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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 ShockVicinity 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

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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

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Cou

rtes

y of

A.

Spi

tkov

ky

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The Earth Bow Shock The Earth Bow Shock

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Geometry of the bow-shock of the Earth magnetosphere

Q|| bow-shock crossing by Cluster

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Giacalone, Schwartz and Burgess, 1993 SLAMS in the vicinity of the Earth SLAMS in the vicinity of the Earth

Bow ShockBow Shock

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Giacalone, Schwartz and Burgess, 1993

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

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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

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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

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Gyro-Surfing accelerationGyro-Surfing acceleration

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

1. Circularly polarized wave2. Particle polulation wich satisfy the resonance condition with the wave3. 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 of the effective energy transport to the transverse component of the ion kinetic energy

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Gyro-resonant mechanism of particle accelerationCircular electromagnetic wave: B=B() and E=E()

0

const

B B

B

Background magnetic field: B0

1rot

div 0c t

ﾶ

BE

E/ | |

d t

v

k r

k

wave-phase 1 2, , , ,v v v v v P P

Components of particle velocity

Equation of motion

012

021

2 1

| | | |( ) sin

| | | |( ) cos

| |cos sin

q qdvv v v

dt mc mcq qdv

v v vdt mc mc

dv qv v

dt mc

ﾶﾶ ﾶﾶ

ﾶ

B B

B B

B

P

P

P

0

| |( ) sin

| |sin

| | | |cos

qdvv v

dt mcdv q

vdt mc

v vq q

mc v mc

ﾶ ﾶ

ﾶﾶ ﾶﾶ

ﾶ ﾶ

ﾶ

B

B

B B

P

P

P&

First approximation 0| |q

mc B&

0 & &Gyroresonance

0

0

0

| |sin

| |sin

| |

qdv

dt mckdv q

vdt mc

q

mc

ﾶﾶ ﾶﾶ ﾶ

B

B

B

P

&

&

& / /v k v k v P& &

One needs to compensate Lorentzforce of wave

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Effect of Electrostatic field0

0

0

| |sin

| |sin

| |

qdv

dt mckdv q

vdt mc

q

mc

ﾶ ﾶﾶﾶ ﾶﾶﾶ ﾶﾶﾶ

B

B

B

P

&

&

&

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

0

20

02 2

0

| | , 0

| || |sin

| |0 sin

dvconst

dt

qdv

dt m c kqE q

vm mc

ﾶ ﾶﾶ

ﾶﾶ ﾶﾶ

B

B B

B

P

P

&

220

2

| |1

2

q Edv

dt m ck

B P

220| |

2

q Ev mt

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 of magnetic field

0 ( )x x z zB B x B e e ( ) / ( ) 1x zx B B x =

( )

/

kz k x dx t

v k const

Wave-phase

202

02

0

| |( ) 1 sin

1| |

sin1| |

qdv dv v v

dt dt mcdv qd

v vdt dt mc

qv v

mck

ﾶﾶ ﾶﾶ ﾶ

B

B

B

P

PP

P

Equations of motion in gyro-resonance

22 2 0

0 02 2 20 0

2 1 1( )x

x

v vk

� � � �� �

Initial conditions:

20 0( , )v

0 0 /x xqB mc

2 20v v 1/30 0 / 2x Energy gain corresponds to

4/3 1/3

2 2 2 0 00 02

1max 2 2 ,

2x xv v v

� � � �� � � �� � � �

� �� � � � Pro

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Particle trajectories

Trajectory in plane perpendicular to magnetic field

Energy gain corresponds to resonant condition

( ) / 0d dt

Energy as function of time

System parameters

0 0

0 0

0 0 0

0 0 0 0

(1 / )

/ , /

/

/ , /

z

x x

B B x

B B b B B

v mc qB

u v v k kv mc qB

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2

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Energy distributionOnly resonant particles are considered

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Energy distribution

All ensemble with initial energy v0 is considered

Energy distribution

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

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012The distance of SC1 (black) and

SC3 to the bow shock along the magnetic field line; it can be observed 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 polarizationWave polarization

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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

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012The 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 observed together with the marked beam-like distribution of the solarwind.

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Particle fluxesParticle fluxes

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r 3-

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detected aboard C1: the SLAMS boundaries are marked with arrows. Here the ion distributions are shown in the close vicinity of 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 isslightly higher than of the ions forming the solar wind beam; typical characteristics of a seedion population

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Electric field on the boundaryElectric field on the boundary

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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

Conclusions Conclusions