Kelvin–Helmholtz waves at Earth’s magnetopauseShiva Kavosi, H. E. Spence, Jimmy Raeder

University of new Hampshire, Durham, NH

Kelvin Helmholtz clouds observed on Saturday, May 17, 2014 at Tupper Lake, New York

Kelvin-Helmholtz Instability in coronal mass ejections observed by SDO/AIA

Kelvin-Helmholtz Instability in Saturn's outer magnetosphere observed by Cassini

Observations of Kelvin-Helmholtz Waves in the Earth’s Magnetotail Near the Lunar Orbit , Ling, Y. et al.

Princeton Plasma Physics Laboratory, Feb 11, 2021

The research is supported from NASA(Grant no. 80NSSC18K0661), NASA Grant 80NSSC18K1365.

Kelvin–Helmholtz waves at Earth’s magnetopause

Transport of solar wind energy into a planetary magnetosphere

•  Studies of Earth’s magnetosphere provide us with a template for studying the solar wind-magnetosphere interaction in the case of other systems

•  Magnetic reconnection and growth of the Kelvin-Helmholtz (K-H) instability are two processes that promote energy transport across Earth’s magnetopause

2

MAGNETIC RECONNECTION

GROWTH OF THE KELVIN-HELMHOLTZ

INSTABILITY

time

v1 v2

Interface B1

B2

Taken from Paschmann, GRL (2008)

Overview

§ Background and KH Identification

§ KH THEMIS survey

§ Plasma transport and KHI

§ MMS electron microinjections associated with

KHI

§ Seasonal and diurnal variation of KHI and its

dawn-dusk asymmetry: New hypotheses

Kelvin–Helmholtz waves at Earth’s magnetopauseMagnetopause reconnection

Dungey, J. W., PRL, 6, 47-48, 1961.

Dungey, J. W., in Geophysics: The Earth’s Environment, eds., C. Dewitt et al., 1963.

Breakdown of ideal MHD in a thin layer around the magnetopause implies that the solar wind field and plasma has access to the magnetosphere.

Dungey (1955) proposed the idea that Kelvin-Helmholtz instability might occur at the magnetopause boundary separating solar wind and magnetosphere plasma.

Soon after:

Transport of solar wind energy into a planetary magnetosphere

•  Studies of Earth’s magnetosphere provide us with a template for studying the solar wind-magnetosphere interaction in the case of other systems

•  Magnetic reconnection and growth of the Kelvin-Helmholtz (K-H) instability are two processes that promote energy transport across Earth’s magnetopause

2

MAGNETIC RECONNECTION

GROWTH OF THE KELVIN-HELMHOLTZ

INSTABILITY

time

v1 v2

Interface B1

B2

Taken from Paschmann, GRL (2008) Hasegawa, 1975

H. Hasegawa, et al. 2004, Nature 430.

The first observationof KHI at the Earth MPreported by Otto andFairfield, 2000 usingGeotail data. Later, H.Hasegawa, et al, firstTransport of solarwind into Earth'smagnetospherethrough rolled-upKelvin–Helmholtzvortices, using Clusterdata. The growth ofKHI at themagnetopause leadto the “rolled-up”vortices

Many numerical and observational studiesinvestigate how plasma transport be achieved inassociation with the KHVs?

transverse magnetic field Bz so that the initial thermalpressure is constant in the system and plasma beta (b =thermal pressure/magnetic pressure) is set equal to 0.3.The number density profile is provided with N = N0/2{(1 +a) + (1 ! a)tanh(y/l)}, where a is the asymptotic numberdensity ratio. We varied a between 0.2 and 1.0 in order toexplore how the inhomogeneity in density affects the non-linear evolution of the K-H instability.

3. Results

[5] In the linearly growing stage, each simulation runshows the development of the eigen-mode with the growthrate as expected from the linear analysis. In the non-linearstage, however, the eigen-mode develops differently in eachrun for different a. In the simulation run with a = 0.2, thesecondary instabilities start growing at a time t = 84.38l/V0

(Figure 1B). Newly-induced waves grow at the densityinterface at the outer edge and inside the normal K-Hvortex. As a consequence of such developments of second-ary instabilities, the normal vortex structure collapses andthe system proceeds to the turbulent flow stage (Figure 1C).In the final stage of the simulation run at t = 156.25l/V0

(Figure 1D) fine structures appear with turbulent flows and

the mixing layer approaches the boundary at yb = !10l. Inthis simulation run, two characteristic properties are present:One is the collapse of the normal vortex structure and theother is that the position of the mixing layer moves towardthe -y direction from the center of the simulation domain.The former leads the system to the turbulent structure andenhances the mixing with time. The latter introduces thediffusion of fluids from the dense to the tenuous region.[6] To understand the development of the turbulent

flows, we take an energy spectrum in the x direction withintegrating in the y direction. As results, the energy spectra(Figures 2A, 2B, and 2C) with the final density profiles ofeach run (Figures 2D, 2E and 2F) show that their develop-ment depend on a. When a = 0.2, while the power of thenormal mode remains constant, the energy cascades rapidlyto the shorter wave modes as time goes on (Figure 2A).When a = 0.6, the energy also cascades to the shorterwave modes, although their peak values are rather small(Figure 2B). When a = 1.0, the energy does not cascade tothe shorter wave modes and the normal mode dominates thesystem (Figure 2C). We fitted the spectra at t = 156.25 l/V0

(thick dark red line) with power functions and evaluated thepowers for a = 0.2, 0.6, 1.0 as !1.32, !1.38, !2.49,respectively.[7] Subsequent small scale vortices born after the onset

can be explained by the baroclinic term in the equation of

Figure 1. Number density profiles with flow vectors fora = 0.2 are shown at times (A) t = 71.88l/V0, (B) t =84.38l/V0, (C) t = 89.84l/V0, and (D) t = 156.25l/V0. Theonset of secondary instabilities are observed in (B) aszoomed in the two white frames. The mushroom likestructure zoomed in (C) reminds of the development of theRayleigh-Taylor instability.

Figure 2. The energy spectra are shown in (A) for a = 0.2,(B) for a = 0.6, and (C) for a = 1.0. Time evolution isexpressed by the change in color of the line going from blueto dark red. (D)–(F) show the number density profiles withflow vectors which correspond to the energy spectra of thethick dark red lines (t = 156.25l/V0) in (A)– (C),respectively.

L02807 MATSUMOTO AND HOSHINO: ONSET OF TURBULENCE BY A K-H VORTEX L02807

2 of 4

transverse magnetic field Bz so that the initial thermalpressure is constant in the system and plasma beta (b =thermal pressure/magnetic pressure) is set equal to 0.3.The number density profile is provided with N = N0/2{(1 +a) + (1 ! a)tanh(y/l)}, where a is the asymptotic numberdensity ratio. We varied a between 0.2 and 1.0 in order toexplore how the inhomogeneity in density affects the non-linear evolution of the K-H instability.

3. Results

[5] In the linearly growing stage, each simulation runshows the development of the eigen-mode with the growthrate as expected from the linear analysis. In the non-linearstage, however, the eigen-mode develops differently in eachrun for different a. In the simulation run with a = 0.2, thesecondary instabilities start growing at a time t = 84.38l/V0

(Figure 1B). Newly-induced waves grow at the densityinterface at the outer edge and inside the normal K-Hvortex. As a consequence of such developments of second-ary instabilities, the normal vortex structure collapses andthe system proceeds to the turbulent flow stage (Figure 1C).In the final stage of the simulation run at t = 156.25l/V0

(Figure 1D) fine structures appear with turbulent flows and

the mixing layer approaches the boundary at yb = !10l. Inthis simulation run, two characteristic properties are present:One is the collapse of the normal vortex structure and theother is that the position of the mixing layer moves towardthe -y direction from the center of the simulation domain.The former leads the system to the turbulent structure andenhances the mixing with time. The latter introduces thediffusion of fluids from the dense to the tenuous region.[6] To understand the development of the turbulent

flows, we take an energy spectrum in the x direction withintegrating in the y direction. As results, the energy spectra(Figures 2A, 2B, and 2C) with the final density profiles ofeach run (Figures 2D, 2E and 2F) show that their develop-ment depend on a. When a = 0.2, while the power of thenormal mode remains constant, the energy cascades rapidlyto the shorter wave modes as time goes on (Figure 2A).When a = 0.6, the energy also cascades to the shorterwave modes, although their peak values are rather small(Figure 2B). When a = 1.0, the energy does not cascade tothe shorter wave modes and the normal mode dominates thesystem (Figure 2C). We fitted the spectra at t = 156.25 l/V0

(thick dark red line) with power functions and evaluated thepowers for a = 0.2, 0.6, 1.0 as !1.32, !1.38, !2.49,respectively.[7] Subsequent small scale vortices born after the onset

can be explained by the baroclinic term in the equation of

Figure 1. Number density profiles with flow vectors fora = 0.2 are shown at times (A) t = 71.88l/V0, (B) t =84.38l/V0, (C) t = 89.84l/V0, and (D) t = 156.25l/V0. Theonset of secondary instabilities are observed in (B) aszoomed in the two white frames. The mushroom likestructure zoomed in (C) reminds of the development of theRayleigh-Taylor instability.

Figure 2. The energy spectra are shown in (A) for a = 0.2,(B) for a = 0.6, and (C) for a = 1.0. Time evolution isexpressed by the change in color of the line going from blueto dark red. (D)–(F) show the number density profiles withflow vectors which correspond to the energy spectra of thethick dark red lines (t = 156.25l/V0) in (A)– (C),respectively.

L02807 MATSUMOTO AND HOSHINO: ONSET OF TURBULENCE BY A K-H VORTEX L02807

2 of 4

transverse magnetic field Bz so that the initial thermalpressure is constant in the system and plasma beta (b =thermal pressure/magnetic pressure) is set equal to 0.3.The number density profile is provided with N = N0/2{(1 +a) + (1 ! a)tanh(y/l)}, where a is the asymptotic numberdensity ratio. We varied a between 0.2 and 1.0 in order toexplore how the inhomogeneity in density affects the non-linear evolution of the K-H instability.

3. Results

[5] In the linearly growing stage, each simulation runshows the development of the eigen-mode with the growthrate as expected from the linear analysis. In the non-linearstage, however, the eigen-mode develops differently in eachrun for different a. In the simulation run with a = 0.2, thesecondary instabilities start growing at a time t = 84.38l/V0

(Figure 1B). Newly-induced waves grow at the densityinterface at the outer edge and inside the normal K-Hvortex. As a consequence of such developments of second-ary instabilities, the normal vortex structure collapses andthe system proceeds to the turbulent flow stage (Figure 1C).In the final stage of the simulation run at t = 156.25l/V0

(Figure 1D) fine structures appear with turbulent flows and

the mixing layer approaches the boundary at yb = !10l. Inthis simulation run, two characteristic properties are present:One is the collapse of the normal vortex structure and theother is that the position of the mixing layer moves towardthe -y direction from the center of the simulation domain.The former leads the system to the turbulent structure andenhances the mixing with time. The latter introduces thediffusion of fluids from the dense to the tenuous region.[6] To understand the development of the turbulent

flows, we take an energy spectrum in the x direction withintegrating in the y direction. As results, the energy spectra(Figures 2A, 2B, and 2C) with the final density profiles ofeach run (Figures 2D, 2E and 2F) show that their develop-ment depend on a. When a = 0.2, while the power of thenormal mode remains constant, the energy cascades rapidlyto the shorter wave modes as time goes on (Figure 2A).When a = 0.6, the energy also cascades to the shorterwave modes, although their peak values are rather small(Figure 2B). When a = 1.0, the energy does not cascade tothe shorter wave modes and the normal mode dominates thesystem (Figure 2C). We fitted the spectra at t = 156.25 l/V0

(thick dark red line) with power functions and evaluated thepowers for a = 0.2, 0.6, 1.0 as !1.32, !1.38, !2.49,respectively.[7] Subsequent small scale vortices born after the onset

can be explained by the baroclinic term in the equation of

Figure 1. Number density profiles with flow vectors fora = 0.2 are shown at times (A) t = 71.88l/V0, (B) t =84.38l/V0, (C) t = 89.84l/V0, and (D) t = 156.25l/V0. Theonset of secondary instabilities are observed in (B) aszoomed in the two white frames. The mushroom likestructure zoomed in (C) reminds of the development of theRayleigh-Taylor instability.

Figure 2. The energy spectra are shown in (A) for a = 0.2,(B) for a = 0.6, and (C) for a = 1.0. Time evolution isexpressed by the change in color of the line going from blueto dark red. (D)–(F) show the number density profiles withflow vectors which correspond to the energy spectra of thethick dark red lines (t = 156.25l/V0) in (A)– (C),respectively.

L02807 MATSUMOTO AND HOSHINO: ONSET OF TURBULENCE BY A K-H VORTEX L02807

2 of 4

① Reconnection within a rolled-up KH vortex

The KH Wave in its nonlinear stage candevelop small-scale filamentary field andcurrent structures resulting to magneticreconnection.

② Secondary Instabilities and Turbulence�

Due to the mass difference of the two regions and the centrifugal force exerted by the vortex motion, the boundary inside the rolled-up vortex becomes sensitive to the RT instability. This causes turbulence and a plasma transfer.

§ Figure a shows: The occurrence rate is 35%for near northward IMF, near 20% if the IMFlies in the equatorial plane, and about 10%for southward IMF.

§ Figure b shows: The instability maximizeswhen the magnetic field on either side ofthe shear layer is close to collinear, whichoccurs for 90 cone angle. And minimized in 0,180 cone angles.

KH Survey

Occurrence rate of KHW as a function of solar wind IMF

• The existence of KH waves at the magnetopause has been established for a long time mostly byanalyze of single event. And the KH events were considered to be relatively rare.

• A recent statistical analysis [Kavosi and Raeder, 2015] has shown that KH waves at Earth’smagnetopause are ubiquitous, occurring ∼19% of the time under all solar wind and IMF conditions.

200 300 400 500 600

20%

40%

60%

80%

100%

Perc

enta

ge o

f KH

I Occ

urre

nce

50010001500200025003000350040004500500055006000

Tota

l Eve

nts

11.9

2%

663 17

.24%

4,84

3

17.4

9%

3,28

8

22.6

8% 1,62

7

25.5

8%

1,04

0

Velocity0 5 10 15 20

20%

40%

60%

80%

100%

Perc

enta

ge o

f KH

I Occ

urre

nce

50010001500200025003000350040004500500055006000

Tota

l Eve

nts

15.1

7%

4,90

5

19.8

7%

4,07

7

23.6

1%

1,51

2

23.5

3%

476

20.5

7%

491

Density

0 4 8 12 16 20

20%

40%

60%

80%

100%Pe

rcen

tage

of K

HI O

ccur

renc

e

500100015002000

25003000350040004500

500055006000

Tota

l Eve

nts

11.2

9%

186

15.0

3%

2,44

8

17.5

6%

5,17

2

22.7

0%

2,14

1

23.3

8%

817 21

.52%

697

Mach Number0 4 8 12 16

20%

40%

60%

80%

100%

Perc

enta

ge o

f KH

I Occ

urre

nce

500100015002000

25003000350040004500

500055006000

Tota

l Eve

nts

18.0

2%

3,90

1

18.4

1%

5,73

5

20.8

9%

1,27

8

21.0

8%

351 12

.24%

196

Btot

a)

c) d)

b)

Occurrence rate of KHW as a function of solar wind plasma parameters!

a) The KH occurrence rate increases with solarwind speed.

b) At low densities there is a positive correlation,which tapers out for densities larger than 10/cc.

c) There is a positive correlation with the solarwind Alfven Mach number, which also tapers outat high ( >12) Mach numbers .

d) The IMF magnitude have only an effect forunusual high values (>16 nT).

show the relative KHW occurrence rate

show the number of 5-min KHW intervals in that bin

Detection of Kelvin-Helmholtz Vortices: Single spacecraft method

Detection of Kelvin-Helmholtz VorticesTHEMIS detection of rolled-up KH vortices on 2008 April 15

2468

101214

Ni(/c

c)

-400-300-200-100

0100

Vm(k

m/s)

-200-100

0100200

Vn(K

m/s)

-20-10

01020

Bn(n

T) Bn

05

10152025

Btot

al(nT

) |B|

0.00.10.20.30.4

PT(n

P) total

10

1001000

10000

Ion

eFlux

( ev )

10

1001000

10000

104105

106107

0800 0830 09000.00500.00660.00870.01150.01520.0200

Freq

uenc

y(Hz

)

0800 0830 09000.00500.00660.00870.01150.01520.0200

10-6

10-5

10-4

hhmm2008 Apr 15

Sun

Oct 2

6 20

:35:

46 2

014

LH• Schematic of reconnection

signatures at the trailing edge of arolled-up vortex H hyperbolae point.

• Bipolar signature at H point

• (L) is the center of vortex.

• Total pressure minimizes at the center(L) of the vortices, while it maximizes atthe hyperbolic point (H).

• The magnetosphere-to-magnetosheathtransitions is characterized by rapiddensity increases coincide with maximain the total pressure.

The vertical red dashed lines demonstrate the jumps from the magnetosphereto magnetosheath values coincide with maxima of the total pressure. Theseloci correspond to the hyperbolic points ‘H’ .

The bipolar Bn signatures are centered on the red lines, i.e. the ‘H’ points.

Kavosi, S., Raeder, J. Nat Commun 6, 7019 (2015)

13

Supplementary Table 2. Comparison between the properties of FTEs and Kelvin-Helmholtz Vortices

Signature Kelvin-Helmholtz Vortex FTE

Magnetic field

1. Bipolar BN. 2. Often has a maximum in magnetic field

strength at the edge of the vortex, with less than 10 nT magnitude.

3. Continuous bipolar BN.

1. Bipolar BN. 2. Has a magnetic field strength maximum at the core of FTE, usually larger

than 10 nT magnitude. 3. Bipolar BN separated by a

few minutes quiet.

Plasma

1. Substantial pressure perturbations, minimum at the vortex center and maximum at the edge. A large and rapid density increase

coincides approximately with a maximum in the total pressure at the edge of the vortex.

2. Usually small perturbation in VN. 3. Low-density plasma flowing faster than

sheath velocity.

1. Total pressure maxima at the FTE center.

2. Typically bipolar VN .The VN perturbation is usually larger than those seen in

KHW. 3. No accelerated low-

density plasma.

Duration

and Period

1. Continuous wave trains. 2. 1-4 minute periods.

1. Short (1-2 min) bipolar BN signatures separated by

quiet. 2. Repetition period

typically longer than 4 minutes.

Comparison between the properties of FTEs and Kelvin-Helmholtz Vortices

0.11.0

10.0100.0

Ni(/c

c)

-200-100

0100200300

Vm(km

/s)

-200-100

0100200300

Vn(K

m/s)

-30-20-10

01020

Bn(nT

) Bn

2030405060

Btota

l(nT)

|B|

0.60.81.01.21.41.61.82.0

PT(nP

)

total

10

1001000

10000

Ion eF

lux( e

v )

10

1001000

10000

103104105106107108

1140 12000.00300.00440.00640.00940.01370.0200

Freq

uenc

y(Hz)

1140 12000.00300.00440.00640.00940.01370.0200

10-610-5

10-410-3

hhmm2011 Jan 02

Thu O

ct 30

12:04

:49 20

14

Themis Observations on June 07, 2014

fraction of low-density plasma flowing faster than

magnetosheath plasma.

Themis A 2011/01/02

0 5 10 15 20 25Ion density [/cc]

-300

-200

-100

0

100

200

Vx[K

m/s

]

Detection of Kelvin-Helmholtz Vortices: Single spacecraft method

Ø The red symbols show the first part of the event (11:20-11:50 UT), which were identified as FTEsduring the FTE interval the tangential flows are mostly less than 100 km/s, which clearly separates theFTEs from KHW.

Ø The black symbols show the second part of the event (11:55-12:10 UT), which were identified as KHW.There is some low-density plasma (circled in red) that flows faster than the magnetosheath plasma (~-200 km/s), confirming that rolled-up vortices are present.

.

why KH under southward IMF occurs only at one quarter of the rate compared to northward IMF, and whether or not such waves occur only under specific conditions.

• The occurrence rate is 35% for near northward IMF, and about 10% for southward IMF.

KH Survey

Why KH under southward IMF occurs only at one quarter of the rate compared to northward IMF?

We study Kelvin-Helmholtz under southward IMF using THEMIS observations and Open GGCM simulation

Our data set shows that the majority of the events during southward IMF areirregular, short and polychromatic in compared to regular, long lasting, andmonochromatic waves under northward IMF condition.

KH under Northward IMF:Periodic and regular andmonochromatic oscillationsin density, velocity,magnetic field component,and total pressure.

KH under Southward IMF :Irregular and highfrequency, polychromatic,oscillations of density,velocity, magnetic fieldcomponent and totalpressure.

0

20406080

Ni(/c

c)

-400-200

0200400

Vm(km

/s)

-200-100

0100200300400

Vn(K

m/s)

-40-20

02040

Bn(n

T) Bn

0

20406080

Btota

l(nT)

|B|

0.51.01.52.02.53.0

PT(n

P) total

10

100

100010000

Ion eF

lux( e

v )

10

100

100010000

103104105106107

2300 2330

0.01

0.10

the peir

dens

itywv po

wf (

Hz)

2300 2330

0.01

0.10

0.1

1.0

10.0

P Tot/P

K

hhmm2014 Jun 07

Tue J

un 9

15:00

:53 20

15

FTEs KH/ NW IMFKH/SW IMF

Themis Observations on June 07, 2014 OpenGGCM simulation on June 07, 2014

Current density at equatorial plane z=0.

OpenGGCM Simulation: Constant solar wind

The simulation results also show that the KH waves under southward IMFare irregular, higher frequency, and polychromatic in compared to northward

IMF.

To effectively isolate these differences, we performed OpenGGCM global simulations for constant idealized solar wind under both northward and southward.

02468

1012

rr

-500-400-300-200-100

0100

vx

-300-200-100

0100

vy

-3-2-1012

bx

-3-2-1012

by

-20-10

01020

bz

05

101520

Bt

0.00.10.20.30.4

P_t

ot

0020 0040 01000.001

0.010

vy_w

v_po

wf (

Hz)

0020 0040 01000.001

0.010

10-410-2100102

PTo

t/PK

hhmm1997 Jan 01

Fri J

ul 2

4 22

:53:

11 2

015

05

1015

rr

-300-250-200-150-100

-50

vx

-200-150-100

-50vy

-1.0-0.50.00.51.0

bx

-1.5-1.0-0.50.00.51.01.5

by

0

10203040

bz

0

10203040

Bt

0.00.20.40.60.81.0

P_to

t

0120 0140 02000.001

0.010

vy_w

v_po

wf (

Hz)

0120 0140 02000.001

0.010

10-410-2100102

P Tot/P

K

hhmm1997 Jan 01

Fri J

ul 2

4 22

:55:

00 2

015

V=700 Km/s and Southward IMF,|B|=-5 nT V=700 Km/s and Northward IMF |B|=+5 nT

|B| 5 nT 10 nT 15 nT

Northward KH✔ KH✔ KH✔

Southward KH✔ KH✗ KH✗

Velocity 700 km/s 600Km/s

500Km/s

400Km/s

300Km/s

250Km/s

Northward KH✔ KH✔ KH✔ KH✔ KH✔ KH✔

Southward KH✔ KH✔ KH✔ KH✔ KH✗ KH✗

• KH under Northward IMF is unstable for all velocity ranges, and there is no cut off velocity.

• KH under southward are unstable only for velocity >400 km/s.

THEMIS Survey: Southward IMF

The correlation of KH waves with the solar wind plasma parameters for southward IMF

0 4 8 12 16

20%

40%

60%

80%

100%

Perc

enta

ge o

f KH

I Occ

urre

nce

0

500

1000

1500

2000

2500

3000

Tota

l Eve

nts

11.3

6%

1,68

1

10.7

5%

2,83

8

12.8

8%

660

8.64

%

162

125

Btot

200 300 400 500 600

20%

40%

60%

80%

100%

Perc

enta

ge o

f KH

I Occ

urre

nce

0

500

1000

1500

2000

2500

3000

Tota

l Eve

nts

304

8.86

%

2,32

4

10.2

0%

1,55

9

16.4

7%

765

20.0

4%

514

Velocity0 5 10 15 20

20%

40%

60%

80%

100%

120%

Perc

enta

ge o

f KH

I Occ

urre

nce

0

500

1000

1500

2000

2500

3000

Tota

l Eve

nts

8.17

%

2,24

1

11.0

7%

2,00

6

16.1

7%

736

12.9

0%

248

17.4

5%

235

Density

0 4 8 12 16 20

20%

40%

60%

80%

100%

Perc

enta

ge o

f KH

I Occ

urre

nce

0

500

1000

1500

2000

2500

3000

Tota

l Eve

nts

95

1,24

1

10.2

7%

2,46

3

17.8

0%

944

17.9

5%

351

12.9

0% 372

Mach Number

§ Themis survey shows KH under southward IMF occurs for for velocity high enough to take over the FTEs, and majority of the events occurs for velocites higher than 400 km/s.

§ Themis survey also shows KH under southward IMF occurs for only low |B|. And the occurrences rate decrease by increasing the magnetic field magnitude.

Summary

u Our data set shows that the majority of the events during southward IMF areirregular, short and polychromatic in compared to regular, long lasting, andmonochromatic waves under northward IMF.

• This might explain a few in-situ observations of KH waves under southwardIMF. One reason is that the signatures of KH under southward IMF are quitedifferent than the signatures expected for KH waves under northward IMF.This means that even if the KH waves under southward IMF have beenobserved, they have not been suitable for reporting or publication.

u Our THEMIS dataset and OpenGGCM simulations, show that KHW undernorthward IMF can occur for all solar wind IMF conditions, while KHW undersouthward IMF occurs only under specific conditions: High velocity and Low |B|.This might explain a few in-situ observations of KH waves under southward IMF.

Electron Microinjections Observed by MMS

Fennell+ [2016]

Microinjections appear to be a distinctly different phenomenon from classic substorm injections and unrelated to nightside processes

CharacteristicsEnergy range: ~50-400 keVSpatial distribution: ~8 - 12 Re on nightside (16 to 0 to 9 MLT)At dusk, energy dispersion suggests an origin at earlier MLTOccur in clusters in rapid succession (~10 per hour)Bidirectional field-aligned angular distributionsOften accompanied by ULF perturbationsPossibly observed in ions as well

Observed fairly regularly in the MMS/FEEPS duskside data First observed only at dusk, but that was largely related to MMS orbit/operationMMS orbit rearrangement and FEEPS operation change has permitted observation of microinjections in local morning MLT as well

Fennell+ [2016]

Identifying the Source Region of Microinjections

Fennell+ [2016]

There is some evidence (e.g., Kavosi+ [2018]) that duskside microinjections are related to dayside magnetopause boundary dynamics (KH waves/FTEs)

Particle tracing from the MMS location backwards in time

Impact/Importance: Microinjections could provide an additional source of seed electrons that has not yet been considered in radiation belt dynamics

Electron Pitch Angle Distributions for 21:00-25:30 UT on 6 August 2015

02468

10

Ni(/

cc)

-500-400-300-200-100

0100

Vx(k

m/s

)

-50

050

100150200250

Vy(k

m/s

)

-15-10-505

10

Bx(n

T)

-10-505

1015

By(n

T)

0.00.10.20.30.40.5

PT(n

P)

0000 0100 02000.00080.00190.00450.01070.02530.0600

Freq

uenc

y(H

z)

0000 0100 02000.00080.00190.00450.01070.02530.0600

10-6

10-5

hhmm2015 Aug 09

Wed

Nov

29

23:1

0:52

201

7

[a]

[f]

[d]

[b]

[c]

[g]

[e] subinterval 1 subinterval 2 subinterval 3

subinterval 1

subinterval 2

subinterval 3

KHW

KHW

FTE

FTE

02468

10

Ni(/

cc)

-500-400-300-200-100

0100

Vx(k

m/s

)

-50

050

100150200250

Vy(k

m/s

)

-15-10

-505

10

Bx(n

T)

-10

-505

1015

By(n

T)

0.00.10.20.30.40.5

PT(n

P)

0000 0100 02000.00080.00190.00450.01070.02530.0600

Freq

uenc

y(H

z)

0000 0100 02000.00080.00190.00450.01070.02530.0600

10-6

10-5

hhmm2015 Aug 09

Wed

Nov

29

23:1

0:52

201

7

[a]

[f]

[d]

[b]

[c]

[g]

[e] subinterval 1 subinterval 2 subinterval 3

subinterval 1

subinterval 2

subinterval 3

KHW

KHW

FTE

FTE

02468

10

Ni(/

cc)

-500-400-300-200-100

0100

Vx(k

m/s

)

-50

050

100150200250

Vy(k

m/s

)

-15-10

-505

10

Bx(n

T)

-10

-505

1015

By(n

T)

0.00.10.20.30.40.5

PT(n

P)

0000 0100 02000.00080.00190.00450.01070.02530.0600

Freq

uenc

y(H

z)

0000 0100 02000.00080.00190.00450.01070.02530.0600

10-6

10-5

hhmm2015 Aug 09

Wed

Nov

29

23:1

0:52

201

7

[a]

[f]

[d]

[b]

[c]

[g]

[e] subinterval 1 subinterval 2 subinterval 3

subinterval 1

subinterval 2

subinterval 3

KHW

KHW

FTE

FTE

KHWs[2-3 min]

KHWs + FTEs [4-5min]

FTEs[6 min]

Color-coded current density in the equatorial plane

Dusk terminator Magnetopause

MMS

Ø We used Open Geospace General Circulation Model(OpenGGCM), a global MHD model of the Earth’smagnetosphere (Raeder et al., 1998) with upstreamsolar wind input parameters from OMNI data.

Identifying the Source Region of Microinjections: OpenGGCM

Comparison of Simulation and ObservationsMMS1 FEEPS TOP side survey mode level 2 electron intensity

0.

50.

100.

150.

Clo

ck A

ngle

[deg

]

EPOCH (Timestamp)

101

102

[1/(c

m^2

s s

r keV

)]

0.2

0.3

0.4

0.5

0.6

Pto

t [nP

a]

130

keV

OMNI 1MF

MMS1 FEEPS Electron Intensity

Total Pressure OpenGGCM

[a]

[b]

[c]

[d]

[e]

0

90

180C

one

Angl

e(de

g)

0

90

180

Clo

ck A

ngle

(deg

)

1

54

107

160

130

keV

[1/(c

m^2

s s

r keV

)]

0.2

0.3

0.4

0.5

0.6

Ptot

(nPa

)

0.00200.0032

0.0050

0.0080

0.01260.0200

Freq

uenc

y[H

z]

0.00200.0032

0.0050

0.0080

0.01260.0200

0.1

1.0

0000 0030 0100 0130 0200 02300.00200.0032

0.0050

0.0080

0.01260.0200

Freq

uenc

y[H

z]

0000 0030 0100 0130 0200 02300.00200.0032

0.0050

0.0080

0.01260.0200

10-6

10-5

hhmm2015 Aug 09

Wed

May

2 0

0:28

:56

2018

Electron Flux Wavelet Power Spectrum

P –total wavelet Power Spectrum

NW IMF

Flux of 130 keV electron from MMS1

Total pressure from Simulation

OMNI IMF Clock angle

SW IMF CA ~ 900

Back-tracer and forward-tracer during the time of KHWs

[a] [b]BackwardTracing BackwardTracing

X [RE]

00- 450600 -900-

100 – 400450 – 800-

X [RE]X [RE]

Y [R

E]

MMS

150

300

450

600

750

900

Y [R

E]

MMS

Y [R

E]

X [RE]X [RE]

00 -450600 -900-

Y [R

E]

MMS

150 - 450

600- 900

[d]Forward Tracing

[c]

rectangularbox

[a] [b]BackwardTracing BackwardTracing

X [RE]

00- 450600 -900-

100 – 400450 – 800-

X [RE]X [RE]

Y [R

E]

MMS

150

300

450

600

750

900

Y [R

E]

MMS

Y [R

E]

X [RE]X [RE]

00 -450600 -900-

Y [R

E]MMS

150 - 450

600- 900

[d]Forward Tracing

[c]

Source region for electrons observed by MMS

Back-tracing shows the field-linedelectrons have drifted from the post-noon MP.

The trajectories of a 100-keV electronwith different pitch angles 15°-90° withcolored circle points where they passthe simulated MP.

Back-tracing

The positions of 100 keV electronswith different pitch angles rangingfrom 15°-90° when electrons arelaunched at the different points in thesmall box near the duskmagnetopause inner boundary layer.

Forward –tracing

Forward tracing result that theelectrons with pitch angles <60° areinjected into the magnetosphere andreach the location of MMS, whileelectrons with pitch angles ≥60° traceto locations much deeper in the tailor are lost further down the dusksidemagnetopause.

MMS/FEEPS Observations of Electron Microinjections Due

to Kelvin-Helmholtz Waves and Flux Transfer

Events: A Case Study

S. Kavosi1 , H. E. Spence 1 , J. F. Fennell 2 , D. L. Turner 2 , H. K. Connor 3 , and J. Raeder 1

1 University of New Hampshire, Institute for the Study of Earth, Oceans and Space, Durham, NH, USA, 2 The Aerospace

Corporation, El Segundo, CA, USA, 3 Department of Physics, University of Alaska Fairbanks, Fairbanks, AK, USA

Abstract The Energetic Particle Detector (EPD) suite onboard the Magnetospheric Multiscale (MMS)

spacecraft observes dispersive and repetitive uxes of high-energy (50 400 keV) electrons within the Pc5fl –

frequency band (2 8 MHz) in the dusk to midnight region of Earth s magnetotail. These microinjections are a– ’

new phenomenon in this region of the magnetosphere, presently poorly understood, but clearly a new

signature that remotely senses large-scale magnetospheric boundary dynamics. It is therefore important to

understand their properties and driver mechanisms. Here we have combined global magnetohydrodynamic

simulations and particle tracing results with the MMS EPD Fly s Eye Energetic Particle Spectrometer (FEEPS)’

observations to investigate possible origins and source regions of the electron microinjections. Our

simulation results suggest that the electron microinjections, observed in the dusk to premidnight sector,

are associated with Kelvin-Helmholtz waves (KHWs) and ux transfer events (FTEs). Energetic electronsfl

launched from a limited range of locations near the postnoon dusk magnetopause and at times when KHWs

and FTEs pass by that region have drift paths that connect with MMS and thus create time-dependent

microinjection electron signatures. Test-particle tracing results in the magnetohydrodynamic elds alsofi

support the eld-aligned nature of electron microinjections observed by MMS. Though identifying thefi

mechanism by which KHWs and FTEs might periodically inject electrons is beyond the scope of this

Journal of Geophysical Research: Space Physics

RESEARCH ARTICLE10.1029/2018JA025244

Special Section: Dayside Magnetosphere

Interaction

Key Points:

• Microinjections are a new observation

with an unknown source

• Simulations point to a source on the

postnoon magnetopause

• Simulation results sug gest

Kelvin-Helmholtz waves (KHWs) and

flux transfer events (FTEs) as the

source mechanisms for the observed

microinjections in the current

case study

Supporting Informatio n:

• Supporting Information S1

• Movie S1

• Movie S2

Correspondence to:

S. Kavosi,

shiva.kavosi@unh.edu;

kavosi.shiva@gmail.com

!!

" View in website Page 1 / 15 # $ % & ' ( )

Sorathia, K. A, et al, 2017

Direct observational evidence of sourceorigins for the observed electronmicroinjections is needed to investigate thepotential processes by which energeticelectrons near the magnetopause are injectedonto drift paths connected with theMMS/FEEPs in the dusk region of themagnetosphere.

K-H instability and Double mid-latitude reconnection

I 3D Hall-MHD simulations of K-Hinstability retaining high-latitude

stabilization

I Di↵erential advection (field lines):- at Vphase at low latitude- at 0/Vsolar wind at high latitudes

) Favorable conditions for reconnectionat mid latitudes

I Creates flux tubes closed on the Earth

but partially populated by solar wind

particles: direct entrya

I Can explain the e�cient mixing:De↵ ⇠ 109m2/s

I Double reconnection is not simplyrelated to the N-S symmetry, but to thebraiding and necessary unbraiding ofmagnetic field lines

aFaganello EPL 2012

Keppens et al.,2012, MPI-AMRVAC

Electron particle trajectories in the DMLR, as caused by the Kelvin-Helmholtz instability at the magnetopause will be studied in order to identify the acceleration mechanisms.

Ongoing research on Identifying the energization mechanism with KHV

Auroral Vortex Observations

DMSP SSUSI FUV image showing auroral bead structure at13–18 MLT when Kelvin-Helmholtz vortices were simultaneously observed at the magnetopause boundary on the dusk flank by THEMIS C on April 23, 2008 09:35–09:43 UT. These structures are thought to be associated with Kelvin-Helmholtz vortices. MLT, magnetic local time.

Kelvin–Helmholtz instability and Aurora beads

1. IntroductionVelocity shears in the magnetopause boundary layer of Earth and other planets have been correlated with auroral arcs and field-aligned currents (Lundin & Evans, 1985; Sonnerup, 1980). Free energy from the shear is also known to drive Kelvin-Helmholtz instabilities (KHIs) (Johnson et  al.,  2014) leading to the slow development of Kelvin-Helmholtz (KH) vortex structures (H. Hasegawa et al., 2006, 2009). Some of the most commonly observed auroral features are folds and vortex-like curls (Hallinan & Davis, 1970). Periodic brights spots have been detected by the ultraviolet (UV) imager on the Viking spacecraft (Lui et al., 1989; Potemra et al., 1990). Lui et al. (1989) suggested that the bright spots may be associated with the KHI, which couples to the ionosphere through a field-aligned current system. Figure 1a shows an example of the au-roral bead structures detected by the DMSP SSUSI FUV instrument (Paxton et al., 1993) when a KH vortex was simultaneously observed at the magnetopause boundary. Recently, the Cassini spacecraft has detected the presence of bright auroral substructures with a characteristic size ranging from 500 km to thousands of km in the prenoon sector (Grodent et al., 2011) as shown in Figure 1b. The fragmentation of the main ring of emission into small-scale spots appears to be associated with structuring of the field-aligned current system based on magnetic field perturbations observed with Cassini/MAG (Delamere et al., 2013; Talboys, Arridge, Bunce, Coates, Cowley, & Dougherty, 2009; Talboys, Arridge, Bunce, Coates, Cowley, Dougherty et al., 2009; Talboys et al., 2011). Such field-aligned currents naturally develop as KH vortices twist magnetic field lines leading to the suggestion that the vortices result from KHI.

The currents and auroral precipitation associated with KH structures are controlled by the coupling of the magnetopause boundary layer with the ionosphere (Echim et al., 2007, 2008; Lotko et al., 1987; Lyons, 1980; Wei & Lee, 1993). Ionospheric currents are driven by the electric field of the vortex, which maps into the ionosphere. Vortices can drive upward currents in the center of the vortex, and field-aligned potential drops that develop to carry the current can accelerate electrons, which precipitate in the ionosphere. In the case of shear layers, it has been shown that physical properties of the current generator can be inferred from the ionospheric signatures (Echim et al., 2019; Simon Wedlund et al., 2013). In this paper, we examine how the boundary layer and ionospheric parameters control the currents and precipitation, and we examine the differences between vortex driven currents and shear flow driven currents.

Abstract Auroral bright spots have been observed at Earth, Jupiter, and Saturn in regions that map to the magnetopause boundary layer. It has been suggested that the bright spots are associated with the Kelvin-Helmholtz (KH) instability. We utilize a quasistatic magnetosphere-ionosphere coupling model driven by a vortex in the boundary layer to determine how the field-aligned current structure depends on ionospheric and boundary layer parameters. We compare vortex induced currents with shear-flow induced currents. We find that the strength of the maximum currents are comparable, but the structure is significantly different. For a vortex, the current and electron precipitation maximize when the vortex size mapped to the ionosphere is approximately 1.5L, where is the auroral scale length, ΣP is the Pedersen conductivity, and κ is the Knight parameter. For a vortex, the current width provides a direct measure of the size, ∆, of the boundary layer structure, while the current width of shear-flow aurora is generally determined by the larger of ∆ or L. For comparison with observations, an event is considered where auroral bright spots in the ionosphere are detected by DMSP SSUSI FUV when KH structures are observed on the dusk flank by THEMIS.

JOHNSON ET AL.

© 2021. American Geophysical Union. All Rights Reserved.

Field-Aligned Currents in Auroral VorticesJay R. Johnson1 , Simon Wing2 , Peter Delamere3 , Steven Petrinec4 , and Shiva Kavosi5 1Andrews University, Berrien Springs, MI, USA, 2Applied Physics Laboratory, Johns Hopkins University, Laurel, MD, USA, 3Geophysical Institute, University of Alaska, Fairbanks, AK, USA, 4Lockheed Martin, Advanced Technology Center, Palo Alto, CA, USA, 5University of New Hampshire, Durham, NH, USA

Correspondence to:J. R. Johnson,jrj@andrews.edu

Citation:Johnson, J. R., Wing, S., Delamere, P., Petrinec, S., & Kavosi, S. (2021). Field-aligned currents in auroral vortices. Journal of Geophysical Research: Space Physics, 126, e2020JA028583https://doi.org/10.1029/2020JA028583

Received 13 AUG 2020Accepted 1 DEC 2020

10.1029/2020JA028583RESEARCH ARTICLE

1 of 15

Ongoing project: We currently working on ionospheric signature of KHWS using Open GGCM simulation.

Seasonal and diurnal variation of Kelvin-Helmholtz Instability at the Earth’s Magnetopause

January February March April May June July August Septemb.. October November December

KH MPC KH MPC KH MPC KH MPC KH MPC KH MPC KH MPC KH MPC KH MPC KH MPC KH MPC KH MPC

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Occ

urre

nce

of K

HI

90.94%

9.06%

10.35%

89.65%

11.51%

88.49%

15.71%

84.29%

13.11%

86.89%

92.62%

7.38%

92.37%

7.63%

92.98%

7.02%

13.65%

86.35%

10.61%

89.39%

91.75%

8.25%

93.32%

6.68%

Annual variation WavekindKHMPC

MMS

THM

The results present a comprehensive statistical study to investigate KH occurrence and its distributionalong the magnetosphere using THEMIS and MMS data during one solar cycle, 2007-2019.

THEMIS probes P3, P4, P5, and MMS orbit during 2016-2019 are in the dawn-dusk side of themagnetosphere when MMS is placed in a way that is in opposition to THEMIS, which makes the best dataset to study KHWs dawn-dusk asymmetry.

As shown, the occurrence rate is maximizing during equinoxes, and the minimum occurs during solstices

The KHI occurrence rate during equinoxes is twice greater than thesolstices. The trends shown in figure 1 is in agreement with previouslyreported results by Boiler and Stolov [1970]. Their model falls into theequinoctial class of hypotheses. It proposes that the diurnal and annualvariation of the earth's dipole angle causes a modulation of Kelvin-Helmholtz instability at the flank magnetopause. Boiler and Stolovsuggested that the semiannual variation of geomagnetic activity isassociated with Kelvin Helmholtz instability variation at the earthmagnetopause. They showed that according to theory, KHI dispersionrelation, the probability of KHI varies by the seasonal changes of theorientation of the earth's magnetic dipole to the solar wind flow.

Seasonal and diurnal variation of Kelvin-Helmholtz Instability at the Earth’s Magnetopause

angle YM is 90

KH&vortex&at&the&Earth’s&magnetopause&

! At the planetary magnetopause, the velocity shear between solar wind and magnetospheric plasmas increases with down tail distance.

"KH vortices would grow along the tail-flank magnetopause.

" Indeed, in-situ observations have confirmed the rolled-up vortices there.

[e.g., Fairfield et al., 2000; Hasegawa et al., 2004, 2006, using Geotail, Cluster, THEMIS].

Q. Can the vortex-induced reconnection also occur there?

[Hasegawa et al. ,2006]�[Fairfield et al., 2000]

Equinoxes YM =0 Magnetospheric field lines can not excert stabilizing influence on KHI

Solstices YM =340 and Magnetospheric field lines can excert maximum stabilizing influence on KHI.

The angle YM between the local velocity sheer and the magnetic fields.

when the dipole is along the z axes and perpendicular to the solar wind stream, i.e., equinoxes

If is 90, the magnetosphere magnetic field lines cannot exert stabilizing influences on velocity sheer, and the magnetospheric term is zero. In this case, the inequality becomes in favor of the KH instability., i.e., equinoxes.

Seasonal and diurnal variation of Kelvin-Helmholtz Instability at the Earth’s Magnetopause

KH

1 3 5 7 9 11 13 15 17 19 21

0%

5%

10%

15%

Occu

rren

ce o

f KHI

16.18%

5.88%

6.07%4.96%

4.23%3.49%

13.05%

3.31%

12.32%

2.39%

9.56%

2.02%1.65%

11.21%

0.74%0.92%

December Solistic

KH

1 3 5 7 9 11 13 15 17 19 21 23

0%

5%

10%

15%

Occu

rren

ce o

f KHI 11.40%

4.53%

10.70%

4.07%

5.70%

3.14%

3.02%

6.51%

2.79%

2.79%

2.79%

9.07%

2.44%

7.09%

8.60%

1.05% 1.16%1.74%

1.74%

8.26%

1.40%

Spring Equinox

KH

1 3 5 7 9 11 13 15 17 19 21 23

0%

5%

10%

15%

Occu

rren

ce o

f KHI

14.89%

6.00%6.33%

6.78%

4.78%7.33%

4.11%

7.89%8.22%

1.33% 1.56%

3.00%2.00%

2.22%

9.33%

Fall Equinox

KH

1 3 5 7 9 11 13 15 17 19 21 23

0%

5%

10%

15%

Occu

rren

ce o

f KHI

9.56%

16.95%

6.04%

11.91%

1.85%

4.70%

12.08%

4.03%

2.85%

3.69%

13.09%

13.26%

June solstice

Diurnal variations of KHI occurrences during (a) Winter solstice (b) summersolstice.(c) Spring Equinox and (d) Fall Equinox. The red line shows the line plot ofthe variations and the gray dotted line shows the trend lines for comparison withtheory.least unstable situation at the flanks during the equinoxes occurs

when YM at the maximum angle, which is 78.5- or 101.5-degree during the equinox.

Most unstable situation

The most unstable configuration at solstices occurs when it is YM 78 and 102 degrees.

The least unstable during solstices when is 55 and 125.

Y [Re]

X[Re]

Y [Re]

X[Re]

Y [Re]

X [Re]

Y

How dipole tilt angle affect KHI distribution along the magnetosphere?

Q1 Q2 Q3 Q4

KH MPC KH MPC KH MPC KH MPC

Dawn SouthernHemisphere

NorthernHemisphere

Dusk SouthernHemisphere

NorthernHemisphere

0%

50%

100%

Occu

rrenc

e of K

HI

0%

50%

100%

Occu

rrenc

e of K

HI0%

50%

100%

Occu

rrenc

e of K

HI

0%

50%

100%

Occu

rrenc

e of K

HI

97.25%

2.75%

94.13%

5.87%13.64%

86.36%

11.23%

88.77%

12.83%

87.17%

12.54%

87.46%94.08%

5.92%

90.32%

9.68% 13.97%

86.03%93.91%

6.09%

100.00%

100.00% 98.77%

1.23%10.40%

89.60% 94.95%

5.05%

Fiscal Quarters-35

Dawn Dusk

0

Dawn Dusk

KH MPC KH MPC KH MPC KH MPC

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

50%

55%

60%

65%

Perce

ntag

e of K

HI oc

curre

nce

57.33

%

6.62%

31.50

%

2.48%

31.67

%

4.38%

58.64

%

7.39%

WavekindKHMPC

Northern Hemisphere Southern Hemisphere

The percentage of KHI occurrence broken down by dipole tilt angle and dawn-dusk

This implies that most of the KHI events in ourdataset are observed on the dawn flank duringnegative dipole tilt and on the dusk flank duringpositive

• This scatterplot over the magnetopause serves to visualize the data distribution over the entire set for the south and north hemisphere.

• Normalized occurrence rates indicate that KHI in the northern hemisphere favors the dusk sector when the dipole tilt is negative and favor dawn when the dipole tilt is positive and vice versa for the southern hemisphere.

• Most events with negative dipole tilt occur in the dawn sector, and with positive dipole, tilt occur on dusk sector events in the southern hemisphere.

The dependence of KHWs locations on the geomagnetic dipole tilt angles for northern, and southern hemispheres.

Q1 Q2 Q3 Q4

KH MPC KH MPC KH MPC KH MPC

Dawn SouthernHemisphere

NorthernHemisphere

Dusk SouthernHemisphere

NorthernHemisphere

0%

50%

100%

Occu

rren

ce of

KHI

0%

50%

100%

Occu

rren

ce of

KHI

0%

50%

100%

Occu

rren

ce of

KHI

0%

50%

100%

Occu

rren

ce of

KHI

97.25%

2.75%

94.13%

5.87%13.64%

86.36%

11.23%

88.77%

12.83%

87.17%

12.54%

87.46%94.08%

5.92%

90.32%

9.68% 13.97%

86.03%93.91%

6.09%

100.00%

100.00% 98.77%

1.23%10.40%

89.60% 94.95%

5.05%

Fiscal Quarters-35

Dawn Dusk

0

Dawn Dusk

KH MPC KH MPC KH MPC KH MPC

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

50%

55%

60%

65%

Perc

enta

ge of

KHI

occu

rren

ce

57.33%

6.62%

31.50%

2.48%

31.67%

4.38%

58.64%

7.39%

WavekindKHMPC

Seasonal and diurnal variation of Kelvin-Helmholtz Instability at the Earth’s Magnetopause

The KHI occurrence vs fiscal Quarter and dawn/dusk and north-south hemisphere.

• The seasonal dependence of KHWs locations (KHI unstable regions)along the magnetopause at dawn-dusk and southern and northernhemispheres.

• It is shown how the location of KHWs is distributed alongmagnetopause in dawn-dusk and south and north direction duringfiscal quarters.

• KHWs are observed in the southern hemisphere on the dawn flankduring Q3 and Q4 (July-December) and on the dusk flank during Q1,Q2, and vice versa for the northern hemisphere.

• In the northern hemisphere, most of the events occur on the dawnflank during Q1 and Q2 and dusk flank during Q3.

• The dawn-dusk asymmetry is opposite in the southern and northernhemispheres. It is also reverse during the second half of the year.

• The simple explanation is that during the first six months (WinterSolstice-Spring equinox), the sun is on the right side of the earth, andthe second 6 months is on the left side of the earth.

As Earth orbit around the Sun and its axis, the angle between the Z-axis in (GSM) coordinate system and the Y-axis in, q,and the angle Y between the Earth-Sun line and the dipole axis of the Earth changes. The semiannual and diurnalvariation of these two angles plays a vital role in geomagnetic activities.

The equinoctial hypothesis is based on the anglebetween the Earth-Sun line and the Earth's dipole axis,j , cos j .

Equinoctial hypothesis:

The earth's axis of rotation The earth’s dipole axes

R-M effect: The angle between Z-axis in (GSM) coordinate system and Y-axis in the (GSEQ) coordinate system plays an important role is the controlling factor of geomagnetic activity.

M. Lockwood et al.: J. Space Weather Space Clim. 2020M. Lockwood et al.: J. Space Weather Space Clim. 2020

Seasonal Variation of KHI occurrence with different different IMF polarities

January February March April May June July August Sept.. October November December

KH MPC KH MPC KH MPC KH MPC KH MPC KH MPC MPC KH MPC MPC KH MPC KH MPC KH MPC

0%

20%

40%

60%

80%

100%

Occ

uren

ce o

f K

HI

91.79%

8.21%

25.97%

74.03%

29.00%

71.00%

12.81%

87.19%

14.50%

85.50%

93.16%

6.84%

100.00%

90.91%

9.09%

100.00%

23.89%

76.11%

10.94%

89.06%

90.69%

9.31%

2007-2012

January February March April May June July August September October November December

KH MPC KH MPC KH MPC KH MPC KH MPC KH MPC KH MPC KH MPC KH MPC KH MPC KH MPC KH MPC

0%

20%

40%

60%

80%

100%

Occ

urre

nce

of K

HI

10.67%

89.33% 98

.52%

1.48%

91.09%

8.91% 16.44%

83.56%

12.35%

87.65%

92.41%

7.59%

92.12%

7.88%

93.67%

6.33% 14.41%

85.59%

93.52%

6.48%

94.45%

5.55%

94.28%

5.72%

2013-2019

2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018

-5

0

5

10

15

20

25

30

35

40

Avg.

BY

11.73

36.21

-0.65 -0.56

0.030.250.02

5.75 5.24

7.04 6.97

0.44

January February March April May June July August Sept.. October November December

KH MPC KH MPC KH MPC KH MPC KH MPC KH MPC MPC KH MPC MPC KH MPC KH MPC KH MPC

0%

20%

40%

60%

80%

100%

Occ

ure

nce

of

KH

I

91.79%

8.21%

25.97%

74.03%

29.00%

71.00%

12.81%

87.19%

14.50%

85.50%

93.16%

6.84%

100.00%

90.91%

9.09%

100.00%

23.89%

76.11%

10.94%

89.06%

90.69%

9.31%

2007-2012

January February March April May June July August September October November December

KH MPC KH MPC KH MPC KH MPC KH MPC KH MPC KH MPC KH MPC KH MPC KH MPC KH MPC KH MPC

0%

20%

40%

60%

80%

100%

Occ

urr

ence

of

KH

I

10.67%

89.33% 98.52%

1.48%

91.09%

8.91% 16.44%

83.56%

12.35%

87.65%

92.41%

7.59%

92.12%

7.88%

93.67%

6.33% 14.41%

85.59%

93.52%

6.48%

94.45%

5.55%

94.28%

5.72%

2013-2019

One solar cycle IMF By

Solar Minimum Solar Maximum

The IMF polarity is one of the most important parameters when investigating the seasonal and diurnal variation of geomagnetic activity. Seasonal and Diurnal Variation of Kelvin-Helmholtz instability varies during different IMF polarities

Seasonal Variation of KHI occurrence/dawn-dusk asymmetry with different IMF polarities:

Dawn Dusk

KH MPC KH MPC

0%

20%

40%

60%

80%

100%Oc

curr

ence

of K

HI

16.17%

83.83%

11.01%

88.99%

2007-2012

Dawn Dusk

KH MPC KH MPC

0%

20%

40%

60%

80%

100%

Occu

rren

ce o

f KH

91.02%

8.98%

90.52%

9.48%

2013-2019

-40 -20 0 20

KH MPC KH MPC KH MPC KH MPC

Dawn SouthHemisphere

NorthHemisphere

Dusk SouthHemisphere

NorthHemisphere

0%

50%

100%

Occu

rren

ce o

f KHI

0%

50%

100%

Occu

rren

ce o

f KHI

0%

50%

100%

Occu

rren

ce o

f KHI

0%

50%

100%Oc

curr

ence

of K

HI

15.49%

84.51%93.39%

6.61%

100.00%

100.00% 94.17%

5.83%16.92%

83.08%

100.00%

92.33%

7.67% 13.48%

86.52%

25.00%

75.00%

100.00%

11.02%

88.98% 95.12%

4.88%

By WavekindKHMPC

Dawn Dusk

KH MPC KH MPC

0%

20%

40%

60%

80%

100%

Occu

rren

ce of

KHI

16.17%

83.83%

11.01%

88.99%

2007-2012

Dawn Dusk

KH MPC KH MPC

0%

20%

40%

60%

80%

100%

Occu

rren

ce of

KH

91.02%

8.98%

90.52%

9.48%

2013-2019

-40 -20 0 20

KH MPC KH MPC KH MPC KH MPC

Dawn SouthHemisphere

NorthHemisphere

Dusk SouthHemisphere

NorthHemisphere

0%

50%

100%

Occu

rren

ce of

KHI

0%

50%

100%Oc

curr

ence

of KH

I

0%

50%

100%

Occu

rren

ce of

KHI

0%

50%

100%

Occu

rren

ce of

KHI

15.49%

84.51%93.39%

6.61%

100.00%

100.00% 94.17%

5.83%16.92%

83.08%

100.00%

92.33%

7.67% 13.48%

86.52%

25.00%

75.00%

100.00%

11.02%

88.98% 95.12%

4.88%

By WavekindKHMPC

The KHI occurrence rate is maximum at Dawn southern hemisphere and dusk northern hemisphere with its preference for the dawn-side flank in the southern hemisphere when IMF By is negative and for By positive is reversed.

KHI dawn-dusk asymmetry solar minimum, and solarmaximum. The asymmetry of KHI and its preference fordawn-side during solar minimum, 2007-2012, whenaverage IMF By<0. and its preference for the dusk-sideflank during solar maximum, 2013-2019, when averageIMF By is positive, By>0.

KHI occurrence and spatial distribution along the magnetopause is controlled by IMF By polarity, Angle j and q

Bygs𝑚 = Bygseq cos j + q + 𝐵𝑧𝑔𝑠𝑒𝑞 𝑠𝑖𝑛 j + q

Bzgs𝑚 = −Bygseq sin (j + q) + 𝐵𝑧𝑔𝑠𝑒𝑞 𝑐𝑜𝑠(j+q)

GSM to GSEQ Coordinate transformation

Seasonal and diurnal variation of Kelvin-Helmholtz Instability at the Earth’s Magnetopause: OpenGGCM

Seasonal and diurnal variation of Kelvin-Helmholtz Instability at the Earth’s Magnetopause: OpenGGCM

• KHWs are observed in the dawn flank northern hemisphere and dusk flank southern hemisphere during Q1 and Q2 (Feb-June) and vise versaduring Q3 and Q4 (July-December) and on the dusk flank during Q3, Q4, and vice versa for the northern hemisphere.

Seasonal and diurnal variation of Kelvin-Helmholtz Instability at the Earth’s Magnetopause: OpenGGCM

Conclusions • KHI strongly depend on the dipole tilt angle.

• Kelvin–Helmholtz waves (KHWs) occurrence rates and locations exhibit asemiannual variation; the rate maximizes at the equinoxes and minimizes at thesolstice.

• The dawn-side-northern hemisphere preference at the equinoxes and dusk-side -southern hemisphere preference at the solstices is controlled by both the dipole tiltangle and the polarity of Interplanetary magnetic fields (IMF) By.

• KHW occurrence and dawn-dusk asymmetry can be attributed to the equinoctial andR-M effect hypothesis, respectively.

• Our results are consistent with the prediction, derived with MHD simulation.

Princeton Plasma Physics Laboratory, Feb 11, 2021

Kelvin Helmholtz clouds observed on Saturday, May 17, 2014 at Tupper Lake, New York

Kelvin-Helmholtz Instability in coronal mass ejections observed by SDO/AIA

Kelvin-Helmholtz Instability in Saturn's outer magnetosphere observed by Cassini

Observations of Kelvin-Helmholtz Waves in the Earth’s Magnetotail Near the Lunar Orbit , Ling, Y. et al.

Thank you