[PPT] - Ions Gyro-Resonant Surfing Ions Gyro-Resonant Surfing Acceleration PowerPoint Presentation

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Agapitov O., Artemyev A., Krasnoselskikh V., Kis A.

Ions Gyro-Resonant Surfing Ions Gyro-Resonant Surfing Acceleration by Alfven Waves in the Acceleration by Alfven Waves in the Vicinity of Quasi-Parallel Shock Vicinity of Quasi-Parallel Shock

Processus d’accélération en astrophysique Institut d'Astrophysique de Paris, October 3-5, 2012

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Solar system shocks. Bow Shock:

continuously observed shock wave with different geometric properties

Diffuse ion population
Gyro-resonance acceleration (GRA)
GRA with magnetic field inhomogeneity
Experimental properties of GRA

Outline Outline

Processus d’accélération en astrophysique, October 3-5, 2012 Processus d’accélération en astrophysique, October 3-5, 2012

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AGN - active galactic nucleus SNR - supernova remnant

courtesy of Anatoly Spitkovsky

Mean free path due to Coulomb collisions is:

1 AU in the Solar system
1000 pc in Supernova Remnants
106 pc in galaxy clusters

Mean free path >> all scales of interest. Shocks must be mediated without any collisions but through interaction with collective self- consistent fields

Solar system shocks Solar system shocks

Processus d’accélération en astrophysique, October 3-5, 2012 Processus d’accélération en astrophysique, October 3-5, 2012

Courtesy of A. Spitkovky

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The Earth Bow Shock The Earth Bow Shock

Processus d’accélération en astrophysique, October 3-5, 2012 Processus d’accélération en astrophysique, October 3-5, 2012

Geometry of the bow-shock of the Earth magnetosphere Q|| bow-shock crossing by Cluster

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SLAMS in the vicinity of the Earth SLAMS in the vicinity of the Earth Bow Shock Bow Shock

Processus d’accélération en astrophysique, October 3-5, 2012 Processus d’accélération en astrophysique, October 3-5, 2012

Giacalone, Schwartz and Burgess, 1993

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SLAMS in the vicinity of the Earth SLAMS in the vicinity of the Earth Bow Shock Bow Shock

Processus d’accélération en astrophysique, October 3-5, 2012 Processus d’accélération en astrophysique, October 3-5, 2012

Giacalone, Schwartz and Burgess, 1993

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Diffusive ions are nearly isotropic, energetic (~150 keV) ions observed upstream of the Bow Shock under quasi-parallel conditions Strong correlation known between the diffusive ions and upstream wave filed intensity Suggestive of 1st order Fermi acceleration. In this case Fermi picture predicts N(E) falls exponential with distance from the shock L(E)~E Cluster can directly observe this gradient

Diffuse ions upstream of Earth’s bow shock

Processus d’accélération en astrophysique, October 3-5, 2012 Processus d’accélération en astrophysique, October 3-5, 2012

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The gradients in 4 energy channels ranging from 10 to 32 keV energy channels decrease exponentially with distance. The e-folding distance of the gradients depends approximately linearly on energy and increases from 0.5 Re at 11 keV to 2.8 Re at 27 keV (from Kis et al., 2004).

Diffuse ions upstream of Earth’s bow shock

Processus d’accélération en astrophysique, October 3-5, 2012 Processus d’accélération en astrophysique, October 3-5, 2012

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Gyro-Surfing acceleration Gyro-Surfing acceleration

Processus d’accélération en astrophysique, October 3-5, 2012 Processus d’accélération en astrophysique, October 3-5, 2012

The idea of gyro-surfing acceleration was proposed by Kuramitsu and Krasnoselskikh PRL2005. Three factors are necessary:

1. Circularly polarized wave
2. Particle polulation wich satisfy the resonance

condition with the wave

3. Electrostatic field along the background magnetic field

All these three factors are usual for the vicinity of the Earth quasi-parallel Bow Shock. This allows to expect observation

f the effective energy transport to the transverse component
f the ion kinetic energy

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Gyro-resonant mechanism of particle acceleration

Circular electromagnetic wave: B=B() and E=E

const

δ δ

⊥ = B B B

Background magnetic field: B0

1 rot div c t

δ δ δ

? = − ﾶ = B E E / | | d t vφ φ ω ω = − =

?k r

k

wave-phase

( ) ( )

1 2

, , , , v v v v v θ

⊥ ⊥ ⊥

?

P P

Components of particle velocity Equation of motion ( )

1 2 2 1 2 1

| | | | ( )sin | | | | ( )cos | | cos sin q q dv v v v dt mc mc q q dv v v v dt mc mc dv q v v dt mc

δ φ δ φ δ

φ φ φ φ

⊥ ⊥ ⊥ ⊥ ⊥ ⊥

? = + − ? ﾶﾶ = − − − ? ﾶﾶ = − ﾶ ? B B B B B

P P P

( ) ( ) ( )

| | ( )sin | | sin | | | | cos q dv v v dt mc dv q v dt mc v v q q mc v mc

δ φ δ φ δ

φ θ φ θ θ φ θ

⊥ ⊥ ⊥

ﾶ = − − ﾶﾶﾶ = − − ﾶﾶ − ﾶ = − + − ﾶﾶ B B B B

P P P

&

First approximation

| | q mc θ ? − B & φ θ − = & &

Gyroresonance

| | sin | | sin | | q dv dt mck dv q v dt mc q mc

δ δ

θ φ φ θ

⊥ ⊥

? = ? ﾶﾶ = − ? ﾶﾶ ? − ﾶ ? B B B

P

& & & / / v k v k v

φ φ

φ θ = + = +

P

& &

One needs to compensate Lorentz force of wave

Processus d’accélération en astrophysique, October 3-5, 2012 Processus d’accélération en astrophysique, October 3-5, 2012

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Effect of Electrostatic field

| | sin | | sin | | q dv dt mck dv q v dt mc q mc

δ δ

θ φ φ θ

⊥ ⊥

ﾶ = ﾶﾶﾶ = − ﾶﾶﾶ − ﾶﾶﾶ B B B

P

& & &

Lorentz force can be compensated by electrostatic field (see Kuramitsu & Krasnoselskikh 2005 PRL)

2 2 2

| | , | || |sin | | sin dv const dt q dv dt m c k qE q v m mc

δ δ

φ φ

⊥ ⊥

= = ﾶ = − ﾶﾶﾶﾶ = − ﾶﾶ B B B B

P P

&

2 2 2

| | 1 2 q E dv dt m ck

⊥ = −

B

P 2 2

| | 2 q E v m t mck

⊥

= − B

P

Particles gain energy in the system with EII<0

(Kuramitsu & Krasnoselskikh 2005 PRL)

Growth of energyTrajectory in plane perpendicular to the background magnetic field

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Effect of the Magnetic field inhomogeneity

Lorentz force can be compensated by inhomogeneity

f magnetic field

( )

x x z z

B B x = + B e e ( ) / ( ) 1

x z

x B B x ν = = ( ) / kz k x dx t v k const

φ

φ ν ω ω = − − = =

?

Wave-phase

2 2 2

| | ( ) 1 sin 1 | | sin 1 | | q dv d v v v dt dt mc dv q d v v dt dt mc q v v mck

δ φ δ φ

ν ν ν φ ν ν ν φ ν

⊥ ⊥ ⊥

? = + − + ? + ﾶﾶ = − ? + ﾶﾶ = − + ﾶ ? B B B

P P P P

Equations of motion in gyro-resonance

2 2 2 2 2 2

2 1 1 ( )

x x

v v k ω ν ν ν ν

⊥ ⊥

Ω

= + − + −

Ω
Initial conditions:

2

( , ) v ν

⊥ 0 / x x

qB mc Ω =

2 2

v v

⊥ ⊥

>

( )

1/3 0 / 2 x

ν ω > Ω

Energy gain corresponds to

( )

4/3 1/3 2 2 2 2

1 max 2 2 , 2

x x

v v vφ ν ν ν ω ν ω

⊥ ⊥

Ω Ω

−

= + − =

Processus d’accélération en astrophysique, October 3-5, 2012

Processus d’accélération en astrophysique, October 3-5, 2012

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Particle trajectories

Trajectory in plane erpendicular to magnetic field Energy gain corresponds

resonant condition

( ) / d dt φ θ − =

nergy as function of time System parameters

(1 / ) / , / / / , /

z x x

B B x B B b B B v mc qB u v v k kv mc qB

δ φ φ

α ρ δ ρ = + = = = = =

Processus d’accélération en astrophysique, October 3-5, 2012 Processus d’accélération en astrophysique, October 3-5, 2012

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Energy distribution

ly resonant particles are considered

Processus d’accélération en astrophysique, October 3-5, 2012 Processus d’accélération en astrophysique, October 3-5, 2012

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Energy distribution

All ensemble with initial energy v0 is considered

Energy distribution

Processus d’accélération en astrophysique, October 3-5, 2012 Processus d’accélération en astrophysique, October 3-5, 2012

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The upstream ion event on 18th of The upstream ion event on 18th of February, 2003 February, 2003

Processus d’accélération en astrophysique, October 3-5, 2012 Processus d’accélération en astrophysique, October 3-5, 2012

The distance of SC1 (black) and SC3 to the bow shock along the magnetic field line; it can be

bserved that SC1 was situated

closer to bow shock while SC3 was situated further upstream. The distance between the two spacecraft in the perpendicular direction (i.e., related to the direction of the local magnetic field). The angle between the local magnetic field and the bow shock normal direction. The black arrow marks the time period of the detailed analysis when the seed particle population was recorded.

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Wave polarization Wave polarization

Processus d’accélération en astrophysique, October 3-5, 2012 Processus d’accélération en astrophysique, October 3-5, 2012

The hodograms of the three wave packets observed by Cluster spacecraft in the MVAB reference frame. It can be clearly seen that all three wave packets consist of circularly polarized transversal waves.

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Particle fluxes Particle fluxes

Processus d’accélération en astrophysique, October 3-5, 2012 Processus d’accélération en astrophysique, October 3-5, 2012 The magnetic data recorded by SC3; the first two wave packets are highlighted (red). Attached to this upper panel there are two ion distributions in velocity space taken at the times by SC3 when of the two first wave packets were observed. The two ion distributions presents quite similar characteristics: the highly isothropic ring of the diffuse ions can be

bserved together with

the marked beam-like distribution of the solar wind.

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Particle fluxes Particle fluxes

Processus d’accélération en astrophysique, October 3-5, 2012 Processus d’accélération en astrophysique, October 3-5, 2012 the magnetic field detected aboard C1: the SLAMS boundaries are marked with arrows. Here the ion distributions are shown in the close vicinity

f the magnetic boundary.

Besides the ring of diffuse ions and the solar wind beam (both marked on the figure) it can be observed a highly concentrated beam-like distribution in the antiparallel direction related to the solar wind

beam. It can also be seen

that the velocity of the ions forming the beam is slightly higher than of the ions forming the solar wind beam; typical characteristics of a seed ion population

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Electric field on the boundary Electric field on the boundary

Processus d’accélération en astrophysique, October 3-5, 2012 Processus d’accélération en astrophysique, October 3-5, 2012

The electric field X (in blue color) and Y (in green color) component values recorded by the EFW instrument onboard SC4. The units are in mV/m at the time interval when the magnetic field structure was observed, which can be seen in the lower

panel. It can be clearly observed that at the magnetic boundary (lower panel) there is

no significant jump in the electric field value.

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In spite of the differences between astrophysical and Earth bow shocks there are several important and crucial for the acceleration problem questions, which can be identified and studied in details by in situ observation of physical processes involved into acceleration in the solar system We provide observational evidence of the formation of the so- called seed particles in the foreshock region for the first time. Our results based on multipoint simultaneous measurements in front of the Earth’s quasi-parallel bow shock show that the gyroresonant surfing acceleration on the magnetic field inhomogeneity is indeed an effective ion acceleration mechanism capable of producing the seed ions which is an essential element of the diffusive shock acceleration

Agapitov O., Artemyev A., Krasnoselskikh V., Kis A.

Ions Gyro-Resonant Surfing Ions Gyro-Resonant Surfing Acceleration by Alfven Waves in the Acceleration by Alfven Waves in the Vicinity of Quasi-Parallel Shock Vicinity of Quasi-Parallel Shock

Processus d’accélération en astrophysique Institut d'Astrophysique de Paris, October 3-5, 2012

continuously observed shock wave with different geometric properties

Outline Outline

Mean free path due to Coulomb collisions is:

Mean free path >> all scales of interest. Shocks must be mediated without any collisions but through interaction with collective self- consistent fields

Solar system shocks Solar system shocks

The Earth Bow Shock The Earth Bow Shock

SLAMS in the vicinity of the Earth SLAMS in the vicinity of the Earth Bow Shock Bow Shock

SLAMS in the vicinity of the Earth SLAMS in the vicinity of the Earth Bow Shock Bow Shock

Diffuse ions upstream of Earth’s bow shock

The gradients in 4 energy channels ranging from 10 to 32 keV energy channels decrease exponentially with distance. The e-folding distance of the gradients depends approximately linearly on energy and increases from 0.5 Re at 11 keV to 2.8 Re at 27 keV (from Kis et al., 2004).

Diffuse ions upstream of Earth’s bow shock

Gyro-Surfing acceleration Gyro-Surfing acceleration

The idea of gyro-surfing acceleration was proposed by Kuramitsu and Krasnoselskikh PRL2005. Three factors are necessary:

condition with the wave

All these three factors are usual for the vicinity of the Earth quasi-parallel Bow Shock. This allows to expect observation

Gyro-resonant mechanism of particle acceleration

const

⊥ = B B B

1 rot div c t

? = − ﾶ = B E E / | | d t vφ φ ω ω = − =

?k r

k

, , , , v v v v v θ

?

| | | | ( )sin | | | | ( )cos | | cos sin q q dv v v v dt mc mc q q dv v v v dt mc mc dv q v v dt mc

φ φ φ φ

? = + − ? ﾶ ﾶ = − − − ? ﾶ ﾶ = − ﾶ ? B B B B B

| | ( )sin | | sin | | | | cos q dv v v dt mc dv q v dt mc v v q q mc v mc

φ θ φ θ θ φ θ

ﾶ = − − ﾶ ﾶ ﾶ = − − ﾶ ﾶ − ﾶ = − + − ﾶ ﾶ B B B B

&

| | q mc θ ? − B & φ θ − = & &

| | sin | | sin | | q dv dt mck dv q v dt mc q mc

θ φ φ θ

? = ? ﾶ ﾶ = − ? ﾶ ﾶ ? − ﾶ ? B B B

& & & / / v k v k v

φ θ = + = +

& &

Effect of Electrostatic field

| | sin | | sin | | q dv dt mck dv q v dt mc q mc

θ φ φ θ

ﾶ = ﾶ ﾶ ﾶ = − ﾶ ﾶ ﾶ − ﾶ ﾶ ﾶ B B B

& & &

| | , | || |sin | | sin dv const dt q dv dt m c k qE q v m mc

φ φ

= = ﾶ = − ﾶ ﾶ ﾶ ﾶ = − ﾶ ﾶ B B B B

&

| | 1 2 q E dv dt m ck

B

| | 2 q E v m t mck

= − B

Particles gain energy in the system with EII<0

Effect of the Magnetic field inhomogeneity

( )

B B x = + B e e ( ) / ( ) 1

x B B x ν = = ( ) / kz k x dx t v k const

φ ν ω ω = − − = =

?

| | ( ) 1 sin 1 | | sin 1 | | q dv d v v v dt dt mc dv q d v v dt dt mc q v v mck

ν ν ν φ ν ν ν φ ν

? = + − + ? + ﾶ ﾶ = − ? + ﾶ ﾶ = − + ﾶ ? B B B

2 1 1 ( )

v v k ω ν ν ν ν

= + − + −

( , ) v ν

qB mc Ω =

v v

>

ν ω > Ω

( )

1 max 2 2 , 2

v v vφ ν ν ν ω ν ω

Ω Ω

= + − =

Particle trajectories

( ) / d dt φ θ − =

(1 / ) / , / / / , /

? = + − ? ﾶﾶ = − − − ? ﾶﾶ = − ﾶ ? B B B B B

ﾶ = − − ﾶﾶﾶ = − − ﾶﾶ − ﾶ = − + − ﾶﾶ B B B B

? = ? ﾶﾶ = − ? ﾶﾶ ? − ﾶ ? B B B

ﾶ = ﾶﾶﾶ = − ﾶﾶﾶ − ﾶﾶﾶ B B B

= = ﾶ = − ﾶﾶﾶﾶ = − ﾶﾶ B B B B

? = + − + ? + ﾶﾶ = − ? + ﾶﾶ = − + ﾶ ? B B B