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?
How does the Solar Wind Blow? o does t e So a d o George K. Parks Space Sciences Laboratory Space Sciences Laboratory University of California Berkeley
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 needs to examine carefully what is meant by them. d t i f ll h t i t b th
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 • Magnetosphere is a geomagnetic field confined by the solar wind l i d
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 Spacecraft. ft
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. • Chamberlain (1959) developed a particle theory and Ch b l i (1959) d l d ti l th d 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?
Important Thoughts “Concepts which have proved useful for p p ordering 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 progress is frequently blocked for long i f tl bl k d f l periods by such errors.” Albert Einstein
How does the solar wind expand? H d th l i d d? Solar wind is an outward exension of 10 6 o K 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 R o . o 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.
Wh t i th What is the Solar Wind Problem? S l Wi d P bl ? In hydrodynamic theory, an important assumption is that Coulomb collision mean assumption is that Coulomb collision mean free path λ c << 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.
Wh Where is the problem? i th bl ? 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 V sw at very large distance (Earth) y y g ( ) sw is constrained by the energy available at the base V 2 sw /2 ≈ 5k B T o /m p - M s G/r o + Q o /n o m p V o (1) (1) Enthalpy (heat content) per unit mass due to p + and e - . (1) E th l (h t t t) it d t + d (2) Gravitational binding energy per unit mass (3) Heat flux per unit mass flux (3) Heat flux per unit mass flux
S l Solar wind Calculations i d C l l ti r o ~7x10 8 m, M o ~2x10 30 kg, T~2x10 6 o K, G = 6 67x10 -11 m = 1 67 10 -27 Kg G = 6.67x10 11 , m p = 1.67 10 27 Kg, k B = 1.38x10 -23 J/ o K ~0.8x10 11 J/Kg Enthalpy/mass ( 5k B T o /m pz ) ~ 2x10 11 J/kg Gravity bind energy/mass ( M s G/r o ) Gravity bind energy/mass ( M s G/r o ) 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.
H Heat flux Calculation t fl C l l ti 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 = κ o 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 κ o ~ (3nk B /2) x (2k B T/m) 1/2 λ c (3) (3) Thermal conductivity = (heat capacity/volume)(thermal y ( p y )( speed)(collision mean free path) Here λ c = 1/n π r 2 λ H 1/ 2 c and r c is due to Coulomb collision. d i d t C l b lli i If we use Spitzer model, we get λ c ~ 3x10 7 T 2 /n.
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 [r 2 κ o dT/dr] = 0 d/dr [r κ o dT/dr] 0 (4) (4) With κ o ~T 5/2 , T → 0 at large distance, we find T ∝ r -2/7 and g o 3/2 m e -1/2 T o Q o ~ 3.7x10 7 k B 7/2 /r o
Where is the Problem? (cont’d) V 2 sw /2 ≈ 5kT o /m p - M s G/r o + Q o /n o m p V o (1) Solar wind flux at Earth ~2x10 12 m-2s -1 Flux at the base: n o V o (1) 2 = 5x10 16 x 4x10 5 x(214) 2 Flux at the base: n o V o (1) 5x10 x 4x10 x(214) Put all numbers back into (1) Q o ~ 2x10 11 J kg -1 Q o 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.
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 T 7/2 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 10 6 K exceed 10 6 o K. • With such temperatures, thermal conductivity falls short by an order 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.
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 thermal ones are still collisional. l till lli i l 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.
E Experiments in Space i t i S 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 and B fields are measured with faster than ion cyclotron d B fi ld d ith f t th i l t E 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 !
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