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

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 Agapitov O., Artemyev A., Krasnoselskikh V., Kis A. Processus d’accélération en astrophysique Institut d'Astrophysique de Paris, October 3-5, 2012 1

Outline Outline Processus d’accélération en astrophysique, October 3-5, 2012 Processus d’accélération en astrophysique, October 3-5, 2012 • 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 2

Solar system shocks Solar system shocks courtesy of Anatoly Spitkovsky SNR - supernova remnant Processus d’accélération en astrophysique, October 3-5, 2012 Processus d’accélération en astrophysique, October 3-5, 2012 AGN - active galactic nucleus Courtesy of A. Spitkovky Mean free path due to Coulomb collisions is: •1 AU in the Solar system •1000 pc in Supernova Remnants •10 6 pc in galaxy clusters Mean free path >> all scales of interest. Shocks must be mediated without any collisions but through interaction with collective self- 3 consistent fields

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 Q || bow-shock crossing by Cluster magnetosphere 4

SLAMS in the vicinity of the Earth SLAMS in the vicinity of the Earth Giacalone, Schwartz and Burgess, 1993 Bow Shock Bow Shock Processus d’accélération en astrophysique, October 3-5, 2012 Processus d’accélération en astrophysique, October 3-5, 2012 5 Giacalone, Schwartz and Burgess, 1993

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 6 Giacalone, Schwartz and Burgess, 1993

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 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 1 st 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 7

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 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). 8

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 of the effective energy transport to the transverse component of the ion kinetic energy 9

Gyro-resonant mechanism of particle acceleration Background magnetic field: B 0 Components of particle velocity Circular electromagnetic wave: B  = B  () and E  = E  ( ) ( ) v v , , v v v θ , , Processus d’accélération en astrophysique, October 3-5, 2012 Processus d’accélération en astrophysique, October 3-5, 2012 ? 1 B ? P P 1 2 ⊥ ⊥ ⊥ wave-phase rot E δ = − B B ⊥ δ c ﾶ t Equation of motion ? k r d t φ = − ω 0 δ B const div E 0 = = v φ / | k | δ δ = ω dv q | B | q | B | ( ? ﾶ dv q | B | ( 0 v v v )sin 1 ⊥ δ = + − φ v v )sin ( ) δ ⊥ ? = − φ − θ P ﾶ 2 ⊥ φ dt mc mc P φ dt mc ﾶ ﾶ dv q | B | q | B | ( ﾶ dv ﾶ q | B | 2 0 v v v )cos ⊥ δ = − − − φ ? P ( ) v sin δ 1 P ﾶ = − φ − θ ⊥ φ dt mc mc ﾶ ⊥ dt mc ﾶ ﾶ dv q | B | ﾶ = − v v q | B | q | B | cos P − ( v cos v sin ) δ = φ − φ & ﾶ P φ 0 ( ) δ 2 1 θ + φ − θ ⊥ ⊥ ﾶ dt mc ? mc v mc ﾶ ⊥ q | B | dv ? & sin δ ⊥ = θ φ ? 0 dt mck q | B | ﾶ & 0 One needs to First approximation θ ? − & dv q | B | ﾶ mc P v sin δ compensate Lorentz = − φ ? & & 0 ⊥ dt mc 0 Gyroresonance ﾶ φ − θ = force of wave ﾶ ? − q | B | & & & v / k v / k v 0 = φ + = θ + θ ﾶ P φ φ mc 10 ?

Effect of Electrostatic field & dv ﾶ dv q | B | & Lorentz force can be P sin | B | const dt , 0 ⊥ δ = θ φ = = ﾶ 0 0 dt mck compensated by Processus d’accélération en astrophysique, October 3-5, 2012 Processus d’accélération en astrophysique, October 3-5, 2012 ﾶ electrostatic field (see & dv q | B | ﾶ ﾶ 2 dv q | B || B |sin P v sin δ Kuramitsu & Krasnoselskikh ﾶ 0 = − φ ⊥ δ = − φ ﾶ 0 ⊥ 0 dt mc ﾶ 2 2 dt m c k ﾶ 2005 PRL) ﾶ ﾶ q | B | qE q | B | & ﾶ = ﾶ 0 P θ − 0 v sin ﾶ δ − φ ﾶ mc 0 ﾶ ⊥ ﾶ m mc Growth of energyTrajectory in plane perpendicular to the background magnetic field 2 q | B | E 2 1 dv ⊥ = − 0 P 2 2 dt m ck 2 q | B | E 2 v m 0 P t ⊥ = − 2 mck Particles gain energy in the system with E II <0 11 (Kuramitsu & Krasnoselskikh 2005 PRL)

Effect of the Magnetic field inhomogeneity Wave-phase kz k ( ) x dx t Processus d’accélération en astrophysique, October 3-5, 2012 Processus d’accélération en astrophysique, October 3-5, 2012 φ = − ? ν − ω Lorentz force can be compensated by inhomogeneity v / k const qB 0 / mc Ω = = ω = of magnetic field 0 x x φ B B e B x ( ) e = + = ( ) x B / B x ( ) 1 ν = 0 x x z z x z Equations of motion in gyro-resonance dv d q | B | ( ν ν ? 2 v v v ) 1 sin ⊥ δ = + − + ν φ ? P 0 2 ⊥ 2 φ dt 1 dt mc ( v , ) + ν ν ﾶ 0 0 ⊥ dv q | B | ﾶ d ν ν Initial conditions: P v v sin δ = − φ ? P 0 2 ⊥ dt 1 dt mc + ν ﾶ ﾶ q | B | 2 � � 2 1 1 Ω ω ν 0 v v 2 2 v v 0 x ( ) = − + = + − ν + − ﾶ � � P φ 0 0 mck ⊥ ⊥ 2 2 2 k Ω ν ν ? � � 0 x 0 1/3 Energy gain corresponds to 2 2 ( 0 / 2 ) v v ν > Ω ω > 0 x 0 ⊥ ⊥ 4/3 1/3 1 � � � � � � Ω Ω ( ) 2 2 2 max v v v φ 0 x 2 2 , 0 x − = ν + − ν = ν � � � � � � 0 0 ⊥ ⊥ 2 13 2 � � � � � � ω ν ω

Particle trajectories Processus d’accélération en astrophysique, October 3-5, 2012 Processus d’accélération en astrophysique, October 3-5, 2012 nergy as function of time Energy gain corresponds o resonant condition d ( ) / dt 0 φ − θ = Trajectory in plane erpendicular to magnetic field System parameters B B (1 x / ) = + α ρ z 0 0 B / B b , B / B δ = = 0 x x 0 δ v mc qB / ρ = 0 0 0 14 u v / v , k kv mc qB / = = 0 0 0 0 φ φ

ly resonant particles are considered Energy distribution 15 Processus d’accélération en astrophysique, October 3-5, 2012 Processus d’accélération en astrophysique, October 3-5, 2012

considered All ensemble with initial energy v 0 is Energy distribution Energy distribution 16 Processus d’accélération en astrophysique, October 3-5, 2012 Processus d’accélération en astrophysique, October 3-5, 2012

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 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. 17