SLIDE 1 Three Talks:
- 1. How does the solar wind blow?
2 A Tale of Two Space Plasma Physics
- 2. A Tale of Two Space Plasma Physics
Paradigms
- 3. Why have we not solved the substorm
problem?
SLIDE 2 How does the Solar Wind Blow?
d
Space Sciences Laboratory Space Sciences Laboratory University of California Berkeley
SLIDE 3
Space Plasma Physics
Space Physics began more than 50 years ago with the launch of sputnik on October 4 1957 launch of sputnik on October 4, 1957. Now, middle aged, s/he looks back to see what has been accomplished and if life has been fruitful. After critically examining the field, s/he comes to a surprising conclusion: Many “important” problems have not been “solved ” have not been solved. But s/h also finds a few articles by notable scientists (Axford and Parker), who think most important space ( ), p p physics problems are solved. Important and Unsolved are subjective words. S/he d t i f ll h t i t b th needs to examine carefully what is meant by them.
SLIDE 4 Present Picture of Space Plasma Environemnt
- Solar wind is hydrodynamic
expansion of solar corona
- IMF is solar magnetic field
carried out frozen in the solar wind
- Bow shock forms because solar
wind is super-sonic
- Magnetosheath consists of
thermalized shocked particles
geomagnetic field confined by the l i d solar wind
SLIDE 5
Solar Wind
Planets, comets, stars and galaxies eject matter into space into space. The ejection varies from steady to chaotic, from symmetrical to jet-like. symmetrical to jet like. Mechanisms range from thermal evaporation to explosive events. p Most objects too far so that observations not sufficient to constrain theoretical models. Not in the case of the solar wind, which was actually predicted before measured directly by S ft Spacecraft.
SLIDE 6 History of the Solar Wind
How does the solar wind blow?
- Biermann (1950) first deduced from observations of
comet tails that Sun must be emitting particles.
- Parker (1958) developed a fluid theory and predicted
Parker (1958) developed a fluid theory and predicted that a solar wind speed of a few hundred km/s and super- sonic. Ch b l i (1959) d l d ti l th d
- Chamberlain (1959) developed a particle theory and
predicted a solar wind speed of a few ten km/s (sub-sonic). The debate ended when Spacecraft measurements found p Solar Wind speed was a few hundred km/s and also super-Alfvénic. However a few people still objected to the fluid theory but However, a few people still objected to the fluid theory but they were ignored. What are the objections? Are they justified?
SLIDE 7 Important Thoughts
“Concepts which have proved useful for p p
- rdering things easily assume so great an
authority over us, that we forget their terrestrial origin and accept them as unalterable facts...The road of scientific i f tl bl k d f l progress is frequently blocked for long periods by such errors.” Albert Einstein
SLIDE 8 H d th l i d d? How does the solar wind expand?
Solar wind is an outward exension of 106 oK hot upper solar corona. Close to Sun atmosphere strongly bound The mean gravitational Close to Sun, atmosphere strongly bound. The mean gravitational energy/ion is ~10X the thermal energy. However, because the medium is ionized and very hot, it conducts heat very efficiently. Hence T decreases very slowly with altitude so that the thermal energy becomes greater than the gravitational energy around 10 Ro.
- In static fluid equilibrium, p will not decrease very much beyond this
point, and since p is many times higher than that of the interplanetary medium the corona expands away into space interplanetary medium, the corona expands away into space.
SLIDE 9
Wh t i th S l Wi d P bl ? What is the Solar Wind Problem?
In hydrodynamic theory, an important assumption is that Coulomb collision mean assumption is that Coulomb collision mean free path λc << scale height H. In this case expected distribution function f(r v In this case, expected distribution function f(r, v, t) is a Maxwellian. However observations show f(r v t) departs However, observations show f(r, v, t) departs substantially from the equilibrium Maxwellian form questioning the validity of the form, questioning the validity of the hydrodynamic theory.
SLIDE 10 Wh i th bl ? Where is the problem?
The flow energy of the solar wind must come from the base of the Sun where the solar wind originates Speed there is the Sun where the solar wind originates. Speed there is small. The asymptotic flow speed Vsw at very large distance (Earth) y
sw
y g ( ) is constrained by the energy available at the base V2
sw/2 ≈ 5kBTo/mp - MsG/ro + Qo/nompVo
(1) (1) E th l (h t t t) it d t
+
d (1) Enthalpy (heat content) per unit mass due to p+ and e-. (2) Gravitational binding energy per unit mass (3) Heat flux per unit mass flux (3) Heat flux per unit mass flux
SLIDE 11
S l i d C l l ti Solar wind Calculations
ro ~7x108m, Mo ~2x1030 kg, T~2x106 oK, G = 6 67x10-11 m = 1 67 10 -27 Kg G = 6.67x10 11, mp = 1.67 10 27 Kg, kB = 1.38x10-23 J/oK Enthalpy/mass (5kBTo/mpz) ~0.8x1011 J/Kg Gravity bind energy/mass (MsG/ro) ~ 2x1011 J/kg Gravity bind energy/mass (MsG/ro) 2x10 J/kg Available Enthalpy is Not sufficient to lift the coronal py atmosphere out of Sun’s gravitational field. From (1), we see heat flux Q must be important.
SLIDE 12 H t fl C l l ti Heat flux Calculation
In a collisional medium (λ<<H) we can use the heat In a collisional medium (λ<<H), we can use the heat conduction equation, Q = κo dT/dr (2) Heat is transported mainly by electrons because of much larger thermal speed. κ ~ (3nk /2) x (2k T/m)1/2 λ (3) κo~ (3nkB/2) x (2kBT/m)1/2 λc (3) Thermal conductivity = (heat capacity/volume)(thermal y ( p y )( speed)(collision mean free path) H λ 1/
2
d i d t C l b lli i Here λc = 1/nπr2
c and rc is due to Coulomb collision.
If we use Spitzer model, we get λc~ 3x107T2/n.
SLIDE 13 Heat Flux calculation (cont’d) Heat Flux calculation (cont’d)
Estimate dT/dr at the base. Assume no loss, and use heat balance equation (spherical coordinates) balance equation (spherical coordinates) d/dr [r2 κo dT/dr] = 0 (4) d/dr [r κo dT/dr] 0 (4) With κo ~T5/2, T→0 at large distance, we find T∝r -2/7 and
Qo ~ 3.7x107kB
3/2 me
7/2/ro
SLIDE 14 Where is the Problem? (cont’d)
V2
sw/2 ≈ 5kTo/mp - MsG/ro + Qo/nompVo
(1)
Solar wind flux at Earth ~2x1012 m-2s-1 Flux at the base: noVo (1)2 = 5x1016 x 4x105x(214)2 Flux at the base: noVo (1) 5x10 x 4x10 x(214) Put all numbers back into (1) Qo ~ 2x1011 J kg-1 Qo just balances the binding gravitational energy! Enthalpy term yields terminal velocity of few hundred km s-1 Enthalpy term yields terminal velocity of few hundred km s-1, so enough energy is available to drive the solar wind.
SLIDE 15 What have we learned?
The enthalpy term yields a terminal velocity of a few hundred km s-1, so enough energy is available to drive the solar wind. , g gy
- However, Heat flux varies as T7/2 and very sensitive! With T
~15% smaller Eq (1) becomes negative! ~15% smaller, Eq (1) becomes negative!
- Observations also show the fastest solar wind comes from
coldest region of corona (coronal holes) where T does not d 106 K exceed 106 oK.
- With such temperatures, thermal conductivity falls short by an
- rder of magnitude required to drive the solar wind.
g q
- Fixes? They include injection of additional energy from
microflares, Alfven waves, etc... How these perturbations could provide the right energy in the right place to accelerate could provide the right energy in the right place to accelerate the solar wind is not certain.
SLIDE 16
Need for Kinetic physics
If the mean free path is not small at the base of the solar wind the classical expression of heat flow solar wind, the classical expression of heat flow is not valid. Reason is that Coulomb potential varies as 1/r, Reason is that Coulomb potential varies as 1/r, making their cross section proportional to inverse square of their energy. Hence, the energetic particles which contribute most to heat flux, are collisionless, whereas the th l till lli i l thermal ones are still collisional. An alternative way to describe the medium is then to consider the solar wind as an escaping to consider the solar wind as an escaping exosphere.
SLIDE 17 E i t i S Experiments in Space
Experiments in space have been improving steadily since Sputnik launched on 4 October 1957. p
- Electron and ion distributions obtained in one spin time (~3
s). E d B fi ld d ith f t th i l t
- E and B fields are measured with faster than ion cyclotron
period.
- Multi-spacecraft can measure currents J at boundaries.
p
- Many features observed are beyond the capability of the
fluid theory. For example, boundary thickness ~ gyroradius of a few keV H+ where the fluid assumptions gyroradius of a few keV H+ where the fluid assumptions break down. These observations have encouraged interpreting space plasma observations using kinetic theory !
SLIDE 18 Ki ti P i t f Vi Kinetic Point of View
“U l d” bl i l d “Unsolved” problems include:
- How solar wind is accelerated,
- How the solar corona is heated.
- How the bow shock forms and thermalizes
particles,
- How solar wind particles interact with planetary
magnetic fields to form boundaries
- How the solar wind particles enter the
magnetosphere
- Mechanisms for solar flares, CMEs, auroras,
magnetic storms and substorms
SLIDE 19 Ki ti d l f th l i d Kinetic model of the solar wind
Sun’s photosphere is collisional However near corona Sun s photosphere is collisional. However, near corona, plasma is collisionless. J. H. Jeans (1925) calculated number of neutral particles escaping stellar p p g atmospheres. Important result: >50% electrons have vth >> vesc but only ~1% of ions
+
Solar atmosphere
An Imbalance of charges is produced on the Sun Must find a way to neutralize the charges Must find a way to neutralize the charges.
SLIDE 20
Electric field will maintain charge neutrality
First model: S. Rosseland (1924) and A. Pannekoek (1922) hydrostatic models assumes Maxwellian (1922) hydrostatic models assumes Maxwellian distribution with a potential. This yields ∇2 ΦE = ρc/εo and ∇2 ΦG = -4π Gρm Solution is ΦE = -(mi - me)ΦG / e(Z+1)
Electrons:
vesc(e) = 2 ΦE /me Ions: vesc(i)~ vesc(e) (me/mi)1/2
Sun still charged!
SLIDE 21 Improved Electric Potential Model
E l fl i i h b l Equal fluxes escape to maintain charge balance.
+
Equal fluxes ∇ΦE Φg
r
+
collision dominated photosphere
SLIDE 22 Kinetic model of the solar wind
Determine Escape velocity from Conservation of Energy mv2(r)/2+mΦg(r)+ZeΦE(r) = mv2(ro)/2+mΦg(ro)+ZeΦE(ro) h Φ ( ) GM/ S t Φ ( ) where Φg(r) = -GM/r. Set ΦE(∞) = 0 Escape velocity v*(ro) = [- Φg(ro) - ZeΦE(ro)/m]1/2 p y ( o) [
g( o) E( o)
] Escape Flux F(ro) = Neo(2kTeo/me)1/2[1+ Ueo] e -Ueo where Ueo = v*2 (ro) /2kTeo/me
SLIDE 23
Electric Potential model
Construct potential so ions accelerated outward. Also v > v at r so the ions can escape A potential to Also v > vesc at ro so the ions can escape. A potential to achieve this is obtained from (1 + eΦE/kTe)exp-(1 + eΦ/kT) = (me/mi)1/2 With v*2/2kTeo/me~5, eΦEo ~5kTeo, and for T~106 oK ΦEo ~490 eV. The solar wind blows because plasma maintains charge t lit ! neutrality!
SLIDE 24 Further Improvements are needed
Mean free of the particles in the solar corona is not sufficiently large so that collision can be totally sufficiently large so that collision can be totally ignored. Fokker-Planck treatment has been started by some authors, e.g. LeBlanc and Hubert (2001). Solar plasma where the solar wind originates is unlikely to be Maxwellian to be Maxwellian. Ad hoc approach is to use Kappa distribution instead of the Maxwellian distributjon. Such studies have shown j that suprathermal electrons are important. Energetic electrons have large impact on the solar wind l ti D t il ?
SLIDE 25 References on Kinetic Models of the solar wind References: Ch b l i (1960) J k (1970)
- Chamberlain (1960), Jockers (1970),
Lemaire and Scherer (1973), Scudder (1994), Lie Svendsen et al (1997) Meyer Vernet Lie-Svendsen et al., (1997), Meyer-Vernet and Issautier (1998), Pierrard and Lemaire (1999) Meyer-Vernet (1999) Issautier (2001) (1999), Meyer Vernet (1999) Issautier (2001), Maksimovic et al., (2001), Pierrard et al., (2001) and Zouganelis et al. (2005), Marsch ( ) g ( ), (2006).
SLIDE 26 Basic Equations for space plasmas
Lessons learned from the solar wind problem is that we need to look at the physics from a more fundamental point of p y p view. Th ti f l ll k The equations for plasmas are well known:
- Maxwell Equations of Electrodynamics + Boltzmann
transport equation p q
- Recall that the first 3 moment equations computed from
Boltzmann equation yield Mass, Momentum and Energy. This reduces 6N variables to 3 (n V T) The fluid This reduces 6N variables to 3 (n, V, T). The fluid equations are much simpler but a lot of physics is lost. Future studies of space plasma problems should focus on Kinetic Models.
