Field-aligned and gyrating ion beams in the Earth's foreshock

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1 Field-aligned and gyrating ion beams in the Earth's foreshock Christian Mazelle Centre d'etude Spatiale des Rayonnements,, Toulouse, France Collaborators: K. Meziane 1, M. Wilber 2 1 Physics Department, University of New Brunswick, Fredericton, NB,, Canada 2 Space Sciences laboratory, University of California, Berkeley, USA Cluster and Double Star Symposium, ESTEC, Sept. 2005

2 International Space Science Institute (Bern, Switzerland) working group: "A collaborative Effort to Study the Production and Transport of kev Upstream ions" C. Mazelle 1, K. Meziane 2, J.P. Eastwood 3, A.M. Hamza 2, H. Kucharek 4, D. Le Quéau 5, G. Parks 6, K. Sauer 7, S.J. Schwartz 8, M. Wilber 6 1 Centre d'etude Spatiale des Rayonnements,, Toulouse, France; 2 Physics Department, University of New Brunswick, Fredericton, NB,, Canada; 3 NASA-GSFC, Greenbelt, MD, USA (previously Imperial College, UK); 4 University of New Hampshire, Space Science Center, Durham, NH, USA; U 5 Observatoire Midi-Pyrénées Pyrénées,, Toulouse, France; 6 Space Sciences Laboratory, University of California, Berkeley, USA; U 7 Max-Planck Planck-Institut für Aeronomie, Katlenburg-Lindau Lindau,, Germany; 8 Queen Mary College, University of London, UK.

3 Outline 1- Gyrophase-bunched ion distributions in the ion foreshock 2- Low Frequency wave properties 3- Wave excitation: linear theory Cyclotron resonance 4- Nonlinear coherent wave-particle interaction

4 B TL foreshock B Cluster

5 Planetary Foreshock [after Paschmann et al., 1979] B Diffuse ions Ion foreshock boundary Ions θ Bn n B Reflected Ion beams FABs VS Intermediate distributions Gyrating Ions Electrons Q-// shock Ion foreshock [after Paschmann et al., 1979] B θ Bn n Q- shock Gyrophase-bunched ions [after Tsurutani and Rodriguez, 1981] [Thomsen et al., 1985]

6 Sc1 23:35:33-23:35:37 CLUSTER CODIF Product E = eV B E=8.4 kev 23:35:37-23:35:41 4 s 23:35:41-23:35:45 3D angular distributions (H + ) Projection of the normalized distribution function on a constant energy sphere in the solar wind frame Field-aligned beam ions 23:35:45-23:35:49 23:35:53-23:35:57 23:35:57-23:36:01 B B B Gyrophase-bunched ions 23:36:01-23:36:05 23:36:05-23:36:09 23:36:09-23:36:13 Centered on the background field B (averaged on the observation interval) Subsequent distributions for the energy level of maximum flux (~8 kev) Accumulation time : 4 s Cyclotron period : 7 s Modification of the distribution B B B Large pitch-angles (~60 ) in SW frame Distributions highly non gyrotropic [Mazelle,, et al., Planet Sp. Sci., 2003]

7 Gyrophase-bunched ions LF Waves Field-aligned beams Separation between satellite ~ 1 R E

8 Observations close to the FAB/gyrating ions boundary Observations close to the Solar FAB/gyrating wind ions boundary Field-aligned beams Gyrophase-bunched ions no obvious wave Large amplitude LF coherent waves

9 Observations close to the FAB/gyrating ions boundary Observations close to the Solar FAB/gyrating wind ions boundary Field-aligned beams no obvious wave

10 Quick excursion in the gyrating ions' region beam energy decrease Wave amplitude variations

11 Low Frequency wave properties: Minimum Variance Analysis T ~ 233 sec T cyclotron = 7 sec λ 1 /λ 2 = 1.3 λ 2 /λ 3 = 40.1 θ kb = 12±2 1 δb /B 0 ~ 0.2 δ B /B 0 ~ LH LH Left-hand polarized in s/c frame but θ kv = 140 with upstream propagation in SW frame V phase V Alfven << V sw anomalous Doppler shift Right-Hand mode waves in plasma frame

12 Low Frequency wave properties: Minimum Variance Analysis large amplitude waves T ~ 30 sec T cyclotron = 8 sec λ 1 /λ 2 = 1.1 λ 2 /λ 3 = 48.0 θ kb = 15±1 δb /B 0 ~ 0.63 δ B /B 0 ~ 0.24 LH Left-hand polarized in s/c frame upstream propagation in SW frame with θ kv = 135 again Right-Hand mode waves Similar properties

13 Low frequency multi-spacecraft wave analysis Minimum variance analysis for each individual spacecraft: polarization analysis and k direction Multi-spacecraft analysis: determination of the wave phase velocity and plasma frame frequency without ambiguity Wave front timing method V phase plane wave front ω, k Confirms the right-hand hand polarization in plasma frame

14 possibility of cyclotron resonant wave generation Field-aligned beams: observed just before the gyrating distributions appear in cyclotron resonance with the ULF RH mode waves: ω k // V // + Ω p = 0 frame s/c and sw (= (=T obs Tpred Need for an acurate determination of Vbeam = 2π ω ' if resonance)

15 FABs properties (solar wind frame) ( +=Bo ) Determination of beam velocity See poster P2.6 by K. Meziane et al. [Meziane et al, 2005]

16 Sc1 23:35:33-23:35:37 CLUSTER CODIF Product E = eV B E=8.4 kev 23:35:37-23:35:41 23:35:41-23:35:45 3D angular distributions (H + ) Field-aligned beam ions 23:35:45-23:35:49 23:35:53-23:35:57 23:35:57-23:36:01 B B B Gyrophase-bunched ions 23:36:01-23:36:05 23:36:05-23:36:09 23:36:09-23:36:13 Modification of the distribution at the onset of LF waves B B B

17 possibility of cyclotron resonant wave generation Field-aligned beams: observed just before the gyrating distributions appear in cyclotron resonance with the ULF RH mode waves: s/c sw ω e.g. for at 2335:37 UT // V // + Ω p = V // = 1060 ±50 km/s T pred = 25.4 s while T obs = 25±2.0 s!! k 0 and frame (=T obs Tpred = 2π ω ' if resonance) Parallel wavelength: while λ // exp λ // reson= 2πV// ω+ω p = 7,000 ± 300 km = 6,700 km generation from the ion/ion resonant RH beam instability?

18 Wave dispersion analysis Solution of Maxwell-Vlasov dispersion relation: linear theory Obtained for the observed parameters ω r Ω p Cluster /04/07 Backstreaming Ion Parallel Beam 2335:37 UT n b =0.007 cm 3 V b =1060 km/s T b =130 ev frequency kv A / Ω p ω =kv A Maximum linear growth rate Wavenumber associated to the excited mode [Mazelle,, et al., PSS, 2003] γ Ω p Real frequency (solid line) and linear growth rate (dashed line) right-hand ion/ion instability : V ω r Ω p theory phase λ // λ λ // // Ω γ Ω max res exp p p max max =0.1 =0.05 : cyclotron frequency = 1. 1 V Alfvén = 6670 km = 6700 km V obs phase = 7000 ± 300 km

19 Remote study of shock geometry Use of a bow shock model., 1995] Gyrating ions interval [Cairns et al., 1995] θ Bn ~30 Q-// shock Sun D x D S ~0.5 R E Cluster sc 1 April 7, 2001

20 Interpretation of the observations for these gyrating ion events: Gyrating ion distributions: (1) Properties inconsistent with direct production from the reflection mechanism at the shock surface: 1. observed pitch-angle α exp larger than 45 and different from θ Bn as expected e.g. from a specular reflection where α exp must be < 39 [Schwartz et al., 1983] 2. ions observed at distances from the shock larger than their gyroradius need for a local production mechanism (no remote finite Larmor radius effect). (2) Predicted periods (T pred ) in the spacecraft frame for cyclotron resonance with right-hand mode waves using the parallel velocity of the gyrating ions very close to observed periods possibility of wave-particle interaction Wave generation from the ion beam instability and subsequent nonlinear beam disruption by the wave to produce the gyrating distributions?

21 Non linear wave-particle interaction: wave trapping Invariants of motion of an ion with velocity v in a frame moving // to B 0 at wave speed V phase (E=0): 2 2 // T = w + w = C 1 ψ = π/2 0 (normalized kinetic energy) 2 Ω1 S = ( w// 1) 2 w sinψ = C2 ( // & exchange ) Ω trapped orbits 0 w= k // 01, v Ω Ω 01, = qb Ω1 δb ψ = ϕ +k = / / z 0 gyrophase m Ω0 B0 ψ Hamiltonian S( α, ψ ) with tanα = w w // α Singularity: and ( ) 1/ B 0 α δb for small α o untrapped orbits [Mazelle et al., Nonlinear Processes in Geophysics, 2000] V V ph// initial resonant beam V //

22 Determination of ion properties (SW( frame) Field-aligned Beam Fits of reduced distribution functions Gyrating ions f( V// ) f( V //) f( V ) beam velocity V// V [MezianeMeziane et al, 2005]

23 Comparison with observations (1) Time Gyrating ions // ( km s) V ( km / s) V / 23:38:09 UT α exp 23:38:13 UT :38:25 UT :38:29 UT :38:45 UT [Mazelle et al., PSS, 2003] αotheor = for very good agreement δ B = B

24 Comparison with observations (2) Pitch-angle distribution in the "wave" frame Gyrophase-bunched Ions Constant-energy Sphere in the "wave" frame α o, theory 50 km/s initial resonant beam Consistent with theory (energy conservation)

25 Check of cyclotron resonance Observed wave period versus Predicted (using Tcy,, V //, ω and k) 12 different events very good agreement first quantitative demonstration of the cyclotron resonance in the foreshock

26 Check of 1-wave 1 trapping theory α 0 (theory) depends only on the wave amplitude δb B 16 intervals good agreement

27 Check of wave frame energy conservation good agreement

28 Conclusion: foreshock FABs and gyrating ions Observations of well-defined gyrophase-bunched backstreaming ion distributions in the Earth s s foreshock. Association with quasi-monochromatic, large amplitude, low frequency right-hand hand mode waves. Possibility of resonantly driving these waves unstable from the electromagnetic ion/ion beam instability: good quantitative agreement with the observed field-aligned ion beams. The angular distribution of the gyrophase-bunched ions is peaked at a pitch angle in good agreement with nonlinear single wave phase-trapping orbit theory. These results have implications on the understanding of a planetary foreshock and show the possibility to study some plasma microphysics with Cluster (while( not designed for it).

29 END

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