsch et al., J. Geophys. Res., 1982 IM F

T_|| > T T > T_||

Temperature anisotropy can take both situations

A survey of solar wind properties

• Assuming that solar wind ions expands as an adiabatic gas, then we expect that pressure and density are related by a polytropic law,

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where _γ > 1. Consequently, T and n behaves in the same way, i.e. are decreasing function with the distance.

p = n _BT

p = const _n(1 )_{T = const}

from Belcher et al., 1993

n _⇠ R 2

A survey of solar wind properties

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However, radial profile of solar wind temperature does not evolve adiabatically.

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A large discrepancy is observed.

from Richardson et al., GRL, 1995

T _⇠ R 1/2

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The observed discrepancy suggests that to some extent a certain

amount of heating occurs during the solar wind radial evolution.

•

A plausible candidate for this

heating process is the turbulence cascade mechanism (see e.g.

A survey of solar wind properties

• The other main constituent of solar wind are the electrons.

• Differently from ions, a treatment of solar wind electrons as a single fluid is not possible. Indeed, electron distributions show two different main components:

• a core, associated with a cold and dense population • a halo, representing a hot and sparse population

from Feldman et al., J. Geophys. Res., 1975

•

Both the two populations show a

thermal velocity higher than bulk speed.

A survey of solar wind properties

from Pilipp et al., J. Geophys. Res., 1987

A survey of solar wind properties

• Apart from the core and halo populations, sometime a third component is present: a narrow field-aligned high energy beam, called strahl.

• High energy strahls can propagate very far in the eliosphere without scattering, providing information on the deepest part of solar corona.

• The farthest propagation of strahl can be understood in terms of a very low collision frequency. ei = 8⇥ e4 2p2me Zne Te3/2 ln _⇠ T_e 3/2 = D b_o

A survey of solar wind properties

• One of the general features of both proton and electron distribution functions is its non-Maxwellian character.

• This point suggests that many features of the SW have to be discussed assuming it to be a nonthermal plasma, i.e. in a nonequilibrium state.

• In 1992 A. Scudder suggested that a better distribution function for solar wind kinetic model is a truncated Lorentzian (Kappa) distribution

f = n ⇥3/2 3/2_v3 th ( + 1) ( 1/2)  1 + v 2 v_th2 + v_th2 = ✓ 2 3 ◆ BT m

A survey of solar wind properties

• Solar wind and interplanetary medium is permeated by magnetic field which can lead to hydromagnetic effects.

• Given a magnetic field this can exert a pressure

!

that has to be compared with the gas (kinetic) pressure

!

•

At 1 AU we get pmag = B2 4 pgas = n B(Tp + Te) pmag = 19 pP a pgas = 30 pP a

A survey of solar wind properties

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In spite of the average features described, the solar wind shows a very high variability in its features both in time and in space.

A survey of solar wind properties

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In spite of the average features described, the solar wind shows a very high variability in its features both in time and in space.

A survey of solar wind properties

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Between the various features of this high variability it is important to stress that one of the main properties of the solar wind is the presence of two different types of

SW characterized by different speeds and physical properties.

from Bruno and Carbone, 2005

Fast solar wind

A survey of solar wind properties

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Fast and slow solar wind are characterized by very different physical properties of the constituting plasmas

2.0x105 1.5 1.0 0.5 0.0 T [K] 900 800 700 600 500 400 300 u [km/s] Period # 1 Period # 2 2.0x105 1.5 1.0 0.5 0.0 T [K] 2 3 4 5 6 0.1 2 3 4 5 6 1 2 3 4 5 n [cm-3] Period #1 Period #2

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Fast wind: less dense and hotter

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Slow wind: more dense and colder

from Consolini, 2012 to be submitted

A survey of solar wind properties

A survey of solar wind properties

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This very high variability is due to the inherent magnetic field

dynamics and structures.

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Furthermore the origin of fast and slow solar wind streams have to be connected with the different magnetic structures at the sun (open and closed field lines), as well as with the latitudinal

magnetic field structure

Polar solar wind --> Fast

Equatorial solar wind --> Slow

The interplanetary magnetic field

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The classic description of the interplanetary magnetic field in the outwardly moving solar wind is based on the concept of a frozen-on magnetic field.

from Hundhausen, 1995 B(r) = B₀ ✓ B r ◆2

•

This simple concept however have to be combined with the solar

rotation, which implies that the structure of the interplanetary magnetic field (IMF) is more

complex than that of purely radial magnetic field.

The interplanetary magnetic field

Br(r) = B0 ✓ B r ◆2 B_'(r) = B₀ R u R r

The IMF structure is then that of a Archimedean spiral.

At 1 AU we have

r _⇠ 400km/s

'1AU ⇠ 45

u_{SW ⇠} 400km/s

The interplanetary magnetic field

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The interaction between the solar magnetic field and the solar wind is described by the magnetic force j x B.

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Thus a more realistic model of the IMF and solar wind structure will require the finding of a magnetohydrodynamic system of equations.

u _{· ⇤}u = _⇤p + j _⇥ B + Fg

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The presence of the magnetic field, indeed, affects the spherical symmetry of the solar wind expansion.

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The solution in the case of a isothermal corona in the case of a pure dipolar filed shows the formation of a current sheet and closed field lines overlying the dipole

equator (Pneumann and Kopp, 1971).

The interplanetary magnetic field

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In contrast with its simplicity, the Pneumann and Kopp solution shows many characteristic ingredients of the real coronal magnetic field, which has clearly a more complex structure.

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Indeed a realistic description of the coronal magnetic field will require to include the complex magnetic structures emerging from the sun, so that a simple dipole model is only a very

crude approximation.

The interplanetary magnetic field

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Because the magnetic pattern is neither symmetric about the rotational axis, nor purely dipolar, the extension of this magnetic structure to the interplanetary

medium produces a very complex structure of the IMF

from Hundausen, 1977

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The rotation of the Sun implies that the magnetic pattern sweeps over the Earth, appearing in the so-called magnetic

sectors, observed in the interplanetary

space

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Furthermore, there is a nonzero angle

between the Earth’s orbit and the rotational equator of the Sun, so that the Earth

experiences a predominantly outward/ inward magnetic field every 6 months

The interplanetary magnetic field

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The presence of fast and slow solar wind streams, as well as of very fast solar ejecta (as CME) modify the

pattern of the IMF generating regions of compression/rarefaction.

Solar Wind Interaction with Planetary

Magnetospheres

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Solar wind flowing into the heliosphere interacts with the planetary magnetic

fields, which behaves as obstacles to the plasma flows, generating the planetary magnetospheres.

adapted from De Michelis et al., 1999

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The Earth’s Ring Current

Solar Wind Interaction with Planetary

Magnetospheres

32.5 32.0 31.5 31.0 x10 3 0:00 15-07-2000 12:00 0:00 16-07-2000 12:00 0:00 17-07-2000 Time [UT] BNG (Lat: 4.43°; Long: 18.57°) 1.75 1.70 1.65 1.60 x10 4

BFE (Lat: 55.62°; Long: 11.67°) 1.95 1.90 1.85 1.80 x10 4 NGK (Lat: 52.07°; Long: 12.68°) X [ nT] 2.15 2.10 2.05 2.00 x10 4

FUR (Lat: 48.17°; Long: 11.28°) 15.5

15.0 14.5

x10

3

LOV (Lat: 59.35°; Long: 17.83°)

Solar Wind Interaction with Planetary

Magnetospheres

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The ground-based effects of the solar wind-magnetosphere interaction are the geomagnetic storms and substorms

http://www.oa-roma.inaf.it/cvs/tempeste.html

Solar Wind Interaction with Planetary

Magnetospheres

-20 0 20 By [nT ] 0:00 6-04-2000 7-04-20000:00 8-04-20000:00 9-04-20000:00 Time [UT] -20 0 20 Bz [nT ] -20 0 20 Bx [nT ] 40 30 20 10 0 B [nT ] 600 500 400 300 v[ km /s ] 0:00 6-04-2000 7-04-20000:00 8-04-20000:00 9-04-20000:00 Time [UT] 60 40 20 0 N[ cm -3 ] 600 500 400 300 v[ km /s ] 0:00 6-04-2000 7-04-20000:00 8-04-20000:00 9-04-20000:00 Time [UT] 60 40 20 0 N[ cm -3 ] -300 -200 -100 0 Dst [ nT] 0:00 6-04-2000 0:00 7-04-2000 0:00 8-04-2000 0:00 9-04-2000 Time [UT] 12 0 2 4 6 8 10 14 16 18 20 22 3000 2500 2000 1500 1000 500 0 A E (t ) 10 8 6 4 2 0 t [day]

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Geomagnetic storms and substorms are the

consequences of the solar wind plasma entry into the magnetosphere region,

which activates a complex system of ionospheric

Solar Wind Interaction with Planetary

Magnetospheres

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The main physical mechanism responsible for the energy, momentum and mass transfer from solar wind to magnetosphere is the magnetic reconnection

from INGV site: http://roma2.rm.ingv.it

adapted from MMS-SMART Web site

@

@tB~ = r ⇥ (~u ⇥ B~) + ⌘r 2_B~

M_i = _p 1 Rmi

• In the Sweet-Parker model the reconnection rate (i.e. the velocity of magnetic field energy conversion) is Rmi = Lc_A ⌘ Diffusion Region 2L 2l

Solar Energetic Particles (SEP)

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The solar plasma eruptions (flares) can accelerate plasma to very high speed generating the solar cosmic rays, named SEP.

10-5 10-4 10-3 10-2 10-1 100 101 102 103 104

Average Proton Flux [#/cm

2 s sr MeV]

0.1 1 10 100 Energy E [MeV]

Global Fit

Solar Wind Turbulence: Introduction

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As already said in the previous Lecture, one of the most peculiar features of the solar wind magnetic field and plasma parameters is its very high temporal and spatial variability.

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This variability manifests in fluctuations whose order of magnitude is the same of the average quantities.

!

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This notable fact suggests that a relevant information about the solar wind physics is contained in the fluctuating field.

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Since the early observations of Mariner 2 (Coleman, 1968) it was noted that turbulence might plays a fundamental role in the generation of the observed fluctuation field

x

Solar Wind Turbulence: Introduction

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The first evidence of turbulence in the solar wind was provided by Coleman (1968), which analyzing the spectral densities of solar wind related quantities evidenced how the energy is distributed over an extremely wide range of

frequencies from Russell, 1972 P SD P (f) _⇠ f ↵ Range I : _⇠ 1 _$ f < 10 4Hz Range II : 3 2 < < 5 3 , 10 4  f _ 10 1Hz Range III : _⇠ 2 _, f > 10 1Hz up to 1Hz

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The intermediate range of scales whose typical scaling index is about 1.6

(Bavassano et al., 1982; Tu and Marsch, 1995) is very well in agreement with the typical spectral index predicted by Kolmogorov K41 theory of turbulence and/or by Kraichnan theory of Alfvénic MHD-turbulence.

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Another relevant feature of such a

scale-invariant PSD stands in its evolution with the radial distance (Bavassano et al., 1982;

Denskat and Neubauer, 1983).

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PSD break moves to lower frequencies as the solar wind expands.

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This behavior provides the evidence for the presence of nonlinear interaction

mechanisms

from Bruno and Carbone, 2005

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Another relevant property of the solar wind magnetic and plasma parameter fluctuations is the Alfvénic character of uncompressive fluctuations.

v _±⇥ B 4⇡⇢

from Bavassano et al., 2000

from Bavassano et al., 1998 c = v _· b_⇥ v_⇥2 + b_⇥2 R = h v_i2 _hb_i2 hv_i2 + _hb_i2 Normalized cross-helicity Normalized residual-energy

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Anyway the solar wind fluctuation field is more complex, showing not only

Alfvénic fluctuation but also magnetic structures and compressive fluctuations

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Another characteristic of the solar wind turbulent fluctuations is the occurrence of

intermittency.

from Bruno and Carbone, 2005

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Intermittency manifest in several different quantities: anomalous scaling of structure functions (departure from self-similarity), non-Gaussian and scale-dependent probability distribution functions of observable increments.

from Bruno and Carbone, 2005

S_q( x) = _h(Y (x + x) Y (x))q_{i ⇠} x (q) S_q( x) _' S_p( x)pq S_q( x) Sp( x) p q ⇠ xµ(q,p)

Anomalous scaling of structure functions

Turbulence: general concepts

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The word “turbulence” derives from Latin

word turba, initially used as a synonymous of disordered movements.

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In XX century, the notion was generalized to embrace far-from-equilibrium states in fluids and plasmas.

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Turbulence defines a state of a physical

system with many interacting degree of freedom deviated far-from-equilibrium, showing spatial and temporal irregular

features and accompained by dissipation (adapted from Falkovich, 2008)

Study by Leonardo da Vinci (1452-1519) related to the problem of reducing the rapids in the river

Arno in Florence

“Turbulence still remains the last major unsolved problem in classical physics” Feynman et al. (1977)

Turbulence: general concepts

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The key element of fluid turbulence is the idea of the Richardson cascade (inertial

cascade), according which a perturbation at large scale propagates down to

smaller scales via a cascading mechanism in which the energy, injected by the large scale perturbation, is distributed homogeneously to the smaller scale,

where viscosity dissipates it (microscopic scales).

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Turbulence (fully developed turbulence) is observed when a large scale separation between injection scale and dissipation scales.

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This separation of scales is quantified by the well-known Reynolds number

Turbulence: general concepts

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It is possible to grasp the main features of a turbulent flow by analyzing the Navier-Stokes equation (Landau & Lifshitz, 1959).

⇤u

⇤t + (u · ⇥)u =

1

⇥⇥p + ⇥

2_u

nonlinear term: coupling of scales viscosity term: dissipation

r2u _⇠ u L2 (u _{· ⇥})u u 2 L Re = nonlinear term viscosity term = u2/L u/L = uL

Turbulence: general concepts

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When R >> 1 we assist to a separation of scales, i.e. injection scale L >>

dissipation scale λ (below this scale R < 1).

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This intermediated range of scales is named inertial range and is the range of scale in which the cascade works.

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The first quantitative description of the energy cascade is due to Kolmogorov (1941) via dimensional analysis.

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Let us assume stationarity, homogeneity, isotropy and the conservation of the energy flow in the inertial range along the spectrum,

l ' u2_l ⇤_l = ⇥ ⇥l ' l u_l ⇧l ' u3_l l ' ⇥ ul ' ⇥ 1/3_l1/3

Turbulence: general concepts

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Let us now consider the spectral density at k ∼ 1/l !

from here assuming dk ∼ k ∼1/l, we get for the spectral density, !

That is the very well-known 5/3 Kolmogorov spectrum (K41 theory).

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Along with the previous results, there exists an exact relationship directly

derivable from the Navier-Stokes equation for the 3rd order-parallel structure function valid in the inertial range for fully developed turbulence: the Yaglom law

E(k)dk _⇠ 1 2 u 2 l E(k) _⇠ 2/3l5/3 _/ k 5/3 h⇥v_||(r + l) v_||(r)⇤3_i = 4 5 l

Turbulence: general concepts

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Let us now move to the case of turbulence in a magnetized plasma, which present some differences in respect to the fluid case (see Zimbardo, 2001).

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In this case the starting equations are the momentum equation and the induction equation,

! !

where ν is the viscosity and η is the plasma resistivity, moreover

!

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The two equation display many similarities: are nonlinear, contain a dissipation term acting at smallest spatial scales

r · B = 0 _{r ·} u = 0 @u @t + (u · r)u = 1 ⇢r ✓ p + B 2 8⇡ ◆ + 1 4⇡⇢(B · r)B + ⌫r 2_v @B @t = r ⇥ (u ⇥ B) + c2⌘ 4⇡ r 2_B r2u

Turbulence: general concepts

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These similarities can be better appreciated by introducing the Elsasser variables,

!

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By means of such a variables the previous equations can be written in a compact form:

! ! !

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In the following for brevity we will assume

z = u + pB 4⇡⇢, = ±1 @z @t + (z · r)z = 1 ⇢rP + ⌫ + µ 2 r 2_z+ ₊ ⌫ µ 2 r 2_z r · z = 0 µ = c 2_⌘ 4⇡

µ

=

⌫

Turbulence: general concepts

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The symmetric form of MHD equations written using the Elsasser variables

shows the equal importance of the velocity and magnetic fields in describing the evolution of the magnetofluid. In this framework the energy per unit mass is,

!

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Let us now compare the nonlinear term and the dissipative term

! ! !

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In space plasmas (collisionless and not resistive) so that nonlinear term is very important allowing a very extensive range for turbulence

E = u 2 2 + B2 8⇡⇢ = z+2 + z 2 4 (z _{· r})z _⇠ z 2 L ⌫ + µ 2 r 2_z ⇠ µz L2 Rm = r 4⇡ ⇢ BL c2_⌘ Rm 1

Turbulence: general concepts

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To close consider the effects of nonlinear terms, let us assume a statistically homogeneous system and write:

!

where . Then

!

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Substituting and neglecting dissipative term (R, Rm>>1) get

B = _hB_i + b u = v hu_i = 0 hz _i = phBi 4⇡⇢ = VA z = v + b p 4⇡⇢ ✓ @ @t VA · r ◆ z + ( z _{· r}) z = 1 ⇢rP r · z = 0

Turbulence: general concepts

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Moving to the Fourier space (dropping the δ), equation reduces to

!

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Let us now move to evaluate the spectrum using the same heuristic approach of the fluid case. We start by evaluating the energy flow per mass unit, assuming only local interactions in the Fourier space

!

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Thus,

!

where Tkσ is the energy effective transfer time (analogous to the eddy turnover time in fluid turbulence).

✓ @ @t k · VA ◆ z (k, t) + X p X q [z (q, t) _· ip] z (p, t) k,p+q = ik ⇢ P(k, t) k _⇠ p _⇠ q ⇧_{k '} E (k) T_k

Turbulence: general concepts

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In contrast to fluid turbulence the nonlinear term represents the interaction

among counter-propagating modes, so that this interaction is expected to last a finite time

!

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The mode amplitude change for a single interaction is,

!

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Requiring a significant transfer of energy, i.e. , we obtain for N

⌧_kA _⇠ 1 kV_A dz (k) _⇠ kz (k)z (k)⌧_kA af ter N interactions z (k) _⇠ pN dz (k) z (k) _⇠ z (k) N _⇠ ⇥kz (k)⌧_kA⇤ 2 TkA = N⌧kA ⇠ V_A k[z (k)]2 ⇧_{k ⇠} k[z (k)] 2_{[z (k)]}2 V_A ⌘ ✏

Turbulence: general concepts

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When the flux is constant, we get a stationary state in which

!

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Thus, from the previous equation we obtain

!

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From this result we cal evaluate the spectral energy density obtaining,

z (k) _⇠ z (k) _⇠ z(k) z±(k) _⇠ (V_A✏)1/4k 1/4 E(k)dk _⇠ [z ±_(k)]2 2 ⇠ (VA✏) 1/2_k 1/2 ! E(k) _/ k 3/2 “Kraichnan spectrum”

Turbulence: general concepts

“Evolution of Elsasser variable spectra with radial distance”

• A.J. Hundhausen, The solar wind, in Introduction to the Space Physics, Kivelson M. G. and Russell C.T. eds., Cambridge University Press 1995.

• E.N. Parker, Solar wind, in Handbook of the Solar-Terrestrial Environment, Kamide Y. and Chian A. Editors, Springer 2007.

• R. Bruno & V. Carbone, The Solar Wind as a Turbulence Laboratory, Living Rev. Solar Phys., 2, 2005

• G. Zimbardo, Solar wind magnetohydrodynamic turbulence, in “Sun-Earth connections and Space Weather”, M. Candidi et al. eds., SIF Conf. Proc. 75, 2001

• V. Carbone & A. Poquet, An introduction to fluid and MHD turbulence for astrophysical flows: theory, observational and numerical data, and modeling, Lect. Notes Phys., 778, 71, 2009 • C.T. Russell, Solar wind and interplanetary magnetic field: a tutorial, in Space Weather,

Geophys. Monogr. Ser., vol. 125, edited by P. Song, H. J. Singer, and G. L. Siscoe, pp. 73–89, AGU, Washington, D. C.,