Mar 11, 2014 - 1) Provide overview of plasma generation in SSX. 2) Demonstrate ability to conduct turbulence research in a laboratory plasma (two ways):.
Turbulence Analysis of an MHD wind-tunnel David Schaffner
Swarthmore College, NSF Center for Magnetic Self-Organization
with contributions from M. Brown, V. Lukin, A. Wan ‘15
CMSO General Meeting, Santa Fe, NM March 11 2014 Research supported by US DOE and NSF
Motivating Questions Is the statistical character of MHD turbulence universal?
How can laboratory plasmas be used to study MHD turbulence?
Example: Can laboratory turbulence be compared to solar wind? Space: Solar Wind*
Laboratory: SSX
fλp = 2MHz
*Cluster FGM and STAFF-SC Data: Sahraoui, PRL 2009
Objectives for this Talk
1) Provide overview of plasma generation in SSX 2) Demonstrate ability to conduct turbulence research in a laboratory plasma (two ways): A. Turbulence spectra, variance anisotropy B. Intermittency and scaling with helicity
3) Give overview of simulation efforts and preliminary comparisons
Image: Turbulent Channel Structures, Melissa Green Department of Mechanical and Aerospace Engineering, Princeton
OBJECTIVE 1: OVERVIEW OF PLASMA IN SSX
The SSX Laboratory 10kV/100kA Pulsed power 1mF banks
Cylindrical vacuum chamber (D = 0.5 m, L = 1 m)
Schematic + Simulation
High voltage plasma guns on each end
SSX Diagnostics measure B-field, density, flow, soft X-ray light, ion temperature, and gun I/V Copper Flux Conserver (Wind Tunnel) 16chan, 3 axis Bdot Probe 2-Side (Z-axis) Mach Probe
Off Midplane: HeNe Interferometer Gun Current/Voltage
Ion Doppler Spectrometer (IDS) Al/Zr Metal Soft X-ray Photodiode
Plasma gun produces spheromak; narrow cylinder boundary cause tilt and twist Initial State
Final State Turbulence
Taylor relaxation or selective decay of a plasma is a process where magnetic energy,
is minimized under the constraint that magnetic helicity,
is conserved.
Taylor State (Tilt and Twist) Double Helix Shape
Instability of field structure provides energy for cascade
Hall MHD simulation clearly illustrates plasma evolution
Initial State - Spheromak
Hall MHD simulation clearly illustrates plasma evolution
Field structure tilts
Hall MHD simulation clearly illustrates plasma evolution
Field structure twists
Hall MHD simulation clearly illustrates plasma evolution
Fields turbulent (Time frame for analysis)
Hall MHD simulation clearly illustrates plasma evolution
Fluctuations begin to decay
Hall MHD simulation clearly illustrates plasma evolution
Final State: Taylor State (double helix)
Typical Plasma Parameters Temp: = 25eV, = 10eV β = 0.1 Field: = 5kG ρi = 0.1cm (tunnel diam = 15cm) Density: = 1x1015cm-3 λi = δi = c/ωpi = 0.54cm Velocity: VA > Cs > Axial Flow 256km/s > 31km/s > 20km/s Collisional Plasma – MFP ~ 0.2-3cm
OBJECTIVE 2: TURBULENCE RESEARCH ON SSX – SPECTRA AND ANISOTROPY
B-field spectra extracted from dB/dt signal
B-field spectra extracted from measured dB/dt time series using wavelet transform
Power spectrum
B-field spectra extracted from dB/dt signal
Ensemble Average:
x40+ shots
frequency
B-field spectra extracted from measured dB/dt time series using wavelet transform
time
Power spectrum
Spectra indicate power-law behavior Power-law scaling in Bfield, density and flow as function of frequency
Magnetic fluctuations steepen before flow fluctuations—suggest energy initially in fields, not flow fλp = 2-3MHz
Spectra indicate power-law behavior
If average flow is used to invoke Taylor Hypothesis: Break in B-field spectra near Doppler-shifted ion inertial length fλp = 2-3MHz
B-field spectra exhibit variance anisotropy Power of each component divided into perp/para using local B-field reference (at each timestep)
B(t) B(f)para
B(f)perp
Perp (red) Para (blue)
B-field spectra exhibit variance anisotropy Power of each component divided into perp/para using local B-field reference (at each timestep)
More perp power than parallel Ratio increases with frequency (up to ~1MHz)
Perp (red) Para (blue)
Ratio has power-law scaling ≈ 1/3 Low frequency ratio scales as frequency to the 1/3
Ratio peaks around 1MHz
Ratio shows isotropy at higher frequencies
Ratio shows some time dependence Black - Initial fluctuations (near isotropy)
Scaling increases from purple to blue to light blue
Spatial wavenumber spectra measured directly
Lower resolution spectra, but slopes are closer to a Kolmogorov -5/3 16 measurements along radius Scales between 8cm and 1cm
Frequency spectra steeper than wavenumber spectra Aligned by invoking Taylor Hypothesis with bulk flow of 20km/s Wavenumber spectra does not likely probe dissipation range Some effect causes frequency spectra to be steeper? Some type of dissipation? Not really a direct comparison: radial k versus axial freq
OBJECTIVE 2: TURBULENCE RESEARCH ON SSX – INTERMITTENCY/HELICITY SCALING
PDF constructed from increments in dB/dt
Probability Distribution Functions of Increments constructed by taking difference of dB/dt values at different time separations
PDF of increments have fat tails (intermittency): shows B-dot fluctuations are highly structured
Flatness increases with decreasing time scale
Flatness = normalized 4th moment of a PDF
Flatness = quantification of fat tails, departure from Gaussian the larger the flatness, the more intermittency is observed
Power-law like scaling
Magnetic Helicity can be linearly modified
Mag Flux, Φ
Vary flux by varying strength of field produced by coil
Flatness (intermittency) scales with injected helicity Flatness increases at all timescales with helicity
Average flatness increases with helicity beyond 100 μWb2
Ion temperature bursts scale with helicity, but integrated SXR signal scales inversely Intermittency increases with helicity
Soft X-ray signal decreases with helicity Ti intermittency increases with helicity—mean value hold steady Possibly, trends suggest intermittency caused by current sheets—seen in solar wind turbulence simulation (Greco ApJ 09)
That is, helicity increases number of sites, but decreases their size
Shape/slopes of spectra generally unchanged with increasing helicity Spectra staggered for clarity
Fits (both high and low frequency) and breakpoints do not scale with changing helicity
COMPARISON TO HIFI SIMULATION
Similar turbulence statistics observed
Comparable slope of spectra observed
Similar wavenumber spectra observed
Similar turbulence statistics observed
Variance anisotropy observed
Intermittency increases with smaller scales
Concluding Remarks:
How well does lab plasma turbulence compare to solar wind turbulence? • B-field frequency spectra steeper than solar wind—flow fluctuations driven by magnetic? • Wavenumber spectra closer to Kolmogorov • Variance anisotropy is observed • Spectral break consistent with ion scale if Taylor Hypothesis invoked
• Bdot fluctuations exhibits intermittency—flatness decreases w/scale • Evidence for connection between current sheets/intermittency— found through lab helicity scaling
What is next?—Questions to Answer… • Is the Taylor Hypothesis Valid? – We plan to use multi-tipped probes aligned with the plasma flow to get a direct wavenumber spectrum to compare to the frequency spectrum w/Taylor Hypothesis
• What kind of modes are generated?—we plan to use a probe to measure the simultaneous Bfield and density fluctuations—some theories predict such correlation coupled with anisotropy can determine mode type (i.e. fast, slow, Alfven) [Klein 2012]
What is next?—Questions to Answer… • Does (system) size matter? – Comparison of experiment and simulation are favorable. We want to test how(if) spectra changes if volume is scaled up in simulation, in anticipation of possible larger experiment.
Thank you for your attention.
