applications of mhd turbulence: from sumer to ulysses! steven r. cranmer, harvard-smithsonian cfa...

Applications of MHD Turbulence: from SUMER to Ulysses!

Steven R. Cranmer, Harvard-Smithsonian CfA

Polar coronal hole

protons

electrons

O+5

O+6

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


(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


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!


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


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.


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” . . .


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)


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):


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


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) ???


(2) Proton-electron heat partitioning in the inner solar wind (0.3 to 5 AU)


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.


Cranmer et al. (2007) results

T (K)

reflection coefficient

Goldstein et al.(1996)

Ulysses SWOOPS


Problem: too hot at Ulysses ?

Ulysses Tp

standard (n=1) model

rapid-quenching (n=2) model


Electron heat conduction• At ~1 AU, the modeled T(r) is a

balance between adiabatic cooling & collisionless conduction.

• We’ve used Hollweg (1974):


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.


In situ temperatures (high-speed wind only)


Solve for the heating rates!


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:


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...)


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.”

applications of mhd turbulence: from sumer to ulysses! steven r. cranmer, harvard-smithsonian cfa...

Documents

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ion heating r

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cranmer van ballegooijen

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unh lws solar wind fst