Anastasios Anastasiadis

Transcription

1 Charged Particle Dynamics in Non Linear Fields (the case of Current Sheets) Anastasios Anastasiadis (NOA / NTUA EURATOM GROUP) Institute for Space Applications & Remote Sensing National Observatory of Athens GREECE anastasi@space.noa.gr

2 Contents Introduction Definitions Physical Systems - Examples Orbits - Examples Harris type and X- point configurations Particle Orbits & Dynamics Newtonian & Hamiltonian Approach Type of Orbits Selected Results MHD Numerical Simulations Selected Results References

3 Introduction (definitions) What is a Current Sheet? A boundary layer (a tangential discontinuity transition region) which is usually formed when two initially separate plasma regimes, with their own magnetic field, come into contact with each other. Schematic Representation General topologies

4 Introduction (basic equations) Maxwell s Equations

5 Introduction (examples) Examples Physical Systems Solar Active Regions Flares

6 Introduction (examples) Examples Physical Systems Solar Active Regions Flares (from Aschwanden, 2004)

7 Introduction (examples) Examples Physical Systems Magnetosphere

8 Introduction (examples) Examples Physical Systems Tokamaks (from Aschwanden, 2004)

9 Introduction (numerical simulations) Numerical MHD simulations (from Horiuchi & Sato, 1999) (from Vlahos et al. 2005)

10 Introduction (numerical simulations)

11 Introduction (orbits examples) Regular Orbit Chaotic Orbit Harris Type (from Litvinenko 1996 ; Holman 1985) X Type (from Hannah et al. 2002)

12 Introduction (orbits examples) O Type (from Kliem 1994)

13 The Harris type configuration (geometries)

14 The Harris configuration ( fields) Y V in B y B x B z E X Y= 1 Y= - 1 Z V in There is no E-field outside of the CS and the B- field is constant outside the y =a=1 The B-field components are constant in z and y (from Efthymiopoulos, Gontikakis, Anastasiadis, 2005)

15 The X-point configuration ( fields) ( from Anastasiadis et al, 2008)

16 Particle Orbits Particle Dynamics The Newtonian Approach

17 Particle Orbits Particle Dynamics Q : How can we solve the problem? A : EASY! Particle motion in EM fields Lorenz Force Additional help as E and B fields are stationary in time

18 Particle Orbits Particle Dynamics (Harris Type) Dimensionless coordinate form Normalizations (Litvinenko 1996; Efthymiopoulos, Gontikakis, Anastasiadis, 2005)

19 Particle Orbits Particle Dynamics (Harris Type) Integration once with respect to t and substitution Where x 0, y 0, z 0 initial particle position

20 Particle Orbits Particle Dynamics (Harris type) Solution depends upon the values of and The particle never escapes from the CS, unlimited acceleration along z-axis and The particle oscillates about y=0 and rotates around B. The particle escapes from the CS after a certain time. (Speiser 1978 ; Zhu & Parks 1993 ; Litvinenko 1996)

21 Particle Orbits Particle Dynamics (Harris type) General Case No electric field With electric field (Efthymiopoulos, Gontikakis, Anastasiadis, 2005)

22 Particle Orbits Particle Dynamics (from Anastasiadis et al, 2008)

23 Particle Orbits Particle Dynamics ( from Anastasiadis et al, 2008)

24 Particle Orbits Particle Dynamics We can have all kinds of orbits for the particles interacting with the CS Chaotic orbits leading to escape by stochastic acceleration of the particles Regular orbits leading to escape along the field lines Mirror type orbits leading to trapping of the particles in the CS (Chen & Palmadesso 1986; Gontikakis, Efthymiopoulos, Anastasiadis 2006; Anastasiadis et al. 2008)

25 Particle Orbits Particle Dynamics Analytical estimation Trapped Particle initial values (from Gontikakis, Efthymiopoulos, Anastasiadis 2006)

26 Particle Orbits Particle Dynamics Final vs Initial Kinetic energy of Escaping particles (from Gontikakis, Efthymiopoulos, Anastasiadis 2006)

27 Particle Orbits Particle Dynamics Kinetic Energy Distributions of Particles ELECTRONS PROTONS (from Gontikakis, Anastasiadis, Efthymiopoulos 2007)

28 Particle Orbits Particle Dynamics Pitch Angle Distributions of Particles (from Gontikakis, Anastasiadis, Efthymiopoulos 2007)

29 Particle Orbits Particle Dynamics ( from Anastasiadis et al, 2008)

30 Particle Orbits Particle Dynamics The Hamiltonian Approach

31 Particle Orbits Particle Dynamics Hamiltonian Function Canonical momenta Hamilton s Equations (from Gontikakis, Efthymiopoulos, Anastasiadis 2006)

32 Particle Orbits Particle Dynamics Hamiltonian Function 3 d.o.f. Second Integral of Motion Hamiltonian Function 2 d.o.f.

33 Particle Orbits Particle Dynamics Theoretical Model of Poincaré surface of section (from Gontikakis, Efthymiopoulos, Anastasiadis 2006)

34 Particle Orbits Particle Dynamics (Gontikakis, Efthymiopoulos, Anastasiadis 2006) ENERGY

35 Particle Orbits Particle Dynamics Analytical Calculations Numerical Calculations (Gontikakis, Efthymiopoulos, Anastasiadis 2006)

36 Particle Orbits Particle Dynamics Periodic orbit Quasi Periodic orbits Frequency modulation of y(t) due to z(t) (from Gontikakis, Efthymiopoulos, Anastasiadis 2006)

37 Particle Orbits Particle Dynamics Maximum Kinetic Energy for escaping particles

38 Multiple Interactions (Harris Type)

39 Multiple Interactions (X - Type)

40 Numerical Simulations (from Hoshino 2005)

41 Numerical Simulations ( from Siversky and Zharkova 2009 )

42 Numerical Simulations ( from Siversky and Zharkova 2009 )

43 Numerical Simulations Wave generation from the induced particles ( from Siversky and Zharkova 2009 )

44 References Anastasiadis, A., Gontikakis, C. & Efthymiopoulos C, Sol. Phys. 253, 199 (2008) Aschwanden, M., Physics of the Solar Corona, (Springer Praxis), (2004) Chen, J. & Palmadesso, P. J., J. Geophys. Res., 91, 1499 (1986) Efthymiopoulos, C., Gontikakis, C. & Anastasiadis, A., MNRAS, 368(1), 293 (2006) Gontikakis, C., Efthymiopoulos, C., & Anastasiadis, A., A&A, 443, 663 (2005) Gontikakis, C., Anastasiadis, A., & Efthymiopoulos C., MNRAS, 378, 1019 (2007) Hannah, I. G., Fletcher, L. & Hendry, M. A., ESA SP-506, 295 (2002) Holman, G. D., Astrophys. J., 293, 584 (1985) Horiuchi, R. & Sato, T., Phys. Plasmas, 12(6), 4565 (1999) Hoshino, M. astro-ph/ , (2005) Kliem, B., Astrophys. J. Sup., 90, 719 (1994) Litvinenko, Y. E., Astrophys. J., 462, 997 (1996) Nodes, C., et al, Phys. Plasmas, 10(3), 835 (2003) Siversky T.V. & Zharkova V.V., J. Plasma Phys. in press (2009) Speiser, T. W., J. Geophys. Res., 21, 627 (1978) Zhu, Z. & Parks, G., J. Geophys. Res., 98, 7603 (1993)

45 Remarks I would like to thank my collaborators: C. Efthymiopoulos C. Gontikakis From the Academy of Athens