Magnetospheric Cavity Modes Driven by Solar Wind Dynamic Pressure Fluctuations: Initial results from LFM simulations

Seth G. Claudepierre (Dartmouth College)Scot R. Elkington (LASP/CU)Mike Wiltberger (NCAR/HAO)

Solar Wind Driving of ULF Pulsations

SW SW

ULF Waves Driven by Kelvin-Helmholtz Instability

ULF Waves Driven by Solar Wind Dynamic Pressure Fluctuations

* in this talk, ULF means frequencies less than 20 mHz or so

ULF Pulsations and the Radiation Belts

ULF pulsation power is well-correlated with RB electron flux enhancements (e.g. Rostoker, 1998).

Enegization and transport of RB electrons via ULF waves is mediated through a drift-resonant type interaction (Elkington, 1999; Hudson, 2000):

An electron drifting in the equatorial plane with drift frequency ωd can be energized by a ULF wave with frequency ω = mωd where m is the azimuthal mode number of the wave.

We need: frequency and azimuthal mode number spectrum of the ULF waves

ULF Pulsations and the Radiation Belts

Physical characteristics of magnetospheric ULF waves known to be important for energization and transport of radiation belt electrons:

(i) The frequency spectrum at the discrete frequencies ω = mωd where ωd is the drift frequency of the interacting electron and m is

(ii) The azimuthal mode number of the interacting wave

(iii) The radial extent and

(iv) The azimuthal extent of the ULF waves determines the rate and location at which energization can occur.

(v) The direction of propagation of the ULF waves

A ULF wave with discrete spectral peaks at a particular ω and m determines the drift frequency of electrons that can be energized

EandB

t

BMEvq

dt

dWzD

Solar Wind Driving of ULF Pulsations

SW SW

ULF Waves Driven by Kelvin-Helmholtz Instability

ULF Waves Driven by Solar Wind Dynamic Pressure Fluctuations

* in this talk, ULF means frequencies less than 20 mHz or so

There is a strong correlation between ULF wave power in the magnetosphere and solar wind speed (e.g. Mathie and Mann, 2001).

This observed correlation is often attributed to the Kelvin-Helmholtz instability at the magnetopause

ULF Waves Driven by KHI

ULF Waves Driven by KHIClaudepierre et al., JGR 2008, 113, A05218, doi:10.1029/2007JA012890.

• KH waves generated at both the MP and the IEBL (near dawn and dusk flanks)

over a wide range of Vsw (400-800 km/s); flow vortices at IEBL

• KH wave amplitude depends on Vsw (increases as Vsw increases)

• f ε [5, 10] mHz (and wave frequency is dependent on Vsw)

• λ ε [3, 6] Re and Vphase ε [150, 375] km/s (both dependent on Vsw)

• azimuthal mode numbers, m ≈ 15 (independent of Vsw)

• coupled oscillation of both KH modes (and the entire dawn/dusk flank LLBL)

• KH waves could resonant with radiation belt electrons in the 500 keV range

Solar Wind Driving of ULF Pulsations

SW SW

ULF Waves Driven by KHI ULF Waves Driven by SW Pdyn Fluctuations

ULF Waves Driven by SW Pdyn Fluctuations

Several authors have noted that ULF variations In the solar wind number density can directly drive ULF pulsations in the magnetosphere (e.g. Kepko and Spence, 2003).

The LFM Global MHD Simulation

Lyon-Fedder-Mobarry (LFM): single fluid, ideal MHD equations on 3D grid

outer boundary condition: solar wind

inner boundary condition: ionosphere

computational grid: non-orthogonal, distorted spherical mesh (106x48x64)

numerics: finite volume, 8th order spatial differencing, Adams-Bashforth time-stepping.

caveats: no ring current, plasmasphere or radiation belts

Run the LFM with idealized solar wind input conditions to study the resultant magnetospheric ULF pulsations.

In this study, we examine the magnetospheric response to upstream solar dynamic pressure fluctuations, both monochromatic and broadband.

We examine 4 LFM simulations: three under monochromatic Pdyn driving (f = 5, 10, and 15 mHz) and one under quasi-broadband driving (f in 0 to 20 mHz)

Study Outline and Objectives

SW input parameters: Vx = -600 km/s; Bz = -5 nT; Bx = By = 0; Vy = Vz = 0

…..and number density and sound speed….………

ULF Waves Driven by SW Pdyn Fluctuations

SW

)sin()( 0 tCntn Monochromatic input density time series:

- 3 monochromatic simulations (f = 5, 10, 15 mHz)- 20% oscillation amplitude on top of a background density (n0) of 5 particles/cc (i.e. C = 1).

Monochromatic Pdyn Driving

We also introduce the appropriate out of phase oscillation in the input sound speed so that the thermal pressure is constant in the input conditions ( Pth ~ n Cs

2 ):)sin(

)(0

00, tCn

nctc ss

= 40 km/s

Remaining SW input parameters: Vx = -600 km/s; Bz = -5 nT; Bx = By = 0; Vy = Vz = 0

j

jjtDntn )sin()( 0 Broadband input density time series:

The oscillation amplitude, D, is chosen so that the integrated power of input density time series in the broadband run is on the order of that in the monochromatic run.

Broadband Pdyn Driving

Hold input thermal pressure constant ( Pth ~ n Cs

2 ):

jjj

ss tDn

nctc

)sin()(

0

00,

= 40 km/s

Remaining SW input parameters: Vx = -600 km/s; Bz = -5 nT; Bx = By = 0; Vy = Vz = 0

Broadband Pdyn Driving

Density, sound speed, thermal pressure and dynamic pressure time series in the input and upstream solar wind ( x = 20 Re ) in the broadband simulation

Spectra of the above time series (green is input and blue is upstream).

Simulation Results: Waves Driven by SW Dynamic Pressure Fluctuations

Monochromatic Simulation Results: Ephi RIP in the Equatorial Plane

b

a

f

fdffPRIP )(

10 mHz Simulation 15 mHz Simulation

RIP Over 9.5 to 10.5 mHz RIP Over 14.5 to 15.5 mHz

Monochromatic Simulation Results: Radial PSD Profiles Along 12 LT

10 mHz Simulation 15 mHz Simulation

RIP Over 9.5 to 10.5 mHz RIP Over 14.5 to 15.5 mHz

Note: Bz has amplitude local maxima where Ephi has local minima (IB, MP, and BS)

Monochromatic Simulation Results

Ephi and Bz Radial PSD Profiles Along 12 LT

Ep

hi

Bz

5 mHz Run 10 mHz Run 15 mHz Run

Broadband Simulation Results

Bz PSD

Ephi Radial PSD Along 12 LT Ephi PSD at (6.6, 0, 0)

The magnetosphere is clearly picking out two particular frequencies (~9 and 17 mHz) from the quasi-broadband upstream Pdyn fluctuations.

Simulation Results (mono. and broadband)

10 mHz Run 15 mHz Run5 mHz Run BB Run

Eph

i RIP

Bz

RIP

Key Question: Why do the simulation results look so different under very similar driving (apart from the driving frequency)?

Magnetospheric Cavity Modes

BS

IBA

cav xV

dxT

)(2

mHz2.41

cav

cav Tf (in all 4 sims.)

A simple cavity mode model can explain the simulation results:

Magnetic and electric field oscillations modeled as standing waves between a cavity inner and outer boundary.

Magnetospheric cavity modes are often invoked as drivers of FLR’s and have received substantial attention in theoretical/numerical models of the magnetosphere.

Cavity modes have been studied numerically in simple geometries (e.g. box, cylindrical, and dipole magnetospheres)

n = 2 Cavity Mode in the 10 mHz Run

1) Ephi pulsation amplitude is larger in the 10 mHz run than in the 5 mHz run

2) Ephi pulsation amplitude peak is near the magnetopause in the 5 mHz run but much more earthward in the 10 mHz run (~ 5 Re)

5 mHz Run 10 mHz Run

Eph

i RIP

Bz

RIP

mHz4.82 cavf

n = 4 Cavity Mode in the 15 mHz Run10 mHz Run

Eph

i RIP

Bz

RIP

mHz8.164 cavf

15 mHz Run

3) Ephi pulsation amplitude in the 15 mHz run has two peaks along the noon meridian (near 4 and 8 Re)

4) Bz pulsation amplitude increases strongly towards the simulation inner boundary in the 10 and 15 mHz runs, but not in the 5 mHz run.

n = 2 and 4 Cavity Modes in the BB Run

mHz8.164 cavfmHz4.82 cavf

Eph

i RIP

Bz

RIP

5) There is a clear preferential frequency to the Ephi pulsation power (~9 mHz)

6) The 9 mHz wave power peaks near 5 Re.

7) There is a secondary preferential frequency in the Ephi pulsation power (~17 mHz)

8) The 17 mHz wave power has two radial peaks (near 4 and 8 Re).

Results from a 25 mHz monochromatic simulation (where the n = 6 cavity mode should be excited):

n = 6 Cavity Mode in the 25 mHz Run

No Odd Mode Number Cavity Modes?10 mHz Run 15 mHz Run5 mHz Run BB Run

Eph

i RIP

Bz

RIP

Time Out To Think

- Q of the magnetospheric cavity?

- What happens away from 12 LT?

- Do these cavity modes couple energy into FLR’s?

Some natural questions to consider:

Q

Q of the Magnetospheric Cavity?

period

timefolding-e

2

T

TQ

folde

folde

8

s100

s 130

Q

T

folde

10 mHz Simulationw/ driving turned off

What Happens Away From 12 LT?

BSIB

A rV

drcavf)(

2

1

As you move away from local noon, the cavity configuration changes, and thus the magnetospheric response frequency should change.

MP

BS

1200 LT

1440 LT

1640 LT

1800 LT

X

Y

What Happens Away From 12 LT?

BSIB

A rV

drcavf)(

2

1 MP

BS

1200 LT

1440 LT

1640 LT

1800 LTLT[hr]

1200 1440 1640 1800

fcav

[mHz]

4.2 3.5 1.9 1.25

fmsphere

[mHz]

9 7.5 6.5 6

fmsphere = frequency of magnetospheric response X

Y

FLR’s in the LFM Simulations?

10 mHz Simulation

Er RIP (integrated over 9.5 to 10.5 mHz)

Er Amplitude and Phase(across afternoon sector peak at ~5 Re)

Summary and Conclusions

- ULF oscillations in the solar wind dynamic pressure can directly drive ULF pulsations in the magnetospheric electric and magnetic fields in the dayside (a la Kepko and Spence, 2003).

- when the driving frequency matches the natural frequency of the magnetosphere, cavity modes can be energized

- only even mode number cavity modes appear to be energized in the LFM simulations in this study