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Pitch-angle dependent transport of particles through discontinuities

ISSI, Berne, 10-14 February, 2014. Pitch-angle dependent transport of particles through discontinuities. Y. Kartavykh 1,2. (1) Ioffe Physical-Technical Institute (2) University of Würzburg. 1 . Reflection from the bow shock (events in June 2004). 2 . Event of 20 October 2002.

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Pitch-angle dependent transport of particles through discontinuities

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  1. ISSI, Berne, 10-14 February, 2014 Pitch-angle dependent transport of particles through discontinuities Y.Kartavykh1,2 (1) Ioffe Physical-Technical Institute (2) University of Würzburg ISSI, Berne, 10-14 September 2014

  2. 1. Reflection from the bow shock (events in June 2004) 2. Event of 20 October 2002 From Kartavykh , Dröge, Klecker, JGR, 2013 3. Acceleration of protons by quasi-parallel shocks This event was considered by L.Wang et al., 2011 ISSI, Berne, 10-14 September 2014

  3. Structure of the magnetosphere of the Earth 1. Reflection from the bow shock (events in June 2004) From Baumjohann&Treumann „Basic Plasma Physics“ ISSI, Berne, 10-14 September 2014

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  5. Bi-modal electron pitch angle distributions observed in SEP event on June, 4, 2000 by s/c Wind ISSI, Berne, 10-14 September 2014

  6. Pitch-angle distributions measured by ACE and Wind Energy spectra of outward and inward streaming electrons ISSI, Berne, 10-14 September 2014

  7. The observed by Wind and ACE time profiles ISSI, Berne, 10-14 September 2014

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  12. As an example to fit – event on June, 4, 2000 One-dimensional propagation model First – finite differences approach ISSI, Berne, 10-14 September 2014

  13. Solving equation of focused transport via Monte-Carlo approach System of SDE s(t): coordinate along the magnetic field spiral (t): pitch angle W(t): Wiener process ISSI, Berne, 10-14 September 2014

  14. There is no delay between solar and backstreaming elections within the accuracy of measurements (12 s) ISSI, Berne, 10-14 September 2014

  15. Reflecting Boundary Model Distance Wind – bow shock = 450 000 km (0.003 AU) Somewhat arbitrary assumptions about the reflectivity‘ shape ISSI, Berne, 10-14 September 2014

  16. Adiabatic Transmission Model Magnetic moment of a gyrating particle Mirrow condition: particles are reflected if: ISSI, Berne, 10-14 September 2014

  17. Adiabatic transmission and magnetosheath diffusion model Magnetosheath size Adiabatic changes of pitch angles when go through the bow shock ISSI, Berne, 10-14 September 2014

  18. Corrected omnidirectional and sectored data 2. Event of 20 October 2002 Reflection from beyond the Earth ISSI, Berne, 10-14 September 2014

  19. Similar model, but reflection boundary is located beyond the Earth , at a heliocentric distance , e.g. 1.5 AU (0.8 AU from the Earth along the mfl) ISSI, Berne, 10-14 September 2014

  20. Fokker-Planck equation for the particle’s propagation which can be applied to consider also shock-like structures 3. Acceleration of protons by quasi- parallel shocks – pitch angle diffusion approximation Stochastic differential equations for changes in sand  Convection is included implicitly The pitch angle diffusion coefficient ISSI, Berne, 10-14 September 2014

  21. At certain conditions the solution of the kinetic equation reproduces the results for the diffusive shock acceleration (DSA). Continuous and homogenious in PA cosine injection of particles on the SF Cyan – prediction from the DAS approach t1=10 -20 hours, t2=30-40 , t3=50-60, t4=70-80, t5=90-100, t6=110-120, t7=130-140, t8=150-160 , t9 =170-180, t12=230-240 , t18=350-360, t21=410-420 hours. ISSI, Berne, 10-14 September 2014

  22. Some examples of simulated energy spectra ISSI, Berne, 10-14 September 2014

  23. Pitch angle distributions at different locations in upstream (left) and downstream (right) regions. Compression ratio R = 3.0, 1= 0.01 AU, 2 = 0.001 AU, zup = 0.7 AU, zdown= 0.1 AU. Continuous (in time ) injection of protons at the shock front for 700 hours. Time of counting: 200 - 700 hours ISSI, Berne, 10-14 September 2014

  24. Spatial dependence of accelerated protons From DSA theory density in upstream is proportional whereU is the speed of fluid ISSI, Berne, 10-14 September 2014

  25. In certain range of parametrs, depending on the boundary and initial conditions, this approach gives results similar to the DSA theory On the other hand, the results which are different from DSA approach look more realistic ISSI, Berne, 10-14 September 2014

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  30. C O N C L U S I O N S • -- Model of pitch angle diffusion (PAD) transport is flexible and allows relatively easily track particles through discontinuities • - Equivalence of the results with the DSA theory depends on the initial and boundary conditions • - Model o f PAD transport gives more realistic results for shock acceleration. Thank you for your attention! ISSI, Berne, 10-14 September 2014

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