[PPT] - Observation and Theory of Substorms C. Z. (Frank) Cheng (1,2), T. F. PowerPoint Presentation

SLIDE 1

Observation and Theory of Substorms

C. Z. (Frank) Cheng (1,2), T. F. Chang (2),

Sorin Zaharia (3), N. N. Gorelenkov (4)

(1) Plasma and Space Science Center, National Cheng Kung University, Taiwan (2) Department of Physics, National Cheng Kung University, Taiwan (3) Los Alamos National Laboratory, USA (4) Princeton Plasma Physics Laboratory, USA

Second LSAP Workshop, POSTECH, Korea, June 21-22, 2008

SLIDE 2

Substorm is a global magnetosphere-ionosphere phenomena of energy storage and release process!

Solar wind particles enter magnetosphere and are stored in the plasma sheet. Above certain energy threshold, plasma energy is released to cause rapid large scale change of magnetotail configuration and ionosphere aurora.

SLIDE 3

,

Auroral Arcs

SLIDE 4

,

Substorm Auroral Spiral

SLIDE 5

Substorm Dynamics

Growth Phase (~30 minutes)

– Storage of plasma and magnetic energy in plasma sheet

Expansion Phase (~ 30 minutes)

– Substorm onset: sudden release of plasma and magnetic energy – Current disruption: reduction of cross-tail current

Recovery Phase (~hours)

– Magnetosphere returns to quiet time condition

SLIDE 6

When plasma energy in the plasma sheet exceeds a threshold, substorms are triggered to release energy:

~ 1020 - 1022ergs energy is released in 102 - 103s
~ 1019 - 1021ergs energy is dissipated in ionosphere

causing awesome auroras due to particle precipitation into ionosphere

Auroral substorm is manifestation of magnetospheric substorm !

When, where and how do substorms

ccur and evolve?

(C. Z. Cheng, Space Science Rev., 2004)

SLIDE 7

– what are observational features of substorms?

?

Substorm growth phase, onset & expansion in ionosphere and plasma sheet : When & where? How do they connect?

AMPTE/CCE at ~ 8.8 RE Geotail at ~ 10 RE Region Region

SLIDE 8

Key Features of Substorms

Magnetosphere:

Growth Phase

–B field thins and becomes tail-like as pressure and cross-tail current increase in near-Earth plasma sheet – ULF instability in Pi 2 frequency range (period ~ 60s, Kinetic Ballooning Instability) is initiated in a radially localized region prior to onset

Onset – ULF instability grows

to large amplitude (δB/B ~ 0.5) at most unstable location.

Expansion Phase – spread of

turbulence region causes pressure profile relaxation current disruption, and B dipolarization. Ionosphere:

Growth Phase

– Proton and electron aurora region shrinks in width and moves equatorward – “Breakup” arc (with azimuthal mode number of ~ 200-300) appears in proton precipitation region (poleward side of proton aurora) a few minutes prior to

nset
Onset – “breakup” arc intensifies

and brightenting occurs at a local spot initially.

Expansion Phase – poleward

(mainly) and equatorward expansion of breakup arc emission and diffuse proton and electron aurora.

SLIDE 9

Substorm Observation in Plasma Sheet

Observation of substorm magnetic field turbulence, current disruption and dipolarization by AMPTE/CCE located at X ~ 8.8 RE , 23:30 MLT [Cheng and Lui, GRL, 1998].

UT

γ/ωr ∼ 0.2 ωr /ωci ~ 0.1 ULF Instability (Filtered low frequency fluctuation)

Instability is excited at ~ 23:13:30 UT

when βeq ~ 50 >> βC

MHD ~ O(1)

Substorm onset occurs at ~ 23:14:20 UT
turbulence, cross-tail current reduction,

dipolarization in expansion phase

SLIDE 10

1985 June 1 Event Wavelet Analysis

UT

Pi2 instability excited

SLIDE 11

1985 June 1 Magnetospheric Substorm Event

Lui et al., JGR, 1993.

Substorm onsets at t = 0

AMPTE/CCE
bservation at X ~

−8.8 RE, 23:30 MLT

Pressure

increases in growth phase

Prior to onset

βeq ~ 60

Pressure

decreases and βeq decreases (mainly due to dipolarization) in expansion phase

SLIDE 12

Low Frequency Instability in 86240 Event

SLIDE 13

Key Features of Magnetospheric Substorms

Growth Phase

–B field thins and becomes tail-like as pressure and cross-tail current increase in near-Earth plasma sheet – ULF instability in Pi 2 frequency range (period ~ 60s, Kinetic Ballooning Instability, γ/ω ~0.1−0.2) is initiated in a radially localized region prior to onset

Onset

– ULF instability grows to large amplitude (δB/B ~ 0.5) at most unstable location.

Expansion Phase

– spread of turbulence region causes pressure profile relaxation crosstail current reduction, and B dipolarization.

SLIDE 14

Auroral Substorm Observations

Canadian Auroral Network for the OPEN

Program Unified Study (CANOPUS)

THEMIS All Sky Imagers
FORMOSAT-2/ISUAL

SLIDE 15

Canadian Auroral Network for the OPEN Program Unified Study (CANOPUS) all sky camera

SLIDE 16

CANOPUS Observation of Substorm (2/19/96) (Voronkov et al, 2003)

Protons Hard electrons Soft electrons

– Proton and electron aurora region moves equatorward during growth phase – “Breakup” arc (557.7 nm) appears in proton precipitation region (poleward side of proton aurora) a few minutes prior to onset

SLIDE 17

Trigger Time : 2006/12/21 08:29:20.410 UT Exposure Duration : 1 s Exposure Interval : 1.4 s Filter : 630.0 nm MCP HV : 700 V

2006/12/21 event 2006/12/21 event

FOV SAT.

FORMOSAT FORMOSAT-

2/ISUAL observation

2/ISUAL observation

f
f substorm

substorm auroral auroral breakup arc breakup arc

SLIDE 18

Substorm Substorm breakup arc evolution breakup arc evolution

ISUAL successive images with 1 sec exposure were taken every 1.4

second. Breakup arc brightening begins at 08:28:24 UT. Substorm

expansion onsets at ~08:29:20 UT.

MLAT (degree) GLAT (degree) Time (UT) 2006/12/21

SLIDE 19

Prior to expansion

nset breakup

arc appears at ~ at 08:28:24 UT with azimuthal mode number m ~ 200 and westward phase velocity (Vp)~ 48 km/s.

Arc structure prior to onset of 2006/12/21 substorm auroral breakup

SLIDE 20

2006/12/21 substorm

nset arc

is located at Herang discontinuity

SLIDE 21

Quiet-time and breakup arc structures

Event Date Description 2007/01/15 Quiet time arc; m=700 ; Vp = 0 km/s 2004/08/31 Arc during storm recovery phase: m = 360; Vp = 9.3 km/s 2007/01/18 Substorm breakup arc: m=330; Vp = 38 km/s 2007/01/30 Substorm breakup arc: m=260; Vp = - 9 km/s 2006/12/21 Breakup-arc: m=220; Vp = 48 km/s

SLIDE 22

Key Features of Auroral Substorms

Growth Phase

– Proton and electron aurora region shrinks in width and moves equatorward – “Breakup” arc with azimuthal mode number of ~ 200-300 (separation distance between bright spots ~ 100-200 km) appears in proton precipitation region (poleward side of proton aurora) a few minutes prior to onset

Onset

– “breakup” arc intensifies and brightenting occurs at a local spot initially and spreads along arc.

Expansion Phase

– poleward (mainly) and equatorward expansion of breakup arc emission and diffuse proton and electron aurora.

SLIDE 23

Key Features of Substorms

Magnetosphere:

Growth Phase

–B field thins and becomes tail-like as pressure and cross-tail current increase in near-Earth plasma sheet – ULF instability in Pi 2 frequency range (period ~ 60s, Kinetic Ballooning Instability) is initiated in a radially localized region prior to onset

Onset – ULF instability grows

to large amplitude (δB/B ~ 0.5) at most unstable location.

Expansion Phase – spread of

turbulence region causes pressure profile relaxation current reduction, and B dipolarization. Ionosphere:

Growth Phase

– Proton and electron aurora region shrinks in width and moves equatorward – “Breakup” arc (with azimuthal mode number of ~ 200-300) appears in proton precipitation region (poleward side of proton aurora) a few minutes prior to

nset
Onset – “breakup” arc intensifies

and brightenting occurs at a local spot initially.

Expansion Phase – poleward

(mainly) and equatorward expansion of breakup arc emission and diffuse proton and electron aurora.

SLIDE 24

Critical Physics Issues of Substorm

How does energy build up in the plasma sheet during

growth phase?

How does plasma sheet thinning occur? by plasma pressure

increase in plasma sheet

What is substorm onset mechanism?
Is it kinetic ballooning instability (KBI)? Yes, breakup arc
How are particles accelerated to produce breakup arc? by E|| of

KBI

How does plasma sheet evolve during expansion phase?
How does an instability initially localized in near-Earth

plasma sheet lead to a global multi-scale turbulence? Not known yet

How does the turbulence cause dipolarization & current reduction?

Plasma transport

What is the role of magnetic reconnection?

Probably enhances plasma convection in growth phase, but no direct relationship with substorm onset!

SLIDE 25

Quiet-Time & Growth Phase Magnetospheres:

Profiles Along Sun-Earth Axis

Dashed lines are for typical quiet time values.
Magnetic well at ~ 7.5 RE for growth phase.

2

/ 2 B P = β

Pressure increase in plasma sheet in growth phase

α

ψ ∇ × ∇ = ∇ = × B P B J r r r : m equilibriu static

quasi

Assume

SLIDE 26

3D Magnetic Field in Quiet Time & Growth Phase

Growth Phase Quiet Time

SLIDE 27

Growth Phase Magnetosphere

Jφ β B in (nA/m2) Jφ Current sheet thickness ~ 1 RE .

SLIDE 28

P and B in Equatorial Plane

Quiet Time Field A local magnetic well at X ' – 8 RE for disturbed time case Disturbed Time Field

SLIDE 29

Field-Aligned Currents over Polar Region

Quiet Time Field Growth Phase Field

Jk (in μA/m2)

Disturbed time Birkeland currents move equatorward, are more

localized in latitude and become more intense ~ 3 μA/ m2.

Intense cross tail current region maps to transition region (1o-2o)

between R-1 and R-2 currents in the ionosphere.

SLIDE 30

Growth Phase: Cross-Tail Current density in Equator

eq iono

B P V B B J ) / ( ) / (

2 ||

∇ × ∇

=

r

volume flux tube / = = ∫ B dl V

SLIDE 31

Growth Phase: Birkeland Currents

Birkeland currents

move equatorward, are more localized in latitude and become more intense ~ 3 μA/ m2.

Intense cross tail current

region maps to transition region (1o-2o) between R- 1 and R-2 currents in the ionosphere.

KBI is localized at

center of cross tail current sheet consistent with substorm initial break up location.

SLIDE 32

Energy Consideration

Quiet-Time
Growth Phase

erg 10 7 . 2 erg 10 6 . 5 8 . 70

20 20 3

× ≈ × ≈ ≈

P B E

W W R V

erg 10 8 . 1 is phase expansion during ionosphere in n dissipatio Energy

20

× ≤ ∗

Consider a volume within two boundary fluxes L = 3.5 (θ = 57.7o) and L = 5.4 (θ = 64.5o) of the computed growth phase equilibrium

erg 10 7 . 2 erg 10 9 . 1 490

21 21 3

× ≈ × ≈ ≈

P B E

W W R V

SLIDE 33

Field Lines in Noon-Midnight Meridian

Quiet Time Field Growth Phase Field Inner boundary: L = 3.5 (θ = 57.7±); pink flux surface: L = 4.1 ( θ = 60.5±); blue flux surface: L = 5.2 (θ = 64.1±)

SLIDE 34

Magnetic Fields

Quiet Time Field Growth Phase Field Pink flux surface: L = 4.1 (θ = 60.5±); Blue flux surface: L = 5.2 (θ = 64.1±)

SLIDE 35

Ideal MHD Ballooning Instability

Y (RE ) X (RE )

BC: φ = Δ =0

Most unstable ballooning instability is located at tailward side of the cross-tail current sheet !

f 2 (mHz2) in equatorial plane

SLIDE 36

Ideal MHD Ballooning Instability:

f 2 (mHz2) Contours in Northern Polar region Most unstable ballooning instability is at the transition region between R-1 and R-2 field-aligned currents !

SLIDE 37

Kinetic Theory of Ballooning Modes

Stabilization of MHD ballooning modes [Cheng

and Lui, 1998, Cheng and Gorelenkov, 2004]:

finite ion gyroradius and trapped electron

dynamics enhance δE|| and produce δJ|| which enhances stabilizing field line tension and stabilizes MHD type ballooning modes.

Destabilization of “resonant” type kinetic

ballooning modes:

ω−ωdi = 0 wave-particle drift resonance creates

new “resonant” type KBM instability.

) / (

|| i e

V k V > > ω

SLIDE 38

Quasi-Neutrality Condition

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − > Ψ − < − Ψ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − − = Ψ Δ

∫

de de e T e et et

n F v d ω ω ω ω ω ω ω ω ) (

* * 3 1

( ) [ ]

|| 2 1 1 * 2 2 1 * 1

1 1 1 B B q T I E I G T q n T q n E n n n

e e b pi i e e e i i a e eu et eu

δ ω ω ω ω − + Φ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − + Γ − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − − Φ = Ψ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − Δ +

ω ω ω ω ω ω > Φ < > < − − = Φ ∫

de de T e et et a

n F v d E

* 3 1

[ ]

2 2 0,1 0,1 1 i * i || ||

, ) ( , ) (

1

G ,

ci i i i b i i

m T k b e b I b E

i

ω ω ω η δ

⊥ −

= = Γ Γ − Γ − Γ = Ψ −∇ =

> < > < − − =

⊥

∫

|| 2 * 3 || 1

2 B T v m n F v d B E

e e de T e et et b

δ ω ω ω ω δ

2 * 3 1

J n F v d I

di di T i i i

ω ω ω ω ω ω − − = ∫

1 * 3 2

J J k v T B q n F v d I

i i di T i i i ⊥ ⊥

− − =∫ ω ω ω ω where

max 1

/ 1 / B B R n n

e et

− = ≡

SLIDE 39

Perpendicular Ampere’s Law

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ > < − > Ψ − < − Ψ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = Ψ Δ

⊥

∫

de de T e e e et et

T v m n F v d ω ω ω ω ω ω ) ( 1 2

* 2 3 2

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Ψ Δ + Ψ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − + Φ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + − − − = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + +

2 * 2 2 2 * || 2 2 3

1 2 3 1 1 2 2 2 1 ω ω ω ω β δ ξ β β

pe a pe e e e b e e i

R I E T B q B E I

ω ω ω ω ω ω > Φ < > < − − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = Φ

⊥

∫

de de T e e e et et a

T v m n F v d E

* 2 3 2

2 > < > < > < − − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ =

⊥

∫

|| * 2 2 3 || 2

2 B T v m n F v d B E

de de T e e e et et b

δ ω ω ω ω ω ω δ

2 1 2 * 3 3

J k v T B q n F v d I

i i di T i i i

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − − =

⊥ ⊥

∫

ω ω ω ω where

3 / ) 2 / 1 ( 2

max 1 2

B B R R + =

SLIDE 40

Vorticity Equations

> < > < − − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ =

⊥

∫

|| * 2 3 || 3

2 B T v m n F v d B E

de de T e e e et et b

δ ω ω ω ω ω ω δ

)]} ( 3 1 [ ) 2 / 3 1 ( { 2 ) ( 1 2 ) ( ) 1 )( 1 ( ) (

3 2 1 2 2 * || 3 2 * 2 3 2 * 1 * 2 2 2 2 2

= Ψ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Δ + − + + − − − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − − − + Φ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + − + Φ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − + Γ − − + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ Ψ − Φ ∇

∇
⊥

ω ω ω ω ω δ ω ω ω ω ω ω ω ω ω ω ω ω R R R T q T q B B q T E I E T q T q I G B B k B m T V

Ke Be pe e i i e i i b pe a Ke Be pe e i i e pi ci i i A

r r

ω ω ω ω ω ω ω ω > Φ < > < − − = Φ

∫

de de de T e et et a

n F v d E

* 3 3

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ > < − > Ψ − < − Ψ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = Ψ Δ

∫

de de T e de et et

n F v d ω ω ω ω ω ω ω ω ) ( 1

* 3 3

where

SLIDE 41

Simplified Equations for MHD Type Mode

) (

2 2 * 2 2

= Φ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

∇

× ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

×

+ Φ − + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ Φ ∇

∇
⊥

⊥

BP k P B B k B V k S B B k B

A pi c

r r r r r r r κ β ω ω ω

⎥ ⎦ ⎤ + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − − + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − − − ⎢ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − − − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − + ≅ Φ Ψ − ≡ ω ω ω ω ω ω ω ω ω ω ω ω ω ω ω ω ω ω ω ω β

κ

2 ˆ ˆ ˆ 2 3 2 1 / 1

* * * * * * 2 * * e Be e pi de e pe i e pi i e e i pe pi e eu e c

b T q T q n n S

2 2 || 2 || || ||

), ( ,

ci i i i

m T k b i J E ω ω δ δ

⊥ ⊥

= Ψ − Φ ∇ ∇ = Ψ −∇ =

Assuming ω >> ωdi , KBM equations reduce to

SLIDE 42

Local Stability Analysis

f MHD Type Ballooning Modes

2 || 2 * )

( k S BP k k P B B k k B V

c A pi

= ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

∇

× ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

×

+ −

⊥ ⊥ ⊥ ⊥

r r r r r κ β ω ω ω

2 * )

(

A p c pi MHD c c c

V L R S ω ω ω β β − − =

Local dispersion relation At marginal stability ω ' ω*pi and critical β is given by For magnetosphere

eq 3 c 3 max max

) 10 ( and ) 1 ( , ) 10 ( , 001 . , 002 . / 1 / 1 1 β β β > ≈ ≈ ≈ ≈ = << − − ≈ O O O S n n B B For B B n n

MHD c c e eu e eu

Thus, MHD ballooning modes are stabilized!

SLIDE 43

Stabilizing Kinetic Effects on MHD Ballooning Mode

For a given electric field perturbation electrons move across B

differently from ions due to finite ion gyroradius effect and charge separation is created.

Ions move much slower than the wave phase velocity along B and is

essentially quasi-static.

Electrons move much faster than the wave phase velocity along B and

will play the role of keeping charge quasi-neutral.

Trapped electrons do not contribute much to charge redistribution due

to fast bounce motion.

Untrapped electrons play the dominant role of maintaining charge

quasi-neutrality.

Untrapped electron density is much smaller than trapped electron

density and thus an enhanced parallel electric field is created to move the untrapped electrons to maintain charge quasi-neutrality.

Enhanced parallel electric field produces enhanced parallel current and

thus enhanced field line tension, which stabilizes ballooning modes.

) / (

|| i e

V k V > > ω

SLIDE 44

Kinetic Ballooning Instability

Destabilization of “resonant” type kinetic

ballooning modes:

ω−ωdi = 0 wave-particle drift resonance

allows free energy of pressure gradient in “bad” magnetic field curvature to be released and creates new “resonant” type KBM instability.

) / (

|| i e

V k V > > ω

SLIDE 45

Resonant Kinetic Ballooning Modes

Ideal MHD Ballooning Mode Resonant KBM Assume ne (X = -6.6 RE , Y=0, Z=0) = 2 cm-3, Ti = 11 keV, Te = 5.5 keV (thus ne α P), azimuthal mode number m = 500 ωA0 = 0.03 s-1 X = − R

SLIDE 46

Resonant Kinetic Ballooning Modes

Assume ne (X = -6.6 RE , Y=0, Z=0) = 2 cm-3, Ti = 11 keV, Te = 5.5 keV, azimuthal mode number m = 500 ωA0 = 0.03 s-1

Most unstable mode at X ~ -8 RE is m = 250, f ~ 60 mHz, γ/ω

~ 0.1

If ne is larger, frequency will be lower.

(X = − R) X = −8 RE m

SLIDE 47

Kinetic Ballooning Instability:

Most unstable KBI is located at the transition region between R-1 and R-2 field-aligned currents !

SLIDE 48

Expansion Phase: Dipolarization by Pressure Reduction

Consider B and P averaged over fluctuation time scale

(>> 100 s).

Force balance:
In the near-Earth plasma sheet, a small reduction in P

leads to a large increase in B (dipolarization): P + B2/2 = constant 50 1 gives β = 50 45 6 gives β = 7.5 10% reduction in P causes B to increase 2.45 times and β to decrease 6.6 times, consistent with AMPTE/CCE

bservation!

( )

2 2

2 / B B P κ r ≈ + ∇ ⊥

SLIDE 49

Summary

How does plasma sheet thinning occur during growth

phase? Plasma sheet thinning & high βeq in near-Earth plasma sheet

is due to plasma pressure buildup.

What is substorm onset mechanism?

global Kinetic Ballooning Instability is responsible for aurora

breakup arc formation & structure observed in ionosphere & ULF instability (in Pi 2 frequency range) observed in plasma sheet.

How does plasma sheet evolve during expansion phase?