Collisionless phenomena in space plasma physicsamrel.obspm.fr/~ciardi/xla/abstracts/belmont.pdf · XLA_23_09_2008 4/51 Intro_2: "collision" Plasmas = long range EM interactions Î

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Gérard BELMONTCETP, Vélizy

Collisionless phenomena in space plasma physics

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Outline

• Intro:Collision, collisionless, limits of MHD

• MagnetospheresDescription static/ dynamicRole of reconnection

• Collisionless shocks (few words)

• Solar Wind expansion (few words)

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Intro_1: "collisionless"

In most space plasmas, density small enough collisionless or weakly collisional for all phenomena, whatever their scale L

mfp ληλν diρideρe

L

ideal(collisionless)

non idealcollisionless

non idealcollisional

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Intro_2: "collision"

Plasmas = long range EM interactions Each particle always feels all the others, but mainly via their collective EM field = independent of the individual positions

Collisionless only the collective field sufficient (average)Collisions small fluctuations around average to be taken into accountDiscrete particles at the origin of the field correlations (binary) in the individual positions

small scattering of the individual trajectories with respect to the collisionless ones

mean free path strong deviation (id) not due to the collision with a single particlebut result of numerous small deviations

Notion of collision far from the image of "hard sphere" collisions,which comes from the physics of neutral media (Boltzmann)

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Consequences for description and modeling

Strongly collisional media Fluid theories- description by fluid variables: n, v, p- evolution obeying fluid equations: conservation of mass, momentum, energy (with a closure -state- equation, which can be justified)

Mildly collisional Full N-body problem (still out of reach, worst case)- description by all particles r and v- evolution of each particle under N interactions

Collisionless Kinetic theory (Vlasov) a priori- description by f(v)- evolution by Vlasov equation

But Vlasov = still too heavy handling (for general complex 3-D geometries)Frequent use, even in collisionless plasmas, of fluid theory (MHD) for large scales:

- Often correct because all fluid equations (except closure) are exact conservation laws (and closure not too sensitive to microphysics at large scales)- But many exceptions, mainly when large scales are not independent of the small ones

~ all the examples of this talk

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Limits of MHD

1. Closure equation. Common to all fluid theoriesEmpirical laws, as p = nγ , often sufficient at large scale. But no exact solution in general for collisionless plasmas. Must go back to Vlasovwhenever it leads to unsatisfactory results (heavy)

2. Reduction to a mono-fluid theory ( simple Ohm's law, quasi-neutrality, ...). Valid at low frequency. Easy to correct otherwise: go to bi-fluid theory (e + i). Tractable.

Two very different kinds of limits:

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Are space plasmas "extreme"? A priori, no- No relativistic energies- No quantum effects

Nevertheless,Physics quite similar with "extreme" astrophysical objects for all phenomena where these effects are not of major importance (be careful to collisionality however)

When is the physics similar? Absolute values not relevant: dimensionless parameters necessary (scalings)

An example: Is Magnetosheath physics similar to ITER physics?Terrestrial Magnetosheath: p = nT = 50 106 m-3*106 K

ITER: p = nT = 1020 m-3*108 KBut B also much stronger in ITER (5 T vs 20 10-9 T) βMsth = 4 and βIter = 0.015

ITER is a "colder" plasma ! (with respect to beta)

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Planetary magnetospheres

Earth

Jupiter Saturne

Uranus

Neptune

Mercury

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Out of solar systemPulsar, black holes, ... Models but no direct observations...

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Plasma physics in the terrestrial magnetosphere

Unique in-situmeasurements

spacecraft idealprobes for fields and

particles

(negligible size)

CLUSTER (2000): 4 identical spacecraft with differentseparations (100 to 20 000 km)

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Existence of magnetospheres: why ?Because of the freezing-in property coming from the "ideal Ohm's law" E = -vxB andalways valid at large scales Magnetic field lines move without breaking or reconnecting

boundary

When two magnetized plasma are flowing against each other, they naturally form a tightboundary between them, without any inter-penetration across it (at first approximation), eachplasma remaining confined on its sidePartial breaking of confinement if small scales breaks the freezing-in (reconnection)(the result does depend on the nature of the non ideal effects, collisions or others)

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General morphology of a magnetosphere(static view)

Classical large-scale and laminar image of the SW/ magnetosheath/ magnetosphere system

Solar windB + Plasma

MagnetosphereB + Plasma

magnetopause

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A few orders of magnitude

Density (cm-3) 5

0.0110

1031

1

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Temperature (eV) 1.5

30010

0.1 3000100

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Magnetic field (nT) 5 50

30

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Dynamics of the magnetosphere

Averaged magnetosphere -static and large scale- well-known for long. Can be well interpreted in the MHD frame

Quite different (and more interesting) is the magnetosphere dynamics:- penetration of solar wind,- magnetic storms and substorms,- particle accelerations,- auroras, ...

Subjects of active research and evidence problems of fine cross-scale coupling, probably ~ universal:the small scale side of the phenomena are out of MHD range and depends strongly on the collisionless nature of the medium large scale consequences

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A magnetosphere is not static

auroral zones

Slow penetration of SW flux inside the magnetosphere at MP (reconnection) magnetic compression/ thinning/ elongation of the plasma sheet• "Breaking" internal reconfiguration ("substorms"), associated with

- Acceleration of particles- Precipitation in auroral zones- Auroras, EM radiations

• Go to the initial (more dipolar) configuration

FAR TAIL RECONNECTION

- Storms: due to non stationarities in SW (CMEs)- Substorms = cyclic "spasms" of the magnetospheric tail:

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Penetration of SW via reconnection

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Scales at Magnetopause

Reconnection very likely to exist at MPTheory Small scales needed. Which ones ?Magnetopause thickness, turbulence... ?

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Scales at Magnetopause

thickness:Msth ~10000kmMpse ~600 km

ULF fluctuationsmax energy at λ ~ 2000 kmbut turbulence spectrum ?

Reconnection:Resistive scale = 0 (no collisions)electron scales ~ 5 km (necessary)ion scales ~ 200 km (determining)

Big scale range!

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k-spectra (integrated over ωsc)n

v

B

B direction n direction v direction

Power law ~ k -8/3

(inertial zone ?)

Energy injection at λ ≈ 2000kmLinear Mirror instability(non MHD)

Very strong anisotropy

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Why electron scales are necessary for rconnectionTheory of reconnection has been much improved in last years, motivated by observations in space plasmas and in magnetic fusion plasmas

Basics (reminder)Reconnection is forbidden as long as the EM velocity vEM=ExB/B2 defines the same motion of a field line whatever the point where it is applied

No reconnection whenever E// = 0 everywhere

Ohm's law E//=0 always valid at large scales;but invalid at strong gradients with respect to- the electron scales de and ρe (since collisionless)- the resistive scale λη (when collisions)

reconnection demands E//, which demands such scales (cf. X points)(but stationary reconnection rate mainly fixed by ion scales, cf. GEM* challenge)*Geospace Environment Modelling

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Do the field lines break?

What happens when reconnection occurs?Is there a place where the field lines cannot be defined?

No (in general)It is just their global motion which cannot be defined

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Zoom on the electron diffusion region

E//≠0

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E//≠0

vem

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E//≠0

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E//≠0

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E//≠0

vem

v>>vem + 3d dimension

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E//≠0

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E//≠0

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E//≠0

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E//≠0

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E//≠0

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Laboratory experiments for magnetosphere

A few ones, most recent with fairly good scalings for all MHD parameters

But probably not for the collisional scales (always much too large in laboratory)

well reproduces the general shape at large scale, but no realistic modeling of all dynamic phenomena (reconnection, particle acceleration, substorms, auroras,...), which imply small scales

Rana et al, 2004

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Laboratory experiments for magnetosphere (2)To be mentioned:Terrella: Birkeland (1899)Planeterrella: Lilensten (2006)

Historically important and beautiful pedagogical tool (but no new physics to investigate):

Demonstration of pseudo -auroras in a low pressure tank:One conducting sphere including a magnetic dipole (= Planet)+ one negative electrode outside (= cause of auroral acceleration)

Electrons precipitated toward the sphereCollisions with the gas around the poles

(≈ auroras)

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A few words about shocksShock = another great example of cross-scale plasma phenomenon

•Large scales (existence, localization, jumps) fixed by remote boundary conditions and ~ ideal propagation• Small scales (thickness, internal structure, non stationarity) fixed by local microphysics acceleration and reflection of individual particles, EM radiation, …

• Space data Shocks do exist in collisionless media, i.e.without collisionaldissipation (resistivity/ viscosity): microphysics related to ion and electron dynamics

Terrestrial bow shock = prototype of collisionless shocks

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A few words about shocks

Q-perp

Solar wind Terre

Bo

0°

90°

45°

Q-//Electron foreshock

Ion foreshock

Curvature of the planetary "bow shock" all propagation angles / B

Foreshocks upstream: A proof of a kinetic behavior

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Dissipation without collisions

Ion phase space visualization of the "heating":Broadening of f(v) (heating) due to complex trajectories(reflected and accelerated ions)

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Choc Q-∞MA~5,4

CLUSTER-2 [Horbury et al., 2001]

A few words about shocks

virtual spacecraft(CLUSTER-2)

2-D PIC Simulation

CLUSTER data and PIC simulation

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A few words about solar wind expansion

Solar wind expansion = still another good example of a problem which cannot be reduced to a fluid problemDiscovered at the very beginning of spatial era

Solar Wind due to degassing of the sun:

Parker, 1958Central body in vacuum:gravity is not able to confine a hot atmosphere(at least for isothermal expansion)

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Velocity at 1AU: cst in the fast SW (B radial) ≈ 750 km/s

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Collisions:an intermediate situation- few collisions- but not collisionless

Fluid models (Parker) existence of a transonic solution,which seems to explain the solar wind

But unfortunately, we have observations. There are a few contradictions, especially:final velocity (≈ 1 AU) about twice too small

Discrepancy is robust: not easily solvable by changing a few parameters in the model• Dissipation of solar turbulence may play a role• But the intrinsic limits of fluid models are likely to be the major reason

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"Correct" kinetic models have been performed only many years later

They mainly show that:

- Results don't differ much from Parker's when a Maxwellian distribution is assumed asun

- But the result is quite sensitive to suprathermal electrons, which should explain most of the discrepancy fluid models obviously insufficient

- Some role of collisions fully collisionless models are probably not either fully adequate

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Conclusions

• Space plasmas are most often collisionless or weakly collisional at the scales of the relevant phenomena

• Kinetic effects always of major importance for small scales

•Large scales are well determined by MHD only when independent ofthe small ones MHD insufficient, even at large scale, for all cross-scale phenomena (reconnection, turbulence, ...)

• For Solar Wind, the evolution is at scale ~ mean free path, which is the most tricky situation

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Thanks

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Substorms = "catastrophic events"

Leaky f

Drop

aucet

Large scale slow evolution (± ideal MHD) up to the "breaking point" when a different physics occurs on a short time.After the breaking (reconnection?), slow large scale evolution again from the new initial state

image

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Adimensional parameters

The orders of magnitude in magnetospheres may seem exotic for an astrophysicist (is it vacuum ??)Question: is there something universal in the physics involved ?

As (should be) well known, the physics is the same as soon as theadimensional parameters (β, ωpe/ ωce, ...) are similar, even if the absoluteorders of magnitude are completely differentAnswer: the different plasmas of universe and even of laboratoryplasmas are quite comparable, most often, with the magnetospheric ones

Example: Comparison with ITER (fusion by magnetic confinment)Can one claim (as heared sometimes) that"ITER plasma is much too dense and much too hot to be comparedwith magnetospheric plasmas" ?...

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Comparison ITER/ MagnetosheathParametersMagnetosheath : n = 50 106 m-3 T = 106 K B = 20 10-9 TITER : n = 1020 m-3 T = 108 K B = 5 T

Conclusion:Magnetosheath = "hot plasma" (p dminant)ITER = "cold plasma" (B2 dominant)!

Mistrust too hasty conclusions about orders of magnitude…

In interstellar medium : β ~ 1 (equipartition) ~ magnetosheath

β = 4 in magnetosheathβ = 1.5 10-2 in ITER

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Reconnection: problematic

Theory:The plasma controls reconnection via Ohm’s law (electron dynamics)(cancels E// at large scale)

• Electron scales necessary for reconnection(But they don't necessarily determine the reconnection rate !)

• Resistive term most often negligible, even in collisional media

22edk 22

ek ρ

( )jpjvBjBvE η+∇−−+×+×−= ).(1)()( 2 ett nednemde

mne

0 0 ( )ηλkekdμE//

pee

cdω

=ce

thee

Vω

ρ =i

e

Mm

=μ

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Reconnection models

Sweet Parkercurrent sheet, resistive MHD

one single small scale in the geometryWidth d of the layer:

small to get E// : d= εDlarge to evacuate plasma : v = εVA

contradiction reconnection rate almost zero

dD

one single small scale in the physicsResistive scale: λη = η /μoVA

one small parameter :ε = (λη /D)1/2

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Reconnection models

ddc

D Petschek2 current sheets (shocks):

thickness dc, with separation d,resistive MHD

two small scales in the geometry:E// created by the smallest (dc)

plasma evacuated by the larger (d)no more contradiction possibility of a fast reconnection rate

But :still one single small scale in the physics (λη)

the initial geometry cannot be keptonly transient reconnection

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Reconnection models

"Collisionless models"( simple X point geometry

~ Petschek)

Two nested small scales in the geometry,corresponding to the two natural scales in the physics : ions and electrons

possibility of fast and permanent reconnectionAll models except resistive MHD (Hall-MHD, two-fluid, hybrid, kinetic...)

Conclusion (GEM) : electron scales necessary, but not limitative:reconnection rate fixed by ion scales (cf. Cluster)

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THE END

Documents

Collisionless phenomena in space plasma physicsamrel.obspm.fr/~ciardi/xla/abstracts/belmont.pdf · XLA_23_09_2008 4/51 Intro_2: "collision" Plasmas = long range EM interactions Î