CEDAR 2017

Tutorial on Plasma-Neutral Interactions in the MLT-X

[MLT-eXtended from the Upper Mesosphere through the Middle Thermosphere (80-200 km)]

Jeffrey P. ThayerAerospace Engineering Sciences Department, University of Colorado

The Universality of Plasma-Neutral Interactions

Planetary Space-Atmosphere Interaction Regions

Stellar Chromospheres

Dusty Plasmas

Interplanetary Space Weather (Planetary Habitability)

Interstellar Space Weather (Exoplanets)

Tutorial Outline Earth’s Space-Atmosphere Interaction Regions (SAIR)

Weakly ionized gas description Transport Equations Ionosphere plasma motion Conductivity and Currents Frictional and Joule Heating Rates

Our Sun’s Chromosphere Weakly ionized gas description Plasma mobilities Joule Heating Rates

SAIR Plasma-Neutral InteractionsPlasma-Neutral Chemistry Plasma-Neutral Drag Forces

Plasma-Neutral Frictional Heating Plasma-Neutral Electrodynamics

Earth’s Ionosphere/Thermosphere

Plasma-Neutral Populations

Weakly Ionized Gas (or a strongly neutral gas) below 250 km –plasma-neutral interactions dominate over Coulomb interactions

Partially Ionized Gas Above 250 km – plasma-neutral and Coulomb interactions are equally important

Upper Atmosphere System of EquationsUpper planetary atmospheres must include coupled equations for the neutral gas and plasma (electron and ion) typically defined in a rotating coordinate system.

The equations become system dependent when considering the collisional aspects of the environment and the definition of an average velocity by which all higher moments are defined.

NeutralsIons

Upper Atmosphere Transport System of Equations(Schunk and Nagy: Ionospheres Physics, Plasma Physics, and Chemistry)

Taking velocity moments of the Boltzmann Equation leads to various forms of the transport equations:

5th moment (n=1, u=3, T=1): assumed drifting Maxwellian distribution with isotropic pressure and all higher order moments neglected

13th moment (n=1, u=3, T=1, q=3, τ=5) assumed small departure from Maxwellian with higher order moments expressed in terms of the five variables

20th moment (n=1, u=3, T=1, τ=5, Q=10) assumed large departure from Maxwellian with the full heat flux tensor required to adequately represent the gas or plasma behavior

Maxwell’s EquationsMaxwell Equations in vacuum

0

( ' )cE Gauss s Law

0B

( ' )B

E Faraday s Lawt

0 0 0 ( ' )E

B J Ampere s Lawt

Maxwell Equations applied to Ionosphere

0

cE

0B

0 ( )E E

0B J

Conservation of Charge

0cJt

e iions

n n

Ionosphere Ohm’s Law (in neutral frame)

Charge Neutrality|| ||P H

E Bj E EB

σ σ σ⊥⊥

′ ×′ ′= − +

Upper Atmosphere Transport System of Equations

Two main Points to Remember Throughout this Tutorial:Define your coordinate system and reference frame:

Often determined for mathematical or numerical convenience Pressure coordinates in the vertical are often used to make equations more tractable

mathematically and/or numerically Often Earth-fixed frame

Rotating reference frame

Understand your coordinate system and reference frame: Physical Interpretation

Earth-fixed frame is non-inertial frame: requires Coriolis and Centripetal accelerations Average velocity definition of the system (important for defining higher order

moments (pressure, temperature, viscosity) and describing behavior in a multiconstituent gas

Multiconstituent Momentum Eqs for a Weakly Ionized Gas

( ) ( )ii i i i i i i i i in i n

dVn m P n m g en E V B n m V Udt

υ= −∇ + + + × − −

( ) ( )ee e e e e e e e e en e n

dVn m P n m g en E V B n m V Udt

υ= −∇ + + + × − −

( ) ( )2nn n n n n n n n n ni n i

dUn m P n m g U r n m U Vdt

τ υ = −∇ −∇ + − Ω× −Ω× Ω× − −

Ions:

Neutrals:

Electrons:

11

I/T: Plasma-Neutral Collisions

Richmond, A.D., and J.P. Thayer, Ionospheric electrodynamics: A tutorial, Magnetospheric Current Systems,Geophysical Monograph Volume 118, 2000

,gyrofrequencyqBm

Ω =, ion-neutral collision frequencyinν, electron-neutral collision frequencyenν,mobilityk

νΩ

=

iΩ

eΩinν

enν

|| ||en eiν ν+

Ion and Electron Momentum Eqs for a Weakly Ionized Gas

( ) ( )ii i i i i i i i i in i n

dVn m P n m g en E V B n m V Udt

υ= −∇ + + + × − −

Ion and electron momentum equation accounts for pressure gradient, gravitational, electric, magnetic, and collisional forces

( ) ( )ee e e e e e e e e en e n

dVn m P n m g en E V B n m V Udt

υ= −∇ + + + × − −

Assume only static E- and B-fields and neutral collisions with Un=0,

( )2 3

21

1i i i

ii

k k kV E E B E B BB B Bk

= + × + • +

( )2 3

21

1e e e

ee

k k kV E E B E B BB B Bk

− = + × − • +

Ions:

Electrons:

ii

inwhere k

υΩ

=

ee

enwhere k

υΩ

=

Plasma Drift Measurements – “Frozen-In” Flux

, 2e iE BV

B⊥ ×=

, 1i ewhen k k >>

N

E

ExB

E

Ionosphere Plasma Motionand Currents

• Ion motion perpendicular to B rotates towards the electric field as collision frequency increases with decreasing altitude

• Ion magnitude perpendicular to B decreases with increasing collision frequency

2

21

1i i

ii

k kV E E BB Bk

⊥ = + × +

( )e i ej en V V⊥ ⊥ ⊥= −

• Currents perpendicular to B rotate towards the –ExBdirection

• Current magnitude increases with increasing collision frequency (to a point)

Observed E-region Ion Motion and Electron DensityWhere the Frozen-In Flux gets Slushy

N

E

2

21

1i i

ii

k kV E E BB Bk

⊥ = + × +

Currents and Pedersen Conductivity Resolved in the E-region Ionosphere

N

E

( ) ( ) ( )( )e i ej z eN z V z V⊥ ⊥⊥ = −

Currents and Neutral Winds

Thayer, J.P., Height-resolved Joule heating rates in the high-latitude E region and the influence of neutral winds, JGR 1998

Thayer, J.P., High latitude currents and their energy exchange with the ionosphere-thermosphere system, JGR 2000

Electrodynamics with Neutral Winds

( ) ( )( ) ( )e i e e i n e n e i ej en V V en V U V U en V V j′ ′ ′= − = − − − = − =

|| ||P HE Bj E E

Bσ σ σ⊥

⊥′ ×′ ′= − +

( )2 3

21

1e e e

e e ne

k k kV V U E E B E B BB B Bk

− ′ ′ ′ ′= − = + × − • +

( )2 3

21

1i i i

i i ni

k k kV V U E E B E B BB B Bk

′ ′ ′ ′= − = + × + • +

( )2 2 3 3

2 2 2 2 2 2 2 31 1 1 1 1 1e i e i e i

ee i e i e i

E B Bk k k k k kE E Bj enBk k k k B k k B

′ • ′ ′× = + − − + + + + + + + +

Ion momentum equation:

Electron momentum equation:

Current density:

IonosphericOhm’s Law (in neutral frame): nwhere E E U B′ = + ×

Interpretation of Ohm’s Law is Reference Frame Dependent

|| ||P HE Bj E E

Bσ σ σ⊥

⊥′ ×′ ′= − +

Ohm’s Law (in neutral frame): nE E U B′ = + ×

Ohm’s Law (in plasma frame): pE E V B′ = + ×

neutral plasmaσ σ≠

(Song et al., JGR 2001)

...j pressure term gravity term electric field term current density termt∂

= + + + +∂

Generalized Ohm’s Law:

Ionospheric Ohm’s Law:

Pedersen Mobility (in Neutral Frame)

Figure 12 21 1

i ep p

e i e

k kBeN k k

µ σ = = + + +

ii

ink

νΩ

= ee

enk

νΩ

=

2 21 1i e

Pi e

k kk k

µ = + + +

Pedersen Mobilities

Hall conductivity peaks in lower ionosphere below 120 km Essentially removed at night

(unless aurora)

Pedersen conductivity distributed in two regions E-region greater than F-region

during the daytime

F region greater than E region at night.

Parallel conductivity greater than transverse conductivities everywhere above 90 km.

Ionosphere Conductivity (in Neutral Frame)

PσHσ ||σ

Neutral Frictional Heating Neutral Energy Eq Ion Energy Eq

Approximate Neutral Frictional Heating

2

3...

n

niBn nn nin ii

i i

k T Tn mEm mt m U V

νδδ

− += ++

+ −∑

2

0

3

i

n n ni iB

Et

k T T m V U

δδ

=

∴ − ≅ −

2

2...

n nin nn nin ii

ni i

m V Un mEm mt

m V U

νδδ

− += ++

+ −∑

n n ni i i inn m n mν ν=

3,2

Wm

n ni i in ii

E n m V Utδ νδ

= −∑

n im m≈and

(Thayer and Semeter, JASTP 2004)

Joule Heating Rate (Neutral Frame)

Assume ke is large, valid above 80 km:

Recall, the magnitude of the ion velocity from the momentum equation is

2n ni i in i

iE n m V Ut

δ νδ

= −∑

2ni i in ii

j E n m V Uν

• = −′ ∑

22 21 1

e i pii e i

kk Ej E en E Ek k B

σ

′• = + • =′ ′ ′+ +∑

Joule Heating Rate is “Equal” to the Neutral Frictional Heating rate

( )' ' ' 'i i ei

j E en V V E= −∑

2

2 2''

1i

i i ii i

k Ej E m nk B

= Ω + ∑

( )2 222

2 2''

1i

i i ni

k EV V Uk B

= − =+

Solve for 2

2' ,E

B

2ni i in ii

j E n m V Uν

• = −′ ∑

Interpretation of Joule Heating is Reference Frame Dependent

( ) ( ) ( )2 22j e i i in i n i i in i n

i iq j E V B m n V U J m n V Uν η ν= + × + − = + −∑ ∑

Vasyliūnas, V. M., and P. Song (2005), Meaning of ionospheric Joule heating, J. Geophys. Res., 110, A02301, doi:10.1029/2004JA010615

Note:

2: , 1 90e e e

e e e

m BResistivity above kme n enυ υη = = <<

Ω

( )2

j i i in i ni

q m n V Uν= −∑

Therefore, their form agrees with the form we just derived but approached differently,

Uses plasma velocity as their rest frame Classical Joule heating

Plasma-Neutral Interactions: Solar ChromosphereW

/m2 /

nm

0 50 Wavelength (nm) 100 150 200

Chromosphere / Ionosphere Comparison

Leake, J. E.; DeVore, C. R.; Thayer, J. P.; Burns, A. G.; Crowley, G.; Gilbert, H. R.; Huba, J. D.; Krall, J.; Linton, M. G.; Lukin, V. S.; Wang, W. (2014), Ionized Plasma and Neutral Gas Coupling in the Sun’s Chromosphere and Earth’s Ionosphere/Thermosphere, Space Science Reviews, Volume 184, Issue 1-4, pp. 107-172, doi: 10.1007/s11214-014-0103-1

Earth’s Ionosphere/ThermosphereSolar Chromosphere

Weakly Ionized Gas

[ne]

[nn]

[ne]

[nn]

Solar Chromosphere Earth’s Ionosphere / Thermosphere

Plasma – Neutral CollisionsSolar Chromosphere Earth’s Ionosphere / Thermosphere

Charge Mobilities

2 2

2 21 1e i

He i

k kk k

µ = − + +

2 21 1i e

Pi e

k kk k

µ = + + +

Solar Chromosphere Earth’s Ionosphere / Thermosphere

Solar Chromosphere: Joule Heating22

, Hc p

c p

j where σσ σσ σ

= +

Summary Define and know your coordinate system and reference frame in order to

properly interpret plasma-neutral interactions, enabling more universal interpretation of: Planetary Ionospheres / Thermospheres Stellar Chromospheres

Ionospheric Ohm’s Law provides no causal relationship but simply states the current and electric field are linearly related by conductivities defined for the given reference frame.

Frictional heating may be a more appropriate description of heat transfer in the Ionosphere/Thermosphere system than Joule heating. Can have neutral, ion, and electron frictional heating. However, increased plasma

temperatures will transfer heat to the neutral gas due to temperature differentials. With some approximations this overall heat transfer to the neutrals can be equated to Joule heating (but not in the classical sense).

Leake et al. (2014), Ionized Plasma and Neutral Gas Coupling in the Sun’s Chromosphere and Earth’s Ionosphere/Thermosphere, Space Science Reviews.

Plasma-Neutral Interaction Challengesin the 80 - 200km Domain

“Missing” energy in M-I coupling (lacking adequate conductivity descriptions with dependencies on electron and neutral density)

“Transforming” energy in I-T coupling (lacking sufficient neutral wind observations to determine energy dissipation and generation )

“Modifying” dynamo processes (lacking neutral wind observations coincident with plasma measurements)

“Profiling” neutral and plasma properties in near-spatial and temporal simultaneity (lacking vertical structure description, i.e. gradients)

The MLT-X Grand Challenge Workshop:Frontier Science and Sensing

Coupling and Transport Processes from the Upper Mesosphere through the Middle Thermosphere

(80-200 km)

CEDAR 2017Challenges:

• What is the role of the neutral gas in coupling with the plasma to establishthe predominant state of the Earth’s upper atmosphere and ionosphere between 80 and 200 km?

• How do wave-induced transport, dissipation and turbulence influence the structure, composition and circulation of Earth’s upper atmosphere between 80 and 200 km?

Backup Slides

Ion Frictional Heating

Wind effects can cause appreciable decreases or increases in ion temperaturewith height

( )23n

i n i nB

mT T V UK

= + −

( )22

23 1n i

i nB i

E Bm kT TK k

′= +

+

Electron Temperature Enhancement due to E

( )2*3

ni n i

B

mT T VK

= +

Plasma-Neutral Interactions:Frictional Heating a Grand Challenge

• Grand Challenge in M-I coupling

– “Missing” Energy

• Grand Challenge in I-T Coupling

– “Transforming” Energy

The inability to adequately quantify the most variable energy source of the upper atmosphere, often exceeding EUV solar radiation in the polar regions and dramatically impacting upper atmosphere properties globally,hinders progress in many aspects of M-I and I-T coupling