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Temperature anisotropy in the solar wind

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Temperature anisotropy in the solar wind

Petr Hellinger

Institute of Atmospheric Physics & Astronomical Institute AS CR, Prague, Czech Republic

Kinetic Instabilities, Plasma Turbulence and Magnetic Reconnection, Vienna, February 17, 2009

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1 Introduction Solar wind Linear theory

2 Observations Protons Linear Theory Waves

Electrons

3 Simulations of proton fire hose instabilities 1-D hybrid simulations

Hybrid expanding box simulations

4 Summary

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Solar wind

Solar wind

weak collisions

temperature anisotropies Tk6= T

particle beams/drifting populations signatures of wave-particle interactions signatures of kinetic instabilities important wave activity/turbulence

(4)

Instabilities driven by T

ks

6= T

⊥s

Linear Vlasov-Maxwell system in the long-wavelength, low-frequency limit

Mirror instability with the threshold

s

βs

 Ts Tsk − 1



> 1 +



s

ρsTs Tsk

2

2 ∑

s ρs2 βsk

different from MHD-CGL prediction Fire hose instabilities with the threshold

βk− β> 2 as in MHD-CGL

(5)

Full linear Vlasov-Maxwell system

Tkp< T⊥p Proton cyclotron instability

LH circular polarization cyclotron resonance ℜω. ωcp

wavelengths∼ c/ωpp Mirror instability

linear polarization δ B· B06= 0 Landau resonance ℜω = 0

threshold for k→ 0

Tkp> T⊥p Parallel fire hose

RH circular polarization anomalous cyclotron resonance

ℜω∼ ωcp

wavelengths∼ c/ωpp

Oblique fire hose

linear polarization δ B⊥ B0

both cyclotron resonances ℜω = 0

wavelengths∼ c/ωpp

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WIND/SWE observations

Wind spacecraft, 1995–2001

two Faraday Cup instruments in the Solar Wind Experiment (Kasper et al., 2002; 2006)

+ Magnetic Field Experiment

non-linear least-squares fitting – assuming bi-Maxwellian (core) proton distribution function

proton density

proton temperatures Tkpand T⊥p parallel beta βkp

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Slow solar wind proton anisotropy at 1 AU

WIND/SWE data vsw< 600 km/s

0.01 0.10 1.00 10.00

0.1 1.0 10.0

101 102 103 104

β Tp/Tkp

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Slow solar wind vs linear theory I

Proton cyclotron instability(γmax≥ 10−3ωcp)

0.01 0.10 1.00 10.00

0.1 1.0 10.0

101 102 103 104

βkp Tp/Tkp

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Slow solar wind vs linear theory II

Mirror instability(γmax≥ 10−3ωcp)

0.01 0.10 1.00 10.00

0.1 1.0 10.0

101 102 103 104

β Tp/Tkp

(10)

Slow solar wind vs linear theory III

Parallel fire hose(γmax≥ 10−3ωcp)

0.01 0.10 1.00 10.00

0.1 1.0 10.0

101 102 103 104

βkp Tp/Tkp

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Slow solar wind vs linear theory IV

Oblique fire hose(γmax≥ 10−3ωcp)

0.01 0.10 1.00 10.00

0.1 1.0 10.0

101 102 103 104

β Tp/Tkp

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Comparison

Linear theory:

Dominant proton cyclotron instability for Tkp< T⊥p Dominant parallel fire hose for Tkp> T⊥p

WIND/SWE Observations – Slow solar wind:

Constrained by the mirror instability for Tkp< T⊥p? Constrained by the oblique fire hose for Tkp> T⊥p?

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Discussion

Limitations

Linear theory assumes bi-Maxwellian protons

homogeneous, stationary medium no waves

Observations:

often proton core/beam distributions alpha particles and other minor ions important turbulence/wave activity shell/quasilinear plateau distributions expanding solar wind

+ nonlinear effects?→ numerical simulations

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Alpha particles and cyclotron instabilities

Proton cyclotron instability(γmax≥ 10−3ωcp)

0.01 0.10 1.00 10.00

0.1 1.0 10.0

101 102 103 104

βkp Tp/Tkp

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Alpha particles and cyclotron instabilities

5 % of alpha particles(γmax≥ 10−3ωcp)

0.01 0.10 1.00 10.00

0.1 1.0 10.0

101 102 103 104

β Tp/Tkp

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Instability driven waves?

Magnetic field fluctuations, RMS over 3 s (Bale et al.)

enhancements in amplitude near the thresholds

compressible fluctuations near the mirror threshold – evidence of the mirror mode?

more collisional protons are more isotropic

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Full linear Vlasov-Maxwell system

Tke< T⊥e Whistler instability

RH circular polarization cyclotron resonance ℜω. ωce

wavelengths∼ c/ωpe Mirror instability

linear polarization δ B· B06= 0 Landau resonance ℜω = 0

threshold for k→ 0

Tke> T⊥e (Quasi-)parallel fire hose

LH circular polarization non-resonant

γ∼ ωcp

wavelengths∼ c/ωpe Oblique fire hose

linear polarization δ B⊥ B0

both cyclotron resonances ℜω = 0

wavelengths∼ c/ωpe

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Solar wind electrons I

Solar wind electrons:

bi-Maxwellian core bi-κ halo

strahl populations Wind/3DP observations (Bale et al.)

core more isotropic halo – constraints by whistler and oblique fire hose instabilities

(19)

Solar wind electrons II

Helios, Cluster & Ulysses ( ˇStver´ak et al., 2008)

Core electrons constrained by whistler and oblique fire hose instabilities Similarly for halo electrons

role strahl?

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Standard 1-D hybrid simulations

Hybrid simulation:

ions – kinetic treatment (particle-in-cell method) electrons – massless, charge-neutralizing fluid Nonlinear properties of the proton fire hose instabilities:

Parallel fire hose instability quasi-linear saturation

weak reduction of temperature anisotropy Oblique fire hose instability

self-destructive evolution

inverse cascade of Alfv´enic fluctuations strong reduction of temperature anisotropy

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1-D hybrid simulations, β

pk

= 2.8

Evolution of Ap= Tp/Tpkand δ B2

(22)

1-D hybrid simulations

Evolution of oblique fire hose

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Radial evolution in the solar wind

Expansion – fast solar wind (Matteini et al., 2007)

Tp/Tpkdecreases and βpkincreases with the distance

evolution is not CGL a signature of the cyclotron heating?

Coulomb collisions at larger distances controlled by fire hose instabilities

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Expanding box model

Schematic view – spatial vs temporal:

Spherical expansion Expanding box

R0 R1

t0 t1

(25)

Hybrid expanding box model

Solar wind expansion

assuming a constant solar wind velocity transverse scale expands linearly with time

hybrid approximation, kinetic ions & fluid electrons Slow expansion

CGL evolution when no wave activity is present low frequency waves follow WKB

natural generation of temperature anisotropy

self-consistent competition between the expansion and instabilities.

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2-D Hybrid Expanding Box Simulation I

Expansion vs the parallel fire hose (cf., Matteini et al., 2006)

0.01 0.10 1.00 10.00

0.1 1.0 10.0

101 102 103 104

βkp Tp/Tkp

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2-D Hybrid Expanding Box Simulation II

Expansion vs the oblique fire hose (Hellinger & Travnicek, 2008)

0.01 0.10 1.00 10.00

0.1 1.0 10.0

101 102 103 104

β Tp/Tkp

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2-D Hybrid Expanding Box Simulation III

Evolution of wave energy

0.000 0.005 0.010 0.015 0.020 0.025 0.030

0 1 2 3

-90o -45o 0o 45o 90o

t/te

δB2 /B

2 0

θkB

(29)

Summary

Proton temperature anisotropy

constrained by mirror and proton cyclotron instabilities constrained by both fire hose instabilities.

oblique fire hose sets the final frontier for the anisotropy signatures of generated waves.

Simulation results explain the apparent discrepancy between the linear prediction and WIND/SWE observations.

Electron temperature anisotropy

constrained by whistler and oblique fire hose instability observation of generated waves?

References

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