Download Lecture 2: Theory - Laboratory for Atmospheric and Space Physics

Solar Wind Origin & Heating 2
Steven R. Cranmer
Harvard-Smithsonian Center for Astrophysics
Logistics
Part 1: Observations
1. Background & history
2. In situ solar wind
3. Radio scintillations
4. Coronal remote-sensing
(empirical connections between
corona & solar wind)
Part 2: Theory
1. Photosphere: tip of the iceberg
of the convection zone
2. Chromosphere: waves start to
propagate and bump into the
magnetic field
3. Corona: magnetic field is king;
heating still a “problem”
5. Chromosphere & photosphere
4. “Other” wind acceleration ideas;
evolution of waves & turbulence
6. Future instrumentation
(discussions afterward?)
5. Future directions for theory...?
Everything is online at: http://www.cfa.harvard.edu/~scranmer/NSO/
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
The extended solar atmosphere . . .
Heating is everywhere . . .
. . . and everything is in motion
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Energy budget overview
What sets the temperature?
• Photosphere: optical depth ~unity, with radiation dominating heating/cooling:
• Chromosphere: optically thin, radiation cools the plasma (all photons escape!)
Heating is provided “mechanically,” by irreversible damping of kinetic motions
• Transition region & low corona: complicated balance of radiation, mechanical
heating, downward conduction, and upward advection (enthalpy flux)
• Extended corona: direct heating balances upward advection (adiabatic cooling)
• Heliosphere: advection (adiabatic cooling) balances outward conduction
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Convection excites waves
• All cool stars with sub-photospheric convection undergo “p-mode” oscillations:
• Lighthill (1952) showed how
turbulent motions generate
acoustic power.
Cattaneo et al. (2003)
• These ideas have been more
recently generalized to MHD. . .
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Convection excites waves
• All cool stars with sub-photospheric convection undergo “p-mode” oscillations:
• Lighthill (1952) showed how
turbulent motions generate
acoustic power.
• These ideas have been more
recently generalized to MHD. . .
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Granules and Supergranules
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Inter-granular bright points (close-up)
• It’s widely believed that
the G-band bright points
are strong-field (1500 G)
flux tubes surrounded
by much weaker-field
plasma.
100–200 km
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Waves in thin flux tubes
• Statistics of horizontal BP motions gives
power spectrum of “kink-mode” waves.
• BPs undergo both random walks &
intermittent (reconnection?) “jumps:”
splitting/merging
bending
(kink-mode wave)
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
torsion
longitudinal
flow/wave
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Waves in thin flux tubes
• Statistics of horizontal BP motions gives
power spectrum of “kink-mode” waves.
• BPs undergo both random walks &
intermittent (reconnection?) “jumps:”
splitting/merging
bending
(kink-mode wave)
torsion
longitudinal
flow/wave
In reality, it’s not just the “pure”
kink mode. . . (Hasan et al. 2005)
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
“Traditional” chromospheric heating
• Vertically propagating acoustic waves
conserve flux (in a static atmosphere):
Bird (1964)
• Amplitude eventually reaches Vph and
wave-train steepens into a shock-train.
• Shock entropy losses go into heat; only
works for periods <
~ 1–2 minutes…
• New idea: “Spherical” acoustic wave
fronts from discrete “sources” in the
photosphere (e.g., enhanced turbulence
or bright points in inter-granular lanes)
may do the job with longer periods.
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Time-dependent chromospheres?
• Carlsson & Stein (1992, 1994, 1997, 2002, etc.) produced 1D time-dependent
radiation-hydrodynamics simulations of vertical shock propagation and
transient chromospheric heating. Wedemeyer et al. (2004) continued to 3D...
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Runaway to the transition region (TR)
• Whatever the mechanisms for heating, they must be balanced by radiative losses to
maintain chromospheric T.
• When shock strengths
“saturate,” heating depends
on density only:
• Why then isn’t the corona 109 K? Downward heat conduction smears out the
“peaks,” and the solar wind also “carries” away some kinetic energy. Conduction
also steepens the TR to be as thin as it is.
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
The coronal heating problem
• We still don’t understand the physical processes responsible for heating up the
coronal plasma.
A lot of the heating occurs in a narrow “shell.”
• Most suggested ideas involve 3 general steps:
1. Churning convective motions that tangle
up magnetic fields on the surface.
2. Energy is stored in tiny twisted & braided
“magnetic flux tubes.”
3. Collisions between ions and electrons
(i.e., friction?) release energy as heat.
Heating
Solar wind acceleration!
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Coronal heating mechanisms
• So many ideas, taxonomy is needed!
• Where does the mechanical
energy come from?
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
(Mandrini et al. 2000; Aschwanden et al. 2001)
vs.
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Coronal heating mechanisms
• So many ideas, taxonomy is needed!
(Mandrini et al. 2000; Aschwanden et al. 2001)
• Where does the mechanical
vs.
energy come from?
• How rapidly is this energy
coupled to the coronal
plasma?
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
waves
shocks
eddies
(“AC”)
vs.
twisting
braiding
shear
(“DC”)
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Coronal heating mechanisms
• So many ideas, taxonomy is needed!
(Mandrini et al. 2000; Aschwanden et al. 2001)
• Where does the mechanical
vs.
energy come from?
waves
shocks
eddies
• How rapidly is this energy
coupled to the coronal
plasma?
(“AC”)
interact with
inhomog./nonlin.
vs.
twisting
braiding
shear
(“DC”)
turbulence
reconnection
• How is the energy dissipated
and converted to heat?
collisions (visc, cond, resist, friction) or collisionless
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Coronal heating mechanisms
• So many ideas, taxonomy is needed!
(Mandrini et al. 2000; Aschwanden et al. 2001)
• Where does the mechanical
vs.
energy come from?
waves
shocks
eddies
• How rapidly is this energy
coupled to the coronal
plasma?
(“AC”)
interact with
inhomog./nonlin.
vs.
twisting
braiding
shear
(“DC”)
turbulence
reconnection
• How is the energy dissipated
and converted to heat?
collisions (visc, cond, resist, friction) or collisionless
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Reconnection in closed loops
• Models of how coronal heating (FX) scales with magnetic flux (Φ) are growing
more sophisticated . . .
• Closed loops:
Magnetic reconnection
e.g., Longcope &
Kankelborg 1999
Gudiksen &
Nordlund (2005)
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Properties of MHD waves
• In the absence of a magnetic field, acoustic waves propagate at the sound speed
(restoring force is gas pressure)…
• B-field exerts “magnetic pressure” as well as “magnetic tension” transverse to the
field. The characteristic speed of MHD fluctuations is the Alfvén speed…
• Plasma β = (gas pressure / magnetic pressure) ~ (cs/VA)2
“high beta:” fluid motions push the field lines around
“low beta:” fluid flows along “frozen in” field lines
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Properties of MHD waves
• Phase speeds: Alfven, fast, slow mode; ● = sound speed, ● = Alfven speed
β = 12
β = 2.4
β = 1.2
β = 0.6
β = 0.12
• F/S modes damp collisionally in low corona; Alfven modes are least damped.
• Standard MHD dispersion applies only for frequencies << particle Larmor freq’s.
• For high freq & low β, Alfven mode → “ion cyclotron;” fast mode → “whistler.”
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Alfvén wave evolution
• Energy density & flux:
• Static medium:
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
A(r)
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Alfvén wave evolution
• Energy density & flux:
• Static medium:
A(r)
• Non-zero wind speed (“wave action conservation”):
• Alfvén waves also reflect & refract as the background properties change…
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Ion cyclotron waves in the corona?
• UVCS observations have rekindled
theoretical efforts to understand
heating and acceleration of the plasma in
the (collisionless?) acceleration region
of the wind.
• Ion cyclotron waves (10–10,000 Hz)
suggested as a “natural” energy source that
can be tapped to preferentially heat &
accelerate heavy ions.
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Alfven wave’s
oscillating
E and B fields
ion’s Larmor
motion around
radial B-field
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Ion cyclotron waves in the corona
• Dissipation of ion cyclotron waves produces diffusion in velocity space along
contours of ~constant energy in the frame moving with wave phase speed:
lower Z/A
faster diffusion
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Where do cyclotron waves come from?
Alfvén waves with frequencies > 10 Hz have not yet been observed in the corona or
solar wind, but ideas for their origin abound . . . .
(1) Base generation by, e.g., “microflare”
reconnection in the lanes that border
convection cells (e.g., Axford & McKenzie 1997).
Problem: “minor” ions consume base-generated wave
energy before it can be absorbed by ions seen by UVCS.
(2) Secondary generation: low-frequency Alfvén
waves may be converted into cyclotron waves
gradually in the corona.
Problem: Turbulence produces mainly small-scale
eddies in the direction transverse to the field; these
don’t have high frequencies!
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Where do cyclotron waves come from?
• How then are the ions heated & accelerated?
•
•
•
•
Impulsive plasma micro-instabilities that locally generate high-freq. waves (Markovskii 2004)?
Non-linear/non-adiabatic KAW-particle effects (Voitenko & Goossens 2004)?
Coupling with fast-mode waves that do cascade to high-freq. (Chandran 2006)?
If the corona is filled with thin collisionless shocks, ions can pass through them and aquire gyromotion when the
background field changes direction (Lee & Wu 2000)?
• Collisionless velocity filtration from intrinsically suprathermal velocity distributions (Pierrard et al. 2004)?
• Larmor “spinup” in dissipation-scale current sheets (Dmitruk et al. 2004)?
• KAW damping leads to electron beams, further (Langmuir) turbulence, and Debye-scale electron phase space
holes, which heat ions perpendicularly via “collisions” (Ergun et al. 1999; Cranmer & van Ballegooijen 2003)?
MHD turbulence
something
else?
cyclotron resonancelike phenomena
• We can compute a net heating rate from the cascade, even if we don’t
know how the energy gets “partitioned” to the different particle species.
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Turbulence
• It is highly likely that somewhere in the outer
solar atmosphere the fluctuations become
turbulent and cascade from large to small scales.
• The original Kolmogorov (1941) theory of
incompressible fluid turbulence describes a
constant energy flux from the largest “stirring”
scales to the smallest “dissipation” scales.
• Largest eddies have kinetic energy ~ v2 and a
“turnover” time-scale  =l/v, so the rate of
transfer of energy goes as v2/ ~ v3/l .
• Dimensional analysis can give the spectrum of
energy vs. eddy-wavenumber k: Ek ~ k–5/3
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
MHD turbulence: 2 kinds of “anisotropy”
• With a strong background field, it is
easier to mix field lines (perp. to B)
than it is to bend them (parallel to B).
• Also, the energy transport along the
Z–
Z–
Z+
field is far from isotropic:
(e.g., Hossain et al. 1995;
Matthaeus et al. 1999;
Dmitruk et al. 2002)
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Open flux tubes: global model
• Photospheric flux tubes are shaken by an observed spectrum of horizontal motions.
• Alfvén waves propagate along the field, and partly reflect back down (non-WKB).
• Nonlinear couplings allow a (mainly perpendicular) cascade, terminated by damping.
(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!)
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Alfvén wave amplitudes: Sun to 1 AU
• Pure wave-action conservation produces either too much power at 1 AU, or too
little in the corona. Turbulence seems to damp and heat at just the right level…
Cranmer & van Ballegooijen (2005)
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Solving the Parker solar wind equation
• Parker (1958) noticed that the equation of motion exhibits a “singular point…”
time-steady; isothermal
• Solution depends on knowing T(r); all equations should be solved simultaneously.
• Key issue: Is the heating “deposited” above or below the critical point?
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Alfvén wave pressure (“pummeling”)
• Just as E/M waves carry momentum and
Contours: wind speed at 1 AU (km/s)
exert pressure on matter, acoustic and
MHD waves do work on the gas via
similar net stress terms:
• This works only for an inhomogeneous
(radially varying) background plasma.
P
C
H
• Wave pressure & gas pressure work
together to produce high-speed solar
wind; each point in this grid represents a
solution to the Parker critical pt. eqn.
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
“The kitchen sink”
• Cranmer, van Ballegooijen, & Edgar (2007) computed self-consistent solutions of
waves & background one-fluid plasma state along various flux tubes... going from
the photosphere to the heliosphere. (astro-ph/0703333)
• Ingredients:
• Alfvén waves: non-WKB reflection with full
spectrum, turbulent damping, wave-pressure
acceleration
• Acoustic waves: shock steepening, TdS &
conductive damping, full spectrum, wave-pressure
acceleration
• Radiative losses: transition from optically thick
(LTE) to optically thin (CHIANTI + PANDORA)
• Heat conduction: transition from collisional
(electron & neutral H) to collisionless “streaming”
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Polar coronal hole model: it works!
• Grids of exploratory models led to
the optimal choice for lower
boundary parameters:
• Basal acoustic flux: 108 erg/cm2/s
(equivalent “piston” v = 0.3 km/s)
T (K)
• Basal Alfvenic perpendicular
amplitude: 0.255 km/s
• Basal turbulent scale: 75 km
(G-band bright point size?)
Transition region is too high
(7 Mm instead of 2 Mm),
but otherwise not bad . . .
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
reflection
coefficient
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Magnetic flux tubes
• Vary the magnetic field, but keep lower-boundary parameters fixed.
“active region”
fields
T (K)
reflection
coefficient
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Fast vs. slow wind emerges naturally
• The wind speed & density at 1 AU behave mainly as observed.
Cascade efficiency:
Ulysses
SWOOPS
n=1
n=2
Goldstein et al.
(1996)
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Progress toward better understanding
Existing models are not too bad, but . . .
• Because of the need to determine non-WKB (nonlocal!) reflection coefficients,
it may not be easy to insert into global/3D MHD models.
• Doesn’t specify proton vs. electron heating (they conduct differently!)
• Does turbulence generate enough ion-cyclotron waves to heat the minor ions?
• Are there additional (non-photospheric) sources of waves / turbulence / heating
for open-field regions? (e.g., flux cancellation events)
(B. Welsch et al. 2004)
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Plumes and jets: more reconnection?
• How much do plumes and
jets contribute to the “mean”
solar wind? Still debated…
• Wang (1994, 1998)
suggested that small-scale
magnetic reconnection
events at the coronal base
gives rise to plumes. Is this
what Hinode/XRT sees?
• These events may be hotter
than mean plasma at the
base, but cooler higher up!
(Fisk et al.
1999)
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Future directions for theory
Generation and nonlinear evolution of the solar
wind fluctuation spectra must be understood.
Self-consistent kinetic models (from corona to
wind) of protons, electrons, & ions are needed.
• Because these processes interact
with one another on a wide
range of scales, their impact can
only be evaluated when all are
included together.
• There’s a need for
“phenomenological” terms that
encapsulate what we learn from
micro-scale simulations, so that
macro-scale modeling can
proceed!
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Conclusions
• The past decade, SOHO (especially UVCS)
has led to fundamentally new views of the
collisionless acceleration regions of the solar
wind.
More plasma diagnostics
Better understanding
• Theoretical advances in MHD turbulence are
“feeding back” into global solar wind models.
• The extreme plasma conditions in coronal
holes (T ion >> Tp > Te ) have guided us to
discard some candidate processes, further
investigate others, and have cross-fertilized
other areas of plasma physics & astrophysics.
• There’s a lot to do (theory & observation)!
For more information: http://www.cfa.harvard.edu/~scranmer/
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Extra slides . . .
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
“Opaque” cyclotron damping (1)
• If high-frequency waves originate only at the base of the corona, extended heating
must “sweep” across the frequency spectrum.
• For proton cyclotron resonance only (Tu & Marsch 1997):
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
“Opaque” cyclotron damping (2)
• However, minor ions can damp the waves as well:
• Something very similar happens to
resonance-line photons in winds of
super-luminous massive stars!
• Cranmer (2000, 2001) computed
“tau” for >2500 ion species.
• If cyclotron resonance is indeed
the process that energizes high-Z/A
ions, the wave power must be
replenished continually
throughout the extended corona.
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Charge/mass dependence
• Assuming enough “replenishment” (via, e.g., turbulent cascade?) to counteract
local damping, the degree of preferential ion heating depends on the assumed
distribution of wave power vs. frequency (or parallel wavenumber):
O VI (O+5) measurement
used to normalize heating
rate.
Mg X (Mg+9) showed a
much narrower line
profile (despite being so
close to O+5 in its chargeto-mass ratio)!
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Future diagnostics: additional ions?
• For one specific choice of the power-law index, we can also include either:
enough “local” damping (depending on “tau”) or enough Coulomb collisions
to produce the narrower Mg+9 profile widths . . .
(Cranmer 2002, astro-ph/0209301)
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM
Aside: two other (non-cyclotron) ideas . . .
• Kinetic Alfven waves with nonlinear
amplitudes generate E fields that can
scatter ions non-adiabatically and heat
them perpendicularly (Voitenko &
Goossens 2004).
Solar Wind Origin and Heating 2
http://www.cfa.harvard.edu/~scranmer/NSO/
• If the corona is filled with “thin” MHD
shocks, an ion’s upstream v becomes
oblique to the downstream field. Some
gyro-motion arises before the ion
“knows” it! (Lee & Wu 2000).
Steven Cranmer, June 13, 2007
2007 Solar Physics Summer School, Sunspot, NM