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A Focused Transport Approach to Low Energy Ion Acceleration

SHINE 2006. A Focused Transport Approach to Low Energy Ion Acceleration. J. A. le Roux & G. M. Webb IGPP, University of California, Riverside. TRANSPORT THEORY. STANDARD FOCUSED TRANSPORT EQUATION – GYROPHASE AVERAGED BOLTZMANN EQUATION FOR GYROTROPIC DISTRIBUTION.

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A Focused Transport Approach to Low Energy Ion Acceleration

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  1. SHINE 2006 A Focused Transport Approach to Low Energy Ion Acceleration J. A. le Roux& G. M. Webb IGPP, University of California, Riverside

  2. TRANSPORT THEORY STANDARD FOCUSED TRANSPORT EQUATION – GYROPHASE AVERAGED BOLTZMANN EQUATION FOR GYROTROPIC DISTRIBUTION Particle momentum p’ transformed to plasma flow frame where Ui=0

  3. DRIFT EFFECTS IN FOCUSED TRANSPORT EQUATION THE CONVECTION TERM Electric field drift Guiding center drift alongBi

  4. DRIFT EFFECTS IN FOCUSED TRANSPORT EQUATION PARALLEL MOMENTUM CHANGE TERM Contains curvature drift Magnetic mirroring Parallel guiding center drift

  5. DRIFT EFFECTS IN FOCUSED TRANSPORT EQUATION TRANSVERSE MOMENTUM CHANGE TERM Magnetic mirroring Gyration Grad-B drift Drift along Bi

  6. CONSERVATION OF MAGNETIC MOMENT M TRANSVERSE MOMENTUM CHANGE TERM CAN BE SHOWN TO GIVE:

  7. CONSTANTS OF MOTION AT PARALLEL SHOCK IfE|| =0 CONSTANTS OF MOTION AT PERPENDICULAR SHOCK IfE|| =0 Agrees with shock drift theory

  8. TRANSPORT THEORY - SUMMARY STANDARD FOCUSED TRANSPORT EQUATION INCLUDES: Convection alongBiand electric field driftEnergy changes associated with grad-B drift, curvature drift (part of acceleration drift), parallel drift (cross-shock potential), and compression of plasma flow along BiMagnetic mirroring, mirroring by cross-shock potential, and conservation of magnetic momentTransport Theory consistent with Shock Drift Theory STANDARD FOCUSED TRANSPORT EQUATION NEGLECTS: gradient and curvature drift contribution to convectionEnergy changes associated with part of acceleration drift (polarization drift)Perpendicular diffusion – can be included by randomly varying field angle

  9. PARALLEL SHOCK: (i) Accelerated particle spectra (fluid frame) Strong cross-shock potential No cross-shock potential downstream downstream 1 keV isotropic particle source 1st transmission peak 1st Reflection peak

  10. PARALLEL SHOCK: (ii) Spatial variation across shock Discontinuity in f(z) enhanced by cross-shock potential In fluid frame f(z) discontinuous across shock 100 keV 100 keV 10 keV 10 keV Shock atz = 0

  11. PARALLEL SHOCK:(iii) Anisotropies across shock (fluid frame) Reflection by cross-shock potential 10 keV 1 keV at shock upstream 100 keV downstream 10 keV upstream

  12. OBLIQUE SHOCK(BN = 45o): (i) Accelerated spectra (fluid frame) Magnetic reflection + cross-shock potential reflection Magnetic reflection Hybrid simulationKucharek & Scholer (1995) Spectra harder than expected from standard DSA theory

  13. OBLIQUE SHOCK(BN = 45o): (ii) Spatial variation across shock 100 keV Magnetic reflection contributes substantially towards discontinuity in f(z) across the shock at higher energiesStandard assumption of f1 = f2In DSA theory does not apply 10 keV

  14. OBLIQUE SHOCK (BN = 45o): (iii) Anisotropy across shock (fluid frame) Anisotropy enhanced by magnetic reflectionAnisotropy large at 100 keV – violates standard DSA theory Magnetic reflection 10 keV 1 keV at shock 100 keV upstream 10 keV upstream downstream

  15. QUASI-PERPENDICULAR SHOCKS (BN > 45o):Accelerated spectra (fluid frame) Only particles with E > 9 MeV (v/Ue > 95) can be reflected upstream Only particles with v/Ue > 3 can be reflected upstream BN= 70o BN= 89.4o downstream downstream

  16. NEARLY PERPENDICULAR SHOCK (Variable BN):Accelerated spectra (fluid frame) Deviations from average BNlowers threshold for particle reflection Observed hourly averaged spiral angles by Voyager 1 during 2004

  17. SIMULATIONS: SUMMARY AND INTERPRETATION • (1) SHOCK ACCELERATION RESULTS WITH FOCUSED TRANSPORT MODELDEVIATE FROM STANDARD DSA THEORY BECAUSE OF: Particle reflection at shock by field compression Particle reflection by cross-shock electric field (smaller effect) Particles are tied to field lines – have difficulty to go back upstream Particle momentum is in comoving frame (2) THE MAIN DEVIATIONS FROM DSA THEORY AND SOLUTIONS ARE:Accelerated spectra is power law – but harder than predicted by DSA theoryAt low energies 2 prominent peaksin accelerated spectra downstream - DSA theory solution give smooth power lawSpatial distributiondiscontinuous in form of a spike across shock – even at higher energies – continuous distribution across shock is assumed in DSA theoryUpstreamparticle anisotropies large and field-aligned in direction away from shock even at higher energies - small anisotropies are assumed in DSA theory(3) THE BASIC ACCELERATED SPECTRAL FEATURES PRODUCED BY FOCUSED TRANSPORT MODEL AGREE WITH MORE SOPHISTICATED PARTICLE CODES(4) DISCONTINUOUS INTENSITY SPIKES, AND FIELD-ALIGNED UPSTREAM ANISOTROPIES PRODUCED BY FOCUSED TRANSPORT MODEL ARE PRESENT IN VOYAGER 1 OBSERVATIONS AT TERMINATION SHOCKMAIN CONCLUSION:FOCUSED TRANSPORT WILL PROVIDE A MORE ACCURATE AND REALISTIC DESCRIPTION OF SEP ACCELERATION AT CME SHOCKS THAN STANDARD DSA THEORY

  18. SIMULATIONS: PROBLEMS (1) Particles are tied to field lines - if shock normal angle > 70O, particles have difficulty to achieve multiple shock encounters(2)Can shock acceleration at a nearly perpendicular shock work by randomly varying the field angle without microscopic diffusion in focused transport model?(3) The particle anisotropy at Voyager 1 peaks at some intermediate energy – focused transport model predicts an increase with decreasing energy – could indicate preacceleration should occur upstream of shock at lower energies – particle trapping upstream in non-linear self-generated waves possibly needed

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