applications of mhd turbulence: from sumer to ulysses! steven r. cranmer, harvard-smithsonian cfa...
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![Page 1: Applications of MHD Turbulence: from SUMER to Ulysses! Steven R. Cranmer, Harvard-Smithsonian CfA Polar coronal hole protons electrons O +5 O +6](https://reader035.vdocument.in/reader035/viewer/2022062713/56649f465503460f94c68a9e/html5/thumbnails/1.jpg)
Applications of MHD Turbulence: from SUMER to Ulysses!
Steven R. Cranmer, Harvard-Smithsonian CfA
Polar coronal hole
protons
electrons
O+5
O+6
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Applications of MHD Turbulence from SUMER to Ulysses S. R. Cranmer, Nov. 10, 2008, UNHLWS Solar Wind FST
(1) Theoretical MHD turbulence models as “illustrative context” for SUMER measurements
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Applications of MHD Turbulence from SUMER to Ulysses S. R. Cranmer, Nov. 10, 2008, UNHLWS Solar Wind FST
(1) Solve a semi-empirical ion heating equation with an arbitrary normalization for ion cyclotron wave power. Each ion is modeled independently of others. Normalization varied till agrees w/ data. (CvB2005 used for: up, ρ, VA, B0)
(2) Use the Cranmer & van Ballegooijen (2003, 2005) models to predict the ion cyclotron wave power spectrum at a given height.
New SUMER constraints
• Landi & Cranmer (2009, arXiv:0810.0018) analyzed a set of SUMER line widths that suggest preferential ion heating at r ≈ 1.05 to
1.2 Rs in coronal holes.
• We produced and compared two independent models:
Te
r = 1.07 Rs
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Applications of MHD Turbulence from SUMER to Ulysses S. R. Cranmer, Nov. 10, 2008, UNHLWS Solar Wind FST
Example heating model for O VI• How well do we really know the proton temperature? Vary as free parameter...
SUMER constraints
UVCS constraints
• The yellow/green curves seem to do the best... they imply strong Coulomb collisional coupling at the SUMER heights!
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Applications of MHD Turbulence from SUMER to Ulysses S. R. Cranmer, Nov. 10, 2008, UNHLWS Solar Wind FST
Compare all ions at r = 1.069 Rs
• Colors: different choices for proton temperature. Black curves: theoretical resonant spectra from Cranmer & van Ballegooijen (2003) advection-diffusion model.
y-axis:
wave power needed to
produce ion heating
r = 1.07 Rs
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Applications of MHD Turbulence from SUMER to Ulysses S. R. Cranmer, Nov. 10, 2008, UNHLWS Solar Wind FST
Black curves: anisotropic MHD cascade• Can MHD turbulence generate ion cyclotron waves? Many models say no!
• Simulations & analytic models predict cascade from small to large k ,leaving k ~unchanged. “Kinetic Alfven waves” with large k do not necessarily have high frequencies.
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Applications of MHD Turbulence from SUMER to Ulysses S. R. Cranmer, Nov. 10, 2008, UNHLWS Solar Wind FST
Black curves: anisotropic MHD cascade• Can MHD turbulence generate ion cyclotron waves? Many models say no!
• Simulations & analytic models predict cascade from small to large k ,leaving k ~unchanged. “Kinetic Alfven waves” with large k do not necessarily have high frequencies.
• In a low-beta plasma, KAWs are Landau-damped, heating electrons preferentially!
• Cranmer & van Ballegooijen (2003) modeled the anisotropic cascade with advection & diffusion in k-space and found some k “leakage” . . .
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Applications of MHD Turbulence from SUMER to Ulysses S. R. Cranmer, Nov. 10, 2008, UNHLWS Solar Wind FST
An advection-diffusion cascade model• The Cranmer & van Ballegooijen (2003) advection-diffusion equation:
• “Critical balance” (Higdon/Goldreich/Sridhar/others) was built into the eqns . . .
• Rapid decay to higher k║ is contained in f(x). Cho et al. (2002) examined various functional forms as fits to numerical simulations (not enough dynamic range?).
• CvB2003 solved an approximate version of the advection-diffusion eqn to get:
• Key parameter: β/γ. van Ballegooijen (1986) argued for β/γ ≈ 1 (random walk)
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Applications of MHD Turbulence from SUMER to Ulysses S. R. Cranmer, Nov. 10, 2008, UNHLWS Solar Wind FST
Advection-diffusion cascade results• Taking the anisotropic spectrum and using linear Maxwell-Vlasov dissipation rates,
the ratio of proton vs. electron heating can be derived as a function of position in the fast solar wind (using the Cranmer & van Ballegooijen 2005 model):
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Applications of MHD Turbulence from SUMER to Ulysses S. R. Cranmer, Nov. 10, 2008, UNHLWS Solar Wind FST
Compare all ions at r = 1.069 Rs
• Colors: different choices for proton temperature. Black curves: theoretical resonant spectra from Cranmer & van Ballegooijen (2003) advection-diffusion model.
y-axis:
wave power needed to
produce ion heating
r = 1.07 Rs
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Applications of MHD Turbulence from SUMER to Ulysses S. R. Cranmer, Nov. 10, 2008, UNHLWS Solar Wind FST
Power increase at large Z/A ?
• This is not predicted by simple turbulent cascade models.
• If it is real, it might be:
• Increased wave power from plasma instabilities that are centered around either the alpha (Z/A = 0.5) or proton (Z/A = 1) resonances (Markovskii 2001; Zhang 2003; Laming 2004; Markovskii et al. 2006) ?
• Predicted “spectral flattening” due to oblique propagation and/or compressibility effects in dispersion relation? Harmon & Coles (2005) invoked these effects to model the observed IPS density fluctuation spectra.
• A kind of “bottleneck effect” wherein the power piles up near the dissipation scale, due to nonlocal interactions between disparate scales in k-space (Falkovich 1994; Biskamp et al. 1998) ???
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Applications of MHD Turbulence from SUMER to Ulysses S. R. Cranmer, Nov. 10, 2008, UNHLWS Solar Wind FST
(2) Proton-electron heat partitioning in the inner solar wind (0.3 to 5 AU)
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Applications of MHD Turbulence from SUMER to Ulysses S. R. Cranmer, Nov. 10, 2008, UNHLWS Solar Wind FST
Self-consistent corona/wind models
(Heinemann & Olbert 1980; Hollweg 1981, 1986; Velli 1993; Matthaeus et al. 1999; Dmitruk et al. 2001, 2002; Cranmer & van Ballegooijen 2003, 2005; Verdini et al. 2005; Oughton et al. 2006; many others!)
• Cranmer, van Ballegooijen, & Edgar (2007) computed solutions for the waves & background one-fluid plasma state along various flux tubes... going from the photosphere to the heliosphere.
• The only free parameters: radial magnetic field & photospheric wave properties.
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Applications of MHD Turbulence from SUMER to Ulysses S. R. Cranmer, Nov. 10, 2008, UNHLWS Solar Wind FST
Cranmer et al. (2007) results
T (K)
reflection coefficient
Goldstein et al.(1996)
Ulysses SWOOPS
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Applications of MHD Turbulence from SUMER to Ulysses S. R. Cranmer, Nov. 10, 2008, UNHLWS Solar Wind FST
Problem: too hot at Ulysses ?
Ulysses Tp
standard (n=1) model
rapid-quenching (n=2) model
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Applications of MHD Turbulence from SUMER to Ulysses S. R. Cranmer, Nov. 10, 2008, UNHLWS Solar Wind FST
Electron heat conduction• At ~1 AU, the modeled T(r) is a
balance between adiabatic cooling & collisionless conduction.
• We’ve used Hollweg (1974):
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Applications of MHD Turbulence from SUMER to Ulysses S. R. Cranmer, Nov. 10, 2008, UNHLWS Solar Wind FST
Empirical energy balance
• If these regions really are collisionless, we know (nearly) every term in the proton and electron energy conservation equations . . .
• If the radial derivatives can be taken (without the uncertainty being compounded too much!), it is possible to solve for the heating rates Qp and Qe.
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Applications of MHD Turbulence from SUMER to Ulysses S. R. Cranmer, Nov. 10, 2008, UNHLWS Solar Wind FST
In situ temperatures (high-speed wind only)
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Applications of MHD Turbulence from SUMER to Ulysses S. R. Cranmer, Nov. 10, 2008, UNHLWS Solar Wind FST
Solve for the heating rates!
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Applications of MHD Turbulence from SUMER to Ulysses S. R. Cranmer, Nov. 10, 2008, UNHLWS Solar Wind FST
Proton / electron partitioning
• Inner heliosphere (Helios): well understood with proton-electron equipartition?!
• Do protons really gobble up more energy at r > 1 AU ?
• Plasma β goes up as r goes up. This gives a similar trend as found by, e.g., Quataert & Gruzinov (1999) for purely linear damping of MHD waves.
Very preliminary result:
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Applications of MHD Turbulence from SUMER to Ulysses S. R. Cranmer, Nov. 10, 2008, UNHLWS Solar Wind FST
What to do next?
• Qp vs. Qe: Also put limits on partitioning in corona from UVCS & SUMER.
• Many of the proposed ion heating mechanisms haven’t really been tested with realistic coronal plasma conditions! (i.e., plasma beta, driving wave amplitudes & frequencies, etc.)
• The mechanisms of “parallel cascade” in low-beta plasmas need to be more fully worked out! (the tail that wags the dog?) The CvB (2003) “advection-diffusion” model is a crass local approximation to a truly nonlocal effect.
• What about Len Fisk and Nathan Schwadron? Explore relationships between turbulence and reconnection theory!
• Better measurements are needed:both remote and in situ!
(CPEX Phase-A study will be done inearly 2009... Solar Probe Plusdevelopment gearing up soon, too...)
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Applications of MHD Turbulence from SUMER to Ulysses S. R. Cranmer, Nov. 10, 2008, UNHLWS Solar Wind FST
Conclusions
For more information: http://www.cfa.harvard.edu/~scranmer/
• UV coronagraph spectroscopy has led to fundamentally new views of the collisionless acceleration regions of the solar wind.
• Theoretical advances in MHD turbulence continue to feed back into global models of coronal heating and the solar wind.
• The extreme plasma conditions in coronal
holes (Tion >> Tp > Te ) have guided us to discard some candidate processes, further investigate others, and have cross-fertilized other areas of plasma physics & astrophysics.
• Next-generation observational programs are needed for conclusive “constraints.”