Physics fans on extropians, Robert Bradbury and I have been
discussing offlist various aspects of plasma physics with Amara
Graps, who has obviously put a lotta effort into her replies
in spite of her extremely busy schedule preparing for her PhD
defense in the upcoming months. With her kind permission I
will post a good plasma tutorial written by Amara. The discussion
came about because of Robert's ideas regarding Matrioska
brains. If you want to get up to speed on m-brains, do check
the the extropians archives first as Robert has already posted
tutorial material. Our questions and Amara's answers follow.
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Hi Robert and Spike,
I think that plasma physics is not very intuitive, both to
physicists and nonphysicists (and including me).
Probably it's best to start with some of the plasma basics, and then
lead up to other concepts, in order to answer your questions.
PLASMAS
The plasma state is the fourth state of matter: heating a solid
makes a liquid, heating a liquid makes a gas, heating a gas makes a
plasma. I'm sure that you know that. Plus there are different kinds
of plasma. A completely ionized plasma contains only free negative
electrons and positive ions (= protons). A partially ionized plasma
is partially ionized molecules/atoms with the remainder electrically
neutral normal moleculs and atoms. One can also have an
"ambiplasma", which is a mixture of protons and antiprons, but also
electrons ad positions. When protons and antiprotons collide, Yowza!
Annihilation.
Most of the Universe consists of plasma. Interstellar and
intergalactic plasma, because of its very low density and state of
ionization, differs appreciably from the dense plasma of stars. In
interstellar space the number density is about one atom in every
cubic centimeter, and is partially ionized. In intergalactic space,
the density is about one atom per cubic meter. Our interplanetary
space has a plasma that is dominated by the Sun's solar wind at a
typical density of 1-10 particles per cubic cm. (My reference for
these numbers is Alfven and Longair)
COLLISIONLESS PLASMAS (reference: Longair, pp. 305-307)
The following description shows the long distances involved
between particle collisions in many plasmas; this example is our
solar system, and therefore, why we can call them "collisionless
plasmas".
In a plasma, collisions are mediated between long-range
electrostatic forces between the electrons and protons. A useful
parameter to know for a plasma is how long is the time t_c for a
particle to make a collision. Longair works out a simple expression
using a physical description of a proton of velocity v interacting
with stationary protons and electrons of a plasma, and he determines
that the proton particle suffered a collision if the direction of
its velocity changed 90 degrees. The collisional time (see his text
for how he derives the expression) is:
t_c = [ 2 pi eps_0^2 m^{1/2} (3kT)^{3/2} ] / [Z^2 e^4 N ln(Ga)]
eps_0 = permittivity constant
m = the mass of the proton
k = Boltzmann constant
Z = atomic number
Ga = Gaunt factor
e = electric charge
This is just the simple case, and a more complete treatment is given
in Spitzer: _The Physics of Fully Ionised Gases_ (1962).
To see what 'collisionless' means, apply the above equation
to the interplanetary medium (from Spitzer).
t_c = 11.4 x 10^6 [ (T^{3/2}A^{1/2} ) / (N Z^4 ln(Ga) ) ]
T = temp in K
N = number of particles in cubic meter
A = = the mass number of the particles
For the Solar Wind,
T = 10^6 K
A = 1
N = 5 x 10^6 m^{-3}
Z = 1
ln(Ga) = 28
The mean free path is lamda = v * t_c
v = a typical thermal velocity of a proton in a plasma at
temperature T: (1/2 mv^2 = 3/2 kT).
Therefore lambda, our mean free path = 3 x 10^{13} m
Note: The distance from the Earth to the Sun is 1.5^{11} m !!
Or, putting another way, the mean free path for our proton
is ~5 times the Sun-Pluto distance.
FLUX FREEZING
A long mean free path can be expressed another way: equals a "very
high conductivity". In the limit of infinite conductivity, the
magnetic field behaves as if it were frozen into the plasma. This
phenomena is known as "flux freezing". (Longair, pg. 323)
So you can imagine a collisionless plasma as a volume where the
particles move as "parcels" of [plasma + magnetic field]. This "flux
freezing" (perhaps Hannes Alfven's largest contribution to the
plasma physics field) is a very important aspect of plasma physics
for many astrophysical plasmas. Even though the particles have very
long mean free paths, the presence of even a very weak magnetic
field ties the particles together.
(From Alfven)
Let's assume that the magnetic field in interstellar space is
10^{-5} Gauss (the Earth's magnetic field is about 1/2 Gauss) and
that the plasma particles have a temperature (i.e. thermal motion,
which can be quite "hot" even though space is "cold") of 10^4K. If
the magnetic field was not present, then the atoms would travel
about 10^13 cm before encountering another atom. However with the
presence of the magnetic field, the atom (proton say), would move
about 10^7 cm (250 km) before encountering another particle. So the
feeble magnetic field reduced the freedom of motion of the charged
particle by a factor on the order of millions or billions of times.
You may wonder *how* the presence of the magnetic field reduces the
motion.
When the magnetic field is frozen into the plasma, the charged
particles of the plasma gyrate about the magnetic field direction at
their gyrofrequency. They don't move freely, you see. Not only is
the particle's motion restricted to they gyro-motions, but the
magnetic field typically varies in intensity and direction, which
tightly controls how the particles move. A magnetic field
sufficiently strong enough may propel the particles in opposite
directions. Often, magnetic fields in space act as mirrors, where
the particles oscillate between two turning points in their spiral
orbits. Therefore, their freedom of motion is greatly reduced even
in the direction of the magnetic field.
The gyro motion and radius of ions and electrons move differently
with respect to the same magnetic field. If both kinds of particles
have the same energy, then the gyroradius of the electron is much
smaller than the gyroradius of the ion, and it moves in the opposite
direction. The more energetic the particle, the larger is the
gyroradius.
SHOCK WAVES in COLLISIONLESS PLASMAS (from Longair, pg. 323)
The last concept I wish to introduce is the idea of shock waves in
this collisionless plasma environment. Some or many violent
astrophysical events create shocks. The thickness of the shock front
is the same order as the mean free path of the particles. However
the presence of the magnetic field determines the dynamics of the
shock. The effective friction and viscosity needed to transfer
momentum and energy through the shock wave are provided by the
magnetic field, which is tied to the particles of the plasma. The
distance over which energy and momentum are transferred is, to order
of magnitude, the gyroradius of a particle (so for Solar Wind
events, the gyroradius of the proton in the interplanetary magnetic
field.) The _mechanism_ by which energy is transferred is really
complicated: probably through various forms of plasma wave
interactions involving the magnetic field.
BTW: The Earth's magnetosphere has a "bow shock", which is a
standing shock in the Solar Wind ahead of the Earth's magnetosphere.
The magnetic field of the Earth forms an obstacle to the
supersonically flowing Solar Wind. The bow shock slows the Solar
Wind to subsonic speeds, so that the Solar Wind can flow around the
magnetosphere.
References
Alfven, H. "Plasma Physics" chapter, in _World-Antiworlds: Antimatter
in Cosmology_, 1966.
Longair, Malcolm _High Energy Astrophysics vol 1_, Cambridge, 1992.
------------------------------
Now to see if I can illuminate your questions regarding Coronal mass
ejections:
>a) Is a mass-ejection from a star, primarily an ionized plasma
> and does it remain a plasma as it travels through space?
It's complicated. I'm not even sure that it is clear to the solar
physicists yet. I had to look at some Web sites to get a better idea
of the current understanding of CMEs, but it would be better for you
to look in journal articles. I'll just tell you what I found from my
Web and other readings, in particular:
*I didn't save the URLs, but I found a "report" by the American
Geophysical Union, which had pages with titles: "CMEs Near the Sun",
"CMEs in the Heliosphere", so search on that with google and it will
turn up. That report seemed very factual, with many journal
references. The only possibly negative aspect of the report was it
seem to be about 6 years old.
*_Physics of Solar System Plasmas_ by Thomas Cravens, Cambridge
University Press, 1997.
*_Introduction to Space Physics_, edited by M. Kivelson and C.
Russell, Cambridge University Press, 1995.
Perhaps a good picture of a CME is a "magnetized plasma
cloud/bubble" or a "magnetic flux rope". They carry large amounts of
plasma (probably ionized) and magnetic fields into the heliosphere.
The mass quantity I read in my Time-Life _The Sun_ book (possibly
dated information) is about 10 billion metric tons of material,
which is a significant fraction of what the solar wind disperses in
a day.
CMEs appear to arise from large-scale, preexisting coronal
streamers (NOT from coronal holes, and don't confuse these CMEs with
prominences, either). Many energetic CMEs are actually the
disruption of a preexisting streamer, which increases in brightness
and size for days before erupting (like a balloon.. have you seen
those movies?) as a CME.
I am sure that the CME remains a plasma as it travels through space,
but I'm not certain of the details "how" it travels. My guess that
it would likely be a "plasma wave" with shocks preceding it in the
Solar Wind. Please use the picture that I described above of "Shocks
in Collisionless Plasma". Cravens' book has a diagram on page 245 of
a schematic of a CME. The picture shows a cloud of size about 1AU,
where the coronal gas acts as a "piston" pushing out into the slower
ambient Solar Wind. The shock wave moves out ahead of the
disturbance. Cravens gives the reference: Burlaga, L. et al, "A
magnetic cloud and a coronal mass ejection," Geophys. Res. Lett. 9,
1317, 1982.) CMEs are now thought to be the prime cause of large
geomagnetic storms.
>b) If it is a "hot" plasma traveling through space, why doesn't
> it radiate heat and rapidly cool down?
I think that it does.. but in a "shocking" way :-)
A shock front moving outward through the Solar Wind overtakes the
slower-moving plasma ahead of it, accelerating and heating the
material that it sweeps up. The shock thus transfers momentum and
energy to a widening region of Solar-Wind plasma. Unless such
momntum and energy are continually replenished, the shock must be
decelerated as it moves outward through the solar system.
To understand the generalities of how shocks behave, one must go to
magnetohydrodynamics (MHD). MHD describes the plasma at the level of
the macroscopic fields (electric and magnetic) and quantities such
as the density and bulk-flow velocity. Because MHD does not include
effects due to individual particles ("kinetic" effects), it cannot
tell us anything about how a shock provides dissipation or what the
structure of the shock will be. But it can describe the plasma far
upstream and downstream of the shock.
>From Kivelson, pg. 150
One way to describe the dissipation at a shock is to say that
despite the lack of collisions, there is an "effective resistivity",
producing viscosity, producing heating dependent on velocity
gradients. In this case, the effective resistivity and viscosity
must be provided by changes in particle velocities caused by
perturbations in the fields. In other words, waves in the fields
replace collisions between particles. It's a behavior called:
collective dissipation, because the fields and the particles act
together. More explicitly, look at a current as a result of a
distortion in the particle distibutions. This distortion can drive
instabilities, which produce turbulence within the shock. The
particles feel the turbulence and suffer small changes in their
velocities, which has the same effect as if they were colliding with
other particles.
>c) Related to this is the question of why astronomers point out
> that some gases (say those emitted from supernova explosions
> or spiraling down into black holes) are at temperatures of
> "millions" of degrees (presumably radiating in X-ray regions)?
> Is it related to the velocity of the ions or the degree of
> ionization? If it is the degree of ionization (i.e. all outer
> electrons have been stripped off), what happened to the electrons?
I think that the astronomers have to be clear about what physical
process the temperatures refer to!
Accretion disks' luminosities are often approximated with a
blackbody formula, using the inner and outer radius of the disk:
2(pi r1^2 - pi r2^2) (sigma T^4) = luminosity
Temperature here refers to the velocity of the particles, and so in
thermal equilibrium 1/2 mv^2 = 3/2 kT.
There are different astrophysical processes though, where one finds
temperatures given. Longair's _High Energy Astrophysics_ might be
the best source to sort it out. He has separate chapters for what he
calls "interaction of high energy particles with matter".
Longair's first chapter deals with "ionization losses", which is
part of your question. Here: ionzation loss is the ionization and
excitation of the atoms and molecules of the material. The electrons
are torn off atoms by the electrostatic forces between the charged
high energy particle and the electrons. This is not only a source of
ionization, but also a source of heating of the material because of
the transfer of kinetic energy to the electrons. The "temperature"
would be the energy of the incoming high-energy particle, typically
given in "electron-volts". You can convert the radiation from hot
bodies with this conversion:
E = kT = 1.380E-23 T J
= 8.617E-5 T eV
where the temperature T is in K.
I imagine that the stripped off electrons become part of the plasma,
and in then in some circumstances, recombine.
Longair's next treatment of "interaction of high energy particles
with matter" considers ionization losses of electrons, and then
bremsstralung radiation.
>d) Spike had tried to convince me that in a plasma, hot atoms radiate
> photons that get rapidly reabsorbed (keeping the plasma "hot").
> I had countered with the density of plasmas seemed very low
> and I didn't see how the plasma could keep the photons from
> radiating away into space. What determines the likelyhood
> of interaction between a photon (or an electromagnetic wave)
> and atoms (or ions) of a specific density? (After all light can
> go through solid glass with relatively little interaction...)
Maybe Spike was taking about photoionization?
Photons with wavelengths shorter than 912 angstroms (the Lyman
limit), can photoionize the hydrogen atom, with the excess photon
energy above the energy of the Lyman limit contributing to the
kinetic energy of the freed electron. In reverse, a free electron
may be captured by a free proton with the emission of a photon. If
the electron is captured in an excited stated of hydrogen, it may
subsequently cascade to the ground level by the sequential emission
of a number of line photons. This is called "recombination radiation"
and plays a role in fluorescence.
I think that it is safe to assume that in the case that Spike was
referring, the plasma is not collisionless, and maybe the best
environment for us that shows photoionization is our Earth's
iononosphere. This environment is really complicated: you start with
a neutral atmosphere, and the source for ionization (where ions are
being produced) could be photoionization, or impact ionization. The
photons would come from the Sun. Then, for the impact ionization,
the particles can come from the galaxy (cosmic rays), the Sun, the
magnetosphere, or from the ionosphere. In addition, energetic
electrons can produce more ionizing photons within the atmosphere
via bremstrahlung (braking radiation).
I only mention ion production in the previous paragraph, but you
also have ions being lost, via various recombination mechanisms.
The best reference for ion production and losses that I saw in my
reference books was the chapter: Ionspheres in Kivelson and
Russell's book: _Introduction to Space Physics_.
By the way, dust particles are strongly affected by photons in two
ways: 1) they acquire charge gained by currents generated by
photoelectron emission, 2) radiation pressure force on the dust is
dependent on whether (and how) the particle extinguishes, scatters
and/or absorbs photons. These processes, however, are _independent_
of any characteristics of the plasma.
>e) Katherine Freese and David Graff (heavy hitting theoretical
> physicists) have argued that the interaction between multi-TeV
> gamma rays and the diffuse infrared background radiation
> (see refs at end) constrains the abundance white dwarfs in
> the galaxy. [question follows]
I won't answer this question now, because I need some more time to
think about it, and I'd rather just mail all of this off to you now.
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You are free to forward this message or parts of this message
on to the extropians list too.
Hope that helps,
Amara
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