Heating of Test Particles in Numerical Simulations of MHD Turbulence and the Solar Wind
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1 Heating of Test Particles in Numerical Simulations of MHD Turbulence and the Solar Wind Ian Parrish UC Berkeley Collaborators: Rémi Lehe (ENS), Eliot Quataert (UCB) Einstein Fellows Symposium October 27, 2009
2 Motivation: Solar Wind Solar wind at 1 AU: Fairly collisionless MHD turbulence observed n 10 cm 3 T 10 5 K λ mfp 10 7 km v flow 700 km s 1
3 Motivation: Solar Wind Solar wind at 1 AU: Fairly collisionless MHD turbulence observed Also applies to accretion disk coronae n 10 cm 3 T 10 5 K λ mfp 10 7 km v flow 700 km s 1
4 Presentation Outline
5 Presentation Outline Motivation: The Solar Wind
6 Presentation Outline Motivation: The Solar Wind MHD Turbulence Theory and Observations
7 Presentation Outline Motivation: The Solar Wind MHD Turbulence Theory and Observations Particle Acceleration & Heating Cyclotron Resonance Landau Damping and TTMP
8 Presentation Outline Motivation: The Solar Wind MHD Turbulence Theory and Observations Particle Acceleration & Heating Cyclotron Resonance Landau Damping and TTMP Results and Application to the Solar Wind
9 MHD Turbulence Theory Hydro Turbulence: P (k) k 5/3 (Kolmogorov)
10 MHD Turbulence Theory Hydro Turbulence: P (k) k 5/3 (Kolmogorov) Incompressible MHD: Collection of Alfvén and slow waves
11 MHD Turbulence Theory Hydro Turbulence: P (k) k 5/3 (Kolmogorov) Incompressible MHD: Collection of Alfvén and slow waves Alfvén waves: v = ±v A, ω = k v A
12 MHD Turbulence Theory Hydro Turbulence: P (k) k 5/3 (Kolmogorov) Incompressible MHD: Collection of Alfvén and slow waves Alfvén waves: v = ±v A, ω = k v A Goldreich-Sridhar Theory
13 MHD Turbulence Theory Hydro Turbulence: P (k) k 5/3 (Kolmogorov) Incompressible MHD: Collection of Alfvén and slow waves Alfvén waves: v = ±v A, ω = k v A Goldreich-Sridhar Theory Critical Balance Energy cascades primarily perpendicular to magnetic field.
14 MHD Turbulence: Simulations (Cho & Vishniac, 2000)
15 MHD Turbulence: Observations Cluster spacecraft in situ fields measurements (Bale, 2005)
16 MHD Turbulence: Observations Cluster spacecraft in situ fields measurements Inertial Range: P k 5/3 (Bale, 2005)
17 MHD Turbulence: Observations Cluster spacecraft in situ fields measurements Inertial Range: P k 5/3 Below Ion Gyroradius: Kinetic Alfvén Wave? (Bale, 2005)
18 Presentation Outline Motivation: The Solar Wind MHD Turbulence Theory and Observations Particle Acceleration & Heating Cyclotron Resonance Landau Damping and TTMP Results and Application to the Solar Wind
19 Evidence for Heating in Solar Wind Helios Data Ulysses Data (Cranmer, et al, 2009) r (AU)
20 Evidence for Heating in Solar Wind Helios Data Ulysses Data Voyager Data (Cranmer, et al, 2009) r (AU) (Matthaeus, et al, 1999)
21 Evidence for Heating in Solar Wind Helios Data Ulysses Data Voyager Data (Cranmer, et al, 2009) r (AU) (Matthaeus, et al, 1999) Evidence for extended heating favors waves.
22 Evidence for Heating in Solar Wind Helios Data Ulysses Data Voyager Data (Cranmer, et al, 2009) r (AU) (Matthaeus, et al, 1999) Evidence for extended heating favors waves. Interesting heating signatures: T ion T p > T e T > T
23 Gyromotion Cyclotron Resonance
24 Cyclotron Resonance Gyromotion Electric field in phase with cyclotron motion.
25 Cyclotron Resonance Gyromotion Resonance Condition: ω k u = ±Ω Electric field in phase with cyclotron motion.
26 Cyclotron Resonance Gyromotion Resonance Condition: ω k u = ±Ω Leads to Perpendicular Heating Electric field in phase with cyclotron motion.
27 Landau Damping and Transit Time Damping Parallel Dynamics: du dt = q m E µ B
28 Landau Damping and Transit Time Damping Parallel Dynamics: du dt = q m E µ B Magnetic Moment:
29 Landau Damping and Transit Time Damping Parallel Dynamics: du dt = q m E µ B Magnetic Moment: Landau Damping: Resonance with electric field, E
30 Landau Damping and Transit Time Damping E Parallel Dynamics: du dt = q m E µ B Magnetic Moment: Landau Damping: Resonance with electric field, E
31 Landau Damping and Transit Time Damping E Parallel Dynamics: du dt = q m E µ B Magnetic Moment: Landau Damping: Resonance with electric field, E Ideal MHD, E = 0
32 Landau Damping and Transit Time Damping E Parallel Dynamics: du dt = q m E µ B Magnetic Moment: Landau Damping: Resonance with electric field, E Ideal MHD, E = 0 Transit Time Damping:
33 Landau Damping and Transit Time Damping E Parallel Dynamics: du dt = q m E µ B Magnetic Moment: Landau Damping: Resonance with electric field, E Ideal MHD, E = 0 Transit Time Damping: Resonance with magnetic field fluctuations, µ B
34 Landau Damping and Transit Time Damping µ B Parallel Dynamics: du dt = q m E µ B Magnetic Moment: Landau Damping: Resonance with electric field, E Ideal MHD, E = 0 Transit Time Damping: Resonance with magnetic field fluctuations, µ B
35 Landau Damping and Transit Time Damping µ B Parallel Dynamics: du dt = q m E µ B Magnetic Moment: Landau Damping: Resonance with electric field, E Ideal MHD, E = 0 Transit Time Damping: Resonance with magnetic field fluctuations, Results in parallel heating. µ B
36 Presentation Outline Motivation: The Solar Wind MHD Turbulence Theory and Observations Particle Acceleration & Heating Cyclotron Resonance Landau Damping and TTMP Results and Application to the Solar Wind
37 Results: Heating MHD Simulations (Athena) with test particles: MHD: Evolves turbulent cascade (256) 3 or (512) 3 Particles feel Lorentz Force: dv dt = q ( E + v B m c )
38 Results: Heating Large ρ Small ρ Gyrofrequency MHD Simulations (Athena) with test particles: MHD: Evolves turbulent cascade (256) 3 or (512) 3 Particles feel Lorentz Force: dv dt = q ( E + v B m c )
39 Results: Heating Proxy for Temperature Large ρ Small ρ Gyrofrequency MHD Simulations (Athena) with test particles: MHD: Evolves turbulent cascade (256) 3 or (512) 3 Particles feel Lorentz Force: dv dt = q ( E + v B m c )
40 Results: Heating Cyclotron ( ) resonance Proxy for Temperature Large ρ Small ρ Gyrofrequency MHD Simulations (Athena) with test particles: MHD: Evolves turbulent cascade (256) 3 or (512) 3 Particles feel Lorentz Force: dv dt = q ( E + v B m c )
41 Results: Heating Cyclotron ( ) resonance Proxy for Temperature Large ρ Small ρ Landau ( ) resonance Gyrofrequency MHD Simulations (Athena) with test particles: MHD: Evolves turbulent cascade (256) 3 or (512) 3 Particles feel Lorentz Force: dv dt = q ( E + v B m c )
42 Results: Scattering Low Velocity High Velocity Initial Condition: Delta Function in u, u.
43 Results: Scattering Low Velocity High Velocity Pitch-Angle Scattering Initial Condition: Delta Function in u, u.
44 Results: Non-thermal Heating Cyclotron Resonant Particles
45 Results: Non-thermal Heating Initial Distribution (solid) Cyclotron Resonant Particles
46 Results: Non-thermal Heating Initial Distribution (solid) Cyclotron Resonant Particles Final Distribution (dashed)
47 Results: Non-thermal Heating Initial Distribution (solid) Maxwellian with Tfinal (dotted) Cyclotron Resonant Particles Final Distribution (dashed)
48 Heating in the Solar Wind k,max k 2/3 max
49 Heating in the Solar Wind k,max k 2/3 max Solar wind near1 AU: ρ p cm; ρ e cm; Ω p 0.15 Hz Ω e 300 Hz
50 Heating in the Solar Wind k,max k 2/3 max Ωmax Solar wind near1 AU: ρ p cm; ρ e cm; Ω p 0.15 Hz Ω e 300 Hz
51 Heating in the Solar Wind k,max k 2/3 max Solar wind near1 AU: ρ p cm; ρ e cm; Ω p 0.15 Hz Ω e 300 Hz
52 Heating in the Solar Wind k,max k 2/3 max Solar wind near1 AU: ρ p cm; Ω p 0.15 Hz Max. Cyclotron Resonant Freq: ρ e cm; Ω e 300 Hz Ω max 0.02 Hz Ω p
53 Heating in the Solar Wind k,max k 2/3 max Direct cyclotron resonance does not work in the solar wind Solar wind near1 AU: ρ p cm; Ω p 0.15 Hz Max. Cyclotron Resonant Freq: ρ e cm; Ω e 300 Hz Ω max 0.02 Hz Ω p
54 Conclusions
55 Conclusions Particles with low Ω undergo strong cyclotron ( ) resonance. Particles with high Ω undergo strong Landau ( ) resonance. Heating is very efficient and can produce non-thermal distributions. Relevant to hard X-Ray production in accretion disk coronae. Direct cyclotron acceleration cannot explain solar wind.
56 Conclusions Particles with low Ω undergo strong cyclotron ( ) resonance. Particles with high Ω undergo strong Landau ( ) resonance. Heating is very efficient and can produce non-thermal distributions. Relevant to hard X-Ray production in accretion disk coronae. Direct cyclotron acceleration cannot explain solar wind. In Progress: Particle acceleration in MRI-driven turbulence.
57 Conclusions Particles with low Ω undergo strong cyclotron ( ) resonance. Particles with high Ω undergo strong Landau ( ) resonance. Heating is very efficient and can produce non-thermal distributions. Relevant to hard X-Ray production in accretion disk coronae. Direct cyclotron acceleration cannot explain solar wind. In Progress: Particle acceleration in MRI-driven turbulence. Thanks to: Chandra/Einstein Fellowship & Staff Teragrid for lots of CPU hours.
58 Supplemental Material
59 Interpolation Methods
60 Particle Integration Method
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