Ph.D Thesis Defense: Magnetic Reconnection as a Chondrule Heating Mechanism

Introduction
Methodology
Results
Summary
References
Appendix
Ph.D. Thesis Defense
Magnetic Reconnection as a Chondrule Heating Mechanism
Samuel A. Lazerson
University of Alaska, Geophysical Institute
November 6, 2008
Lazerson (lazersos@gmail.com) UAF GI

Introduction
Methodology
Results
Summary
References
Appendix
Introduction
Motivation
The Question
Previous Theories
The Dusty Plasma
Introduction
The process by which chondrules, the ﬁrst solid objects in the solar
system, formed is widely disputed. A series of numerical
experiments were performed in order to determine if magnetic
reconnection in the dusty plasma of the protosolar nebula could be
responsible. The following were achieved:
The ﬁrst simulations of magnetic reconnection in a dusty
plasma were conducted
A self-consistent model was forwarded for chondrule formation
via magnetic reconnection in a dusty plasma.

Introduction
Methodology
Results
Summary
References
Appendix
Introduction
Motivation
The Question
Previous Theories
The Dusty Plasma
Motivation
Chondrules are the millimeter sized spherical inclusions found in
chondrites (stony meteorites).
Chondrules in the Grassland chondrite.
The process by which
they formed is largely unknown.
They are discussed
as the ﬁrst solids in the solar system.
They are the transitional material
between dust and meter sized stones.
They present a geological
record of the conditions present in the
protosolar nebula.

Introduction
Methodology
Results
Summary
References
Appendix
Introduction
Motivation
The Question
Previous Theories
The Dusty Plasma
The Scientiﬁc Question
Can magnetic reconnection in a dusty plasma explain the heating
necessary for chondrule properties?
Stereotypical Chondrite (Sears, 2004)
4.5 By old

Introduction
Methodology
Results
Summary
References
Appendix
Introduction
Motivation
The Question
Previous Theories
The Dusty Plasma
4.5 By old
nm to mm size

Introduction
Methodology
Results
Summary
References
Appendix
Introduction
Motivation
The Question
Previous Theories
The Dusty Plasma
4.5 By old
nm to mm size
Heating rates in the range
of 2000 − 5000K/hr

Introduction
Methodology
Results
Summary
References
Appendix
Introduction
Motivation
The Question
Previous Theories
The Dusty Plasma
4.5 By old
nm to mm size
of 2000 − 5000K/hr
Multiple heating
events are recorded.

Introduction
Methodology
Results
Summary
References
Appendix
Introduction
Motivation
The Question
Previous Theories
The Dusty Plasma
4.5 By old
nm to mm size
of 2000 − 5000K/hr
Multiple heating
events are recorded.
Exposed to a magnetic
ﬁeld on the order of 1[G].

Introduction
Methodology
Results
Summary
References
Appendix
Introduction
Motivation
The Question
Previous Theories
The Dusty Plasma
Existing Theories
There have been multiple attempts to explain the properties of
chondrules through plasma and astrophysical processes
Impact Melts

Introduction
Methodology
Results
Summary
References
Appendix
Introduction
Motivation
The Question
Previous Theories
The Dusty Plasma
Existing Theories
Impact Melts
Meteor Ablation

Introduction
Methodology
Results
Summary
References
Appendix
Introduction
Motivation
The Question
Previous Theories
The Dusty Plasma
Existing Theories
Impact Melts
Meteor Ablation
Hot Inner Nebula

Introduction
Methodology
Results
Summary
References
Appendix
Introduction
Motivation
The Question
Previous Theories
The Dusty Plasma
Existing Theories
Impact Melts
Meteor Ablation
Hot Inner Nebula
Fu Orionis Outburst

Introduction
Methodology
Results
Summary
References
Appendix
Introduction
Motivation
The Question
Previous Theories
The Dusty Plasma
Existing Theories
Impact Melts
Meteor Ablation
Hot Inner Nebula
Fu Orionis Outburst
Bipolar Flows

Introduction
Methodology
Results
Summary
References
Appendix
Introduction
Motivation
The Question
Previous Theories
The Dusty Plasma
Existing Theories
Impact Melts
Meteor Ablation
Hot Inner Nebula
Fu Orionis Outburst
Bipolar Flows
Nebular Lightning

Introduction
Methodology
Results
Summary
References
Appendix
Introduction
Motivation
The Question
Previous Theories
The Dusty Plasma
Existing Theories
Impact Melts
Meteor Ablation
Hot Inner Nebula
Fu Orionis Outburst
Bipolar Flows
Nebular Lightning
Accretion Shocks

Introduction
Methodology
Results
Summary
References
Appendix
Introduction
Motivation
The Question
Previous Theories
The Dusty Plasma
Existing Theories
Impact Melts
Meteor Ablation
Hot Inner Nebula
Fu Orionis Outburst
Bipolar Flows
Nebular Lightning
Accretion Shocks
Nebular Shocks

Introduction
Methodology
Results
Summary
References
Appendix
Introduction
Motivation
The Question
Previous Theories
The Dusty Plasma
Existing Theories
Impact Melts
Meteor Ablation
Hot Inner Nebula
Fu Orionis Outburst
Bipolar Flows
Nebular Lightning
Accretion Shocks
Nebular Shocks
Magnetic Flares

Introduction
Methodology
Results
Summary
References
Appendix
Introduction
Motivation
The Question
Previous Theories
The Dusty Plasma
The Dusty Plasma
Dust Ions Electrons Neutrals Units
Number Density nk 0.1 1001 1 1x1012
m−3
Charge Number Zk 10, 000 1 1
Mass mk 1x10−16
1.67x10−27
9.11x10−31
1.67x10−27
kg
Temperature Tk 500 500 500 500 K
Plasma Frequency ωpk 0.017 41.7 56.4 s−1
Cyclotron Frequency ωck 0.0016 9600 17.6x106
s−1
Neutral Collision Frequency νkn 0.0004 102 4352 s−1
Debye Length λDk 49 49 1543 m
Inertial Length Scales c
ωpk
17.6x109
7.2x106
5.3x106
m
Magnetization c
ωck
187x109
31, 000 17 m
Plasma Parameter Λ 1
Plasma Beta β 1
Coulomb Coupling Γc 1
We make the following assumptions: σn = 5x10−11
cm2
, vTn = 2030 m/s, B = 10−4
T, and rd = 10−6
m.

Introduction
Methodology
Results
Summary
References
Appendix
Organization
DENISIS
Simulation Parameters
The Numerical Experiment
A numerical experiment is conducted using the DENISIS 4-Fluid
Dusty MHD code.
Harris-like Current Sheet
Ballistic Relaxation
Reconnective Mode
Test Particle Simulation

Introduction
Methodology
Results
Summary
References
Appendix
Organization
DENISIS
The DENISIS Code
The DENISIS (Dust Electron Neutral Ion Self-consistent
Integration Scheme) code has proven useful in studying dusty
plasmas in the space environment. (Schr¨oer et al., 1998).
Fluid Code
Dust, Ion and Neutral Continuity Equations
Electron Density (Quasineutrality)
Dust and Neutral Equations of Motion
Dust, Ion, Electron and Neutral Energy Equations
Induction Equation (intertialess Ion EOM)
Leap-Frog and Dufort Frankel Integration Schemes
3-D Nonuniform Cartesian Grid

Introduction
Methodology
Results
Summary
References
Appendix
Organization
DENISIS
Continuity Equations
∂ρd
∂t
= − · (ρd vd )
∂ρi
∂t
= − · (ρi vi )
∂ρn
∂t
= − · (ρnvn)
ρe = me
ρi
mi
−
Zd ρd
md

Introduction
Methodology
Results
Summary
References
Appendix
Organization
DENISIS
Momentum Equations
∂(ρd vd )
∂t = − · (ρd vd vd ) − (pe + pi + pd )
+ 1
4π × B × B
−νdnρd (vd − vn) − νinρi (vi − vn) − νenρe (ve − vn)
∂(ρnvn)
∂t = − · (ρnvnvn) − pn
+νdnρd (vd − vn) + νinρi (vi − vn) + νenρe (ve − vn)

Introduction
Methodology
Results
Summary
References
Appendix
Organization
DENISIS
Electron Velocity
The electron and ion velocities are related to eachother through
mobilities (µ). The current density carried by the ions and
electrons thus becomes
w = j − Zd end vd = e (ni vi − neve) .
It should now become evident that for low electron densities this
may be rewritten
w = eni vi

Introduction
Methodology
Results
Summary
References
Appendix
Organization
DENISIS
Energy Equations
1
Γi −1
∂pi
∂t = − 1
Γi −1 · (pi vi ) − pi · vi
+ mn
mi +mn
ρi νin (vi − vn)2
+ md
md +mi
ρi νid (vi − vd )2
+ mi
mi +me
ρi νie (vi − ve)2
−2 ρi νin
mi +mn
kB Ti
Γi −1 − kB Tn
Γn−1 − 2 ρi νid
mi +md
kB Ti
Γi
− kB Td
Γd −1
−2 ρi νie
mi +me
kB Ti
Γi
− kB Te
Γd −1
Ion Energy Equation shown for reference. Similar equations exist
for each of the 4 species.

Introduction
Methodology
Results
Summary
References
Appendix
Organization
DENISIS
Induction Equation
∂B
∂t = −mi c
e × pi
ρi
+ × vi × B − η 2B
−mi c
e × [νid (vi − vd ) + νin (vi − vn) + νie (vi − ve)]
Which for a depleted electron regime may be written
∂B
∂t = −mi c
e × pi
ρi
+ mi
md
Zd × ρd
ρi
vd × B
+mi c
4πe × ×B
ρi
× B − η 2B
−mi
e × {nd
ni
Zd − ni
nd
νid + Zd νin vd − νinvn}

Introduction
Methodology
Results
Summary
References
Appendix
Organization
DENISIS
Normalizations
B-Field = 0.1 G Mass Density = 1 × 10−17
kg
Time = 180 s Length = 500 × 106
m
Smallest Grid Scale = 12.5 × 106
m Velocity = 3 × 106
m/s
Normalized Values
Dust Mass Density = 1.0 Dust Charge Number = 10
Ion Mass Density = 0.1 Ion Charge Number = 1
Neutral Mass Density = 1.0 Dust Mass = 1.00
Current Sheet Thickness = 0.2 Ion Mass = 0.01
Grid Dimensions
NX = 49 x ∈ [−10, 10] Equidistant ∆Xmin = 0.41
NY = 49 y ∈ [−2, 2] Non-Equidistant ∆Ymin = 0.0125
NZ = 15 z ∈ [0, 10] Equidistant ∆Zmin = 0.67
Collision Frequencies
Dust-Neutral = 0.026 Dust-Electron = 0.0000001
Ion-Neutral = 1000 Ion-Dust = 0.00128
Electron-Neutral = 0.00 Ion-Electron = 0.00

Introduction
Methodology
Results
Summary
References
Appendix
Reconnective Mode
Resistivity
Adiabatic Index
Chondrule Heating
The simulation begins with a Harris like current sheet proﬁle. (Harris, 1962) Due to collisional interactions and
pressure variations this is not an equilibrium. An equilibrium is achieved through the use of a ballistic relaxation
technique.(Hesse et al., 1993)

Introduction
Methodology
Results
Summary
References
Appendix
Reconnective Mode
Resistivity
Adiabatic Index
Chondrule Heating
Ballistic Relaxation: Final Proﬁles I

Introduction
Methodology
Results
Summary
References
Appendix
Reconnective Mode
Resistivity
Adiabatic Index
Chondrule Heating
Ballistic Relaxation: Final Proﬁles II

Introduction
Methodology
Results
Summary
References
Appendix
Reconnective Mode
Resistivity
Adiabatic Index
Chondrule Heating
Reconnetive Mode
Three choices of reconnective mode were examined. These
included a ’Sweet-Parker’, ’Local Alfv´en’, and ’Diﬀusive
Equilibrium’ modes.

Introduction
Methodology
Results
Summary
References
Appendix
Reconnective Mode
Resistivity
Adiabatic Index
Chondrule Heating
Sweet-Parker

Introduction
Methodology
Results
Summary
References
Appendix
Reconnective Mode
Resistivity
Adiabatic Index
Chondrule Heating
Local Alfv´en

Introduction
Methodology
Results
Summary
References
Appendix
Reconnective Mode
Resistivity
Adiabatic Index
Chondrule Heating
Diﬀusive Equilibrium

Introduction
Methodology
Results
Summary
References
Appendix
Reconnective Mode
Resistivity
Adiabatic Index
Chondrule Heating
Sweet-Parker Movie

Introduction
Methodology
Results
Summary
References
Appendix
Reconnective Mode
Resistivity
Adiabatic Index
Chondrule Heating
Resistivity
The eﬀects of various resistivities on magnetic energy

Introduction
Methodology
Results
Summary
References
Appendix
Reconnective Mode
Resistivity
Adiabatic Index
Chondrule Heating
Resistivity: (Parameter Dependence)
(e) Global Resistivityη = 0.01 (f) Collisional Terms On

Introduction
Methodology
Results
Summary
References
Appendix
Reconnective Mode
Resistivity
Adiabatic Index
Chondrule Heating
The effects of various choices for the collision frequencies were
evaluated
Dust-electron collision frequency (νde) showed little effect
Dust-neutral collision frequency (νdn) showed some sensitivity
for values greater than 0.001
Ion-dust collision frequency (νid ) showed little effect
Ion-neutral collision frequency (νin) had the greatest effect

Introduction
Methodology
Results
Summary
References
Appendix
Reconnective Mode
Resistivity
Adiabatic Index
Chondrule Heating
Dust-Neutral Collision frequency
The eﬀects of various choices for the dust-neutral collision
frequency (νdn)

Introduction
Methodology
Results
Summary
References
Appendix
Reconnective Mode
Resistivity
Adiabatic Index
Chondrule Heating
Ion-Dust Collision frequency
The eﬀects of various choices for the ion-dust collision frequency
(νid )

Introduction
Methodology
Results
Summary
References
Appendix
Reconnective Mode
Resistivity
Adiabatic Index
Chondrule Heating
Ion-Neutral Collision frequency
The eﬀects of various choices for the ion-neutral collision frequency
(νin)

Introduction
Methodology
Results
Summary
References
Appendix
Reconnective Mode
Resistivity
Adiabatic Index
Chondrule Heating
Ion-Neutral Movie

Introduction
Methodology
Results
Summary
References
Appendix
Reconnective Mode
Resistivity
Adiabatic Index
Chondrule Heating
Adiabatic Index
Variation of the Adiabatic Index for the species yielded little eﬀect

Introduction
Methodology
Results
Summary
References
Appendix
Reconnective Mode
Resistivity
Adiabatic Index
Chondrule Heating
Chondrule Heating
So what is the eﬀect of reconnection on the dust particles
themselves (chondrules)?
Neutral heating on the order of 20%.
Large dust-neutral relative velocities on the order of the
Alfv´en velocity.
Enhancements of the current sheet.

Introduction
Methodology
Results
Summary
References
Appendix
Reconnective Mode
Resistivity
Adiabatic Index
Chondrule Heating
Aerodynamic Heating
We may calculate the heating of a dust particle in terms of
aerodynamic heating due to neutral drag via (Wood, 1984)
mdustCdust
dTdust
dt
=
π
2
αr2
dustρgasv3
− 4πβr2
dustσ T4
dust − T4
0
Given our parameters velocities as low as 3000 m/s will begin to
heat the dust at necessary rates for chondrule formation.

Introduction
Methodology
Results
Summary
References
Appendix
Reconnective Mode
Resistivity
Adiabatic Index
Chondrule Heating
Testparticle Subcode

Introduction
Methodology
Results
Summary
References
Appendix
Reconnective Mode
Resistivity
Adiabatic Index
Chondrule Heating
Testparticle Heating

Introduction
Methodology
Results
Summary
References
Appendix
Summary
Chondrule Formation Model
Future Work
Summary
The following has been accomplished
Multi-ﬂuid quasi-equilibrium Harris-like dusty current sheet
First simulations of magnetic reconnection in a dusty plasma
First self-consistent dusty plasma explanation of chondrule
heating

Introduction
Methodology
Results
Summary
References
Appendix
Summary
Future Work
This model of chondrule heating has succeeded in the following
ways
Produces heating of chondrules necessary for formation
Process is associated with the nebular environment
Magnetic ﬁelds are relevant to the process
The dust is accounted for as a charge carrier

Introduction
Methodology
Results
Summary
References
Appendix
Summary
Future Work
Future Work
The following future work has begun
Testing and development of a fully ionized dusty plasma code
(MHDust)
Inclusion of a neutral gas component (nMHDust)
Simulations of magnetic reconnection in other dusty plasmas
Evaluation of variable dust charge

Introduction
Methodology
Results
Summary
References
Appendix
References
1 D. Sears. The Origin of Chondrules and Chondrites. Cambridge Planetary Science, Cambridge (2004).
2 M. K. Joung, M. M. Low and D. S. Ebel. Astro. J.. 606 (2004).
3 A. Schr¨oer, G. T. Birk and A. Kopp. Comp. Phys. Comm. 112 (1998).
4 E. G. Harris. Il Nuovo Cimento. 23 (1962).
5 M. Hesse and J. Birn. J. Geo. Res. 98 (1993).
6 J. A. Wood. Earth and Plan. Sci. Lett. 70 (1984).

Introduction
Methodology
Results
Summary
References
Appendix
The Protosolar Nebula
Mobilities

Introduction
Methodology
Results
Summary
References
Appendix
Mobilities
Electron and Ion Mobilities
Parallel Hall Pederson
µ µE×B
µ⊥
Electron 4.04 × 107 9990 2.47
Ion 9.39 × 105 9960 106
vi /ve 0.232 0.997 42.9
ji /je 23.2 998 42900
Mobilities given in units of C·s
kg .

Ph.D Thesis Defense: Magnetic Reconnection as a Chondrule Heating Mechanism

Recommended

Recommended

More Related Content

Viewers also liked

Viewers also liked (20)

Similar to Ph.D Thesis Defense: Magnetic Reconnection as a Chondrule Heating Mechanism

Similar to Ph.D Thesis Defense: Magnetic Reconnection as a Chondrule Heating Mechanism (20)

Recently uploaded

Recently uploaded (20)

Ph.D Thesis Defense: Magnetic Reconnection as a Chondrule Heating Mechanism