Kelvin-Helmholtz Instabilities in the Earth's Magnetotail as a Transport Mechanism for Solar Plasma into the Magnetosphere. 6. Results. 1. Abstract. 2. Motivation. Credit: NASA. 3. Theory. 7. Ideal MHD Simulation. 4. Parameters. Laser. y. B θ. × j. Target. x. Field of view of
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Kelvin-Helmholtz Instabilities in the Earth's Magnetotail as a Transport Mechanism for Solar Plasma into the Magnetosphere
7. Ideal MHD Simulation
Field of view of
S. Wright, R. Presura, S. Neff, C. Plechaty, T. Cowan
Nevada Terawatt Facility, University of Nevada, Reno
The parameters indicate that the plasma expands in an MHD regime.
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.
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)
(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
Plasma guidance along magnetic field
Plasma guidance perpendicular to the magnetic field.
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.
I = 581 kA
τT-Z = 120 ns
τ2s-T = 21 ns
τ2d-T = 28 ns
ET = 2 J
I = 588 kA
τT-Z = 166 ns
τ2s-T = 17 ns
τ2d-T = 24 ns
ET = 2 J
As expected, plasma traveling along the magnetic field shows no evidence of instabilities at the boundary.
I = 574 kA
τT-Z = 129 ns
τ2s-T = 34 ns
τ2d-T = 41 ns
ET = 2 J
therefore the magnetic field is strong enough to stabilize the plasma.
In these frames we can see that instabilities have formed along the boundary.
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.
Kelvin 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.
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
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.
Pulsed Power Generator Zebra:
I ≈ 1 MA, τrise ≈ 90 ns
experiment: I ≈ 0.6 MA, τrise ≈ 200 ns
Bθ ≤ 60 T
B(T) = 100/R(mm)
r = 0.5 mm; d = 0.1 mm; Eabs= 2 J;v0= 0 m/s; T0≈ 350 eV
Earth magnetic field
-low density plasma
M = 6
MA = 9
β = 1
Rem = 9×108
mfp (cm) = 1012
rLi (cm) = 6×106
c/ωpi (cm) = 107
D (cm) = 107
96% Hydrogen plasma:
n (cm-3) = 5
u (cm/s) = 4×107
Te (eV) = 20
Ti (eV) = 10
B (G) = 5×10-5
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
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.
This figure illustrates the general density gradient range where the Schlieren diagnostics are sensitive.
n(cm-3) = 1
Ti(eV) = 100
B(G) = 1x10-5
vth,I = 600 km/sec
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.
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.
This work was supported by the US Dept of Energy under UNR grant DE-FC52-06NA27616 .
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 Commerce
National 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).
(shadow, schlieren; 532nm, 0.15ns)
I ≤ 1016 W/cm2
E ≤ 4 J
t ≈ 4 ps
D ≈ 0.1 mm