9. Acknowledgments
description
Transcript of 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
I = 588 kAτT-Z = 166 nsτ2s-T = 17 nsτ2d-T = 24 ns
ET = 2 JR28/Z699
I = 574 kAτT-Z = 129 nsτ2s-T = 34 nsτ2d-T = 41 ns
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