9. acknowledgments

Kelvin-Helmholtz Instabilities in the Earth's Magnetotail Kelvin-Helmholtz Instabilities in the Earth's Magnetotail as a Transport Mechanism for Solar Plasma into the as a Transport Mechanism for Solar Plasma into the

MagnetosphereMagnetosphere

9. Acknowledgments

10. References

3. TheoryKelvin Helmholtz instabilities arise when two fluids traveling parallel to

each other have a velocity relative to each other. In the absence of

surface tension, perturbations due to the velocity shear at the boundary

grow. A surface tension suppresses perturbation growth when the relative

velocity is small, but not when the relative velocity is large. In plasma, a

parallel magnetic field has the same effect as a surface tension on the two

fluids (Chandrasekhar, 1981).

However, in the case of a velocity shear between two fluids in a transverse

magnetic field, the transverse magnetic field has no stabilizing effect on

the instabilities. In this case the perturbations grow even for very small

relative velocity. This is the case in the equatorial plane of the earth’s

magnetosphere.

Kelvin-Helmholtz waves (or vortices) in the magnetotail are

responsible for much of the solar plasma transport into the earth's

magnetosphere. The plasma motion in these vortices, stretches

and contorts the magnetic field lines, and compresses the

magnetic flux. The movement of the field lines allows for magnetic

reconnection to occur and solar plasma to penetrate.

The Cluster satellites were positioned as shown in the figure to

monitor and map the plasma density gradient in the earth's

magnetotail.

1. Abstract

Ideally the earth's magnetosphere is a barrier that protects the earth from the solar wind. Measurements in situ and theoretical studies have shown that Kelvin-Helmholtz instabilities (KHI) are one of the primary means for solar plasma to enter the earth's magnetosphere. The vortices characteristic of these instabilities are places of magnetic reconnection and become a location for plasma to transfer across the magnetic field into the earth's magnetopause. Understanding just how these instabilities occur and grow is of vital interest to predicting space weather. Coronal mass ejections (CME) have been directly correlated to increased magnetosphere plasma activity. Here we analyze an experiment that couples a terawatt class pulsed-power laser with a mega-ampere pulsed power z-pinch to understand the interaction of plasma with an external magnetic field. We found instabilities in these experiments with a growth rate that is comparable to KH instabilities.

r = 0.5 mm; d = 0.1 mm; Eabs = 2 J; v0 = 0 m/s; T0 ≈ 350 eV

This is a 3D simulation. The top frames show the plasma dynamics in the plane of the magnetic field lines. The bottom shows the evolution in the plane perpendicular to the magnetic field.

7. Ideal MHD Simulation

B(T) = 100/R(mm)

8. Conclusions

uuk

21

21

2AM

We have shown that when we launch a plasma perpendicular to a

magnetic field, KHI form along the flanks of the plasma. The

magnetic field traps the electrons at the boundary and the electrons

drag on the faster moving protons inside the plasma. This creates

the velocity shear that is responsible for the formation of KHI. The

vortices in our plasma resemble the vortices the Cluster satellites

observe in the earth's magnetotail.

In the future we plan to better understand our plasma parameters so that

we can see how close we are to observations. We would like to use that

to design an experiment that significantly resembles the conditions that

Cluster sees. To this end we plan to improve diagnostics so that we can

find the magnetic field in our plasma vortices and determine if there is

material transport across the magnetic field.

At Present: Future Plans:

2. Motivation

Understanding plasma transport into the earth's magnetosphere is of utmost

importance. Data taken by the Cluster satellites located in the earth’s magnetotail

have conclusively shown that Kelvin-Helmholtz instabilities form along the flanks of

the magnetotail. Some of the most powerful CME on record took place between mid-

October 2003 and early November 2003. The CME that were earth directed had far

reaching and devastating effects ranging from blackouts and communication

disruptions to doses of solar radiation equivalent to a chest x-ray for astronauts and

some air travelers. Some of the airlines redirected their high altitude flights to avoid

the worst of the radiation (Rosen, 2004). Around 60% of NASA’s earth and space

science missions were in some way affected and aurorae were seen as far south as

Spain and Florida. Therefore, a better understanding of how the plasma transport

occurs can lead to better predictions of space weather.

5. Experiment

This experiment uses Zebra, a pulsed power generator, to create a high magnetic field. Around current peak, the high intensity laser Tomcat strikes a plastic target to create a plasma. Shadow and Schlieren diagnostics are used to investigate the evolution of the plasma.

Ekspla(shadow,

schlieren;

532nm,

0.15ns)

Tomcat(ablation) I ≤ 1016 W/cm2

E ≤ 4 J

t ≈ 4 ps

D ≈ 0.1 mm

Lab overviewExperimental setup

Y

Inside

Zebra

4. Parameters

Steele Hill

Solar wind-collisionless

-magnetized

-supersonic

-superalfvenic

-fully ionized

96% Hydrogen plasma:

n (cm-3) = 5

u (cm/s) = 4×107

Te (eV) = 20

Ti (eV) = 10

B (G) = 5×10-5

M = 6

MA = 9

β = 1

Rem = 9×108

mfp (cm) = 1012

rLi (cm) = 6×106

c/ωpi (cm) = 107

D (cm) = 107

Plasma flow:

Laser Tomcat: Ec ≤ 10 J; τ ≤ 1 ps

λ = 1057 nm

experiment: Ec ≈ 2-4 J; τ ≈ 5 ps

I > 1015 W/cm2

λ = 1057 nm

target: CH2

Magnetic field:

Pulsed Power Generator Zebra:

I ≈ 1 MA, τrise ≈ 90 ns

experiment: I ≈ 0.6 MA, τrise ≈ 200 ns

Bθ ≤ 60 T

Bθ(r) 1/r

The ExperimentNature

Earth magnetic field

-low density plasma

Magnetotail Parameters:

n(cm-3) = 1

Ti(eV) = 100

B(G) = 1x10-5

vth,I = 600 km/sec

Credit: NASA

The KHI growth rate perpendicular to the magnetic field is given by

where k is the wavenumber and Δu is the relative velocity. The approximate equality holds when the densities of the two media are comparable.

A parallel magnetic field is stabilizing for the KHI when

6. Results

B

Plasma guidance along magnetic field

I = 581 kAτT-Z = 120 nsτ2s-T = 21 nsτ2d-T = 28 ns

ET = 2 JR61/Z709

As expected, plasma traveling along the

magnetic field shows no evidence of instabilities

at the boundary.

2s 2d


ET = 2 JR28/Z699


ET = 2 JR48/Z703

In these frames we can see that instabilities

have formed along the boundary.

Plasma guidance perpendicular to the magnetic field.

Plasma regime:

(For B = 20 T, n =1019 1/cm3 and T =50 eV)

Magnetic Reynolds Number: RM ≈ 40

diffusion time: τd = 4 ns

electron magnetization: ωete = 3.5 slightly magnetized

ion magnetization: ωiti = 0.1 not magnetized

Experimental Plasma

Plasma shell parameters:

expansion velocity: v ≈ 106 m/s

density: ne ≈ 1017 – 1019 cm-3

field strength: B ≈ 10 – 20 T (at front)

temperature: Ti = Te = 20 – 100 eV

length scale: Ln ≈ 100 μm (schlieren)

The parameters indicate that the plasma expands in an MHD regime.

In experiment for flow parallel to magnetic field:B ≥ 20 T. For ni ≈ 1018 cm-3 → ρ ≈ 10-5 g/cm-3 ,

sovA ≈ 200 km/s

→ MA ≈ 0.5

Open question: flow asymmetry

For the current experiment with plasma perpendicular to the magnetic field:

λ ≤ 1 mm and Δu ≥ 100 km/s, so

γ-1 ≤ 3 ns is the KH growth ratevp ≈ 50 km/s, (0.35 mm in 7 ns between laser

diagnostics frames)

Bθ

×j x

yLaser

Target

Plasma plume

Field of view oflaser diagnostics

z

Bθ Bθ

↓ jz

Laser Rod

Targetx

H. Haswgawa2004

H. Haswgawa, M. Fujimoto, T.-D. Phan, H. Reme, A. Blogh, M. W. Dunlop, C. Hashimoto, and R. TanDokoro, “Transport of solar wind into the Earth's magnetosphere through rolled up Kelvin-Helmholtz vortices”, Nature 430, 755 (2004).

R. D. Rosen, D. L. Johnson “Service Assessment Intense Space Weather Storms October 19 – November 07, 2003 ”, U.S. Department of CommerceNational Oceanic and Atmospheric Administration,National Weather Service,Silver Spring, Maryland, April 2004.

S. Chandrasekhar, “Hydrodynamic and Hydromagnetic Stability”, Dover, 1981.

D. Ryu, T. W. Jones, and A.Frank, “The magnetohydrodynamic Kelvin-Helmholtz instability: a three-dimensional study of nonlinear evolution”, Astrophys. J. 545, 475 (2000).

A. Esaulov

This figure illustrates the general density gradient range where the Schlieren diagnostics are sensitive.

This work was supported by the US Dept of Energy under UNR grant DE-FC52-06NA27616 .

S. Wright, R. Presura, S. Neff, C. Plechaty, T. Cowan

Nevada Terawatt Facility, University of Nevada, Reno

I would like to thank the laser diagnostics team especially Abdelmoula Haboub and Alexey Morozov for all of their help and patience.

I would also like to thank A. Esaulov for his MHD simulation results, and M. Bakeman for building the targets,

And finally I would like to thank our technical team for all of their support.

therefore the magnetic field is strong enough to stabilize the plasma.

Electrode

Target

B

1 mm

9. acknowledgments

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