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Introduction to Space Plasmas
! The
Plasma State
What is a plasma?
Basic plasma properties:
Qualitative & Quantitative
Examples of plasmas
! Single particle motion in a magnetized plasma
Gyromotion
Bounce motion
Drift motion
! Generating electric currents in plasmas
! Fluid approximation for plasmas
The Plasma State
What is a Plasma?
A gas of charged particles with equal numbers of free
positive and negative charge carriers... “4th state of
matter”
Ordinary Gas
Atoms or molecules have
no electric charge
(neutral)
Add Energy (i.e. photon)
Strip off electron from
atom (or molecule)
Plasma
Ionized gas (ions &
electrons)
The Plasma State
Occurrence of plasmas:
energy input
solid
liquid
gas
plasma
“exotic” under terrestrial conditions:
⇒  gas discharge, candle flame, electrons in metal,
ionosphere
The Plasma State
Plasmas are everywhere!
The Sun:
Big ball of plasma
The Solar Wind:
Plasma from the sun fills
the space between the
planets of the solar system
Planetary Plasmas:
Neutral gases leak into
space and become ionized
99% of known matter in is in the plasma state… but they only
naturally occur near Earth’s surface as lightning or flames.
Physics of a Plasma
The known concepts for the description of a neutral gas
need to be expanded:
we need to include electromagnetism!
Motion of charged particles is controlled by electric and
magnetic forces (E & B fields)
In turn: motion of charged particles generates currents
which modify E & B
Governing equations:
conservation laws for mass, energy, momentum
+ Maxwell’s equations!
Major difference between plasma and neutral gas:
Neutral gas:
•  particles interact only by means of collisions
•  no interaction of particles between collisions
=> Interaction on short length and time scales!
Plasma:
•  short-scale interactions are irrelevant
•  particles coupled by E&B fields on large scales
=> Collective behavior!
Task:
Determine the length and time scales upon which the
quasi-neutrality (QN) condition is fulfilled!
•  Time scales => plasma frequency
•  Length scales => Debye length
Some basic plasma properties
! 
Quasineutral -- On average the plasma looks
electrically neutral to the outside observer, as
the random distribution of of charged particles
and their electric charge fields mutually cancel.
ne ≈ ∑ ni
n is number
density
i
! 
Free particle -- potential energy from nearest
neighbor << than the mean thermal energy <W>
U << W
where
W = kB T
Some basic plasma properties
A Quick Review: Force, Fields, Energy, Potential
Particle
Property
+
Relationship
Electric field at 1 by 2
Force on 1 by 2
Vector Quantity F12 =
Relationship
€
Scalar Quantity
€
q1 q2
rˆ
2 21
4 πεo r
F12 = −∇U12
€
Potential Energy
at 1 by 2
q1 q2
U12 =
4 πεo r
€
Field
Property
F12 = q1 E12
q2
E12 =
rˆ
2 21
4 πεo r
E12 = −∇φ12
€
Potential at 1 by 2
U12 = q€1 φ12
q2
φ12 =
4 πεo r
Some basic plasma properties
How do we show that electric charge fields mutually
cancel?
⇒ Start Qualitative
Start with your
quasineutral
plasma
Q: What if you
added on extra
ion?
Some basic plasma properties
How do we show that electric charge fields mutually
cancel?
⇒ Start Qualitative
Start with your
quasineutral
plasma
Q: What if you
added on extra
ion?
A: Other ions move away
(a bit), and the
surrounding electrons
move toward the
intruding ion.
Hence, the redistribution
of charge shields out the
effects of the new ion,
and the surrounding
plasma can’t ‘feel’ the
intruder outside a certain
distance.
⇒ Process known as Debye Shielding
Some basic plasma properties
How do we show that electric charge fields mutually
cancel?
⇒ Now Semi-Quantitative
Coulomb potential field
for each charge
q
φC =
4 πεo r
For collective behavior
Debye potential form. Here for
distances r > λD the potential €
rapidly falls off, and the Debye
length, λD, characterizes the
length where thermal particle
€
energy balances with the
electrostatic potential energy.
' r *
q
φD =
exp) − ,
4 πεo r
( λD +
€
1/ 2
$ εo k B Te '
λD = &
2 )
% nee (
Some basic plasma properties
Example: Calculate the Debye Length for a typical
space plasma (in the Earth’s magnetosphere) with kBT
= 10,000 eV , ne = 1 cm-3
1/ 2
$ εo k B Te '
λD = &
2 )
% nee (
kB = 1.38 x 10-23 J / K
εo = 8.9 x 10-12 F / m
T is the temperature of the plasma
ne is the number density
e is the charge of an electron
* Remember to convert to SI (MKS) units throughout
(check Appendix A in the text for constants in SI and
some useful conversions).
Answer: 750 m = .750 km ≈ 1.4 x 10-4 RE
Some basic plasma properties
What defines a plasma?
⇒ Start Qualitative
In order for Debye shielding
to be effective you need to
have a large number of
particles inside the Debye
sphere prescribed by λD,
therefore ND >> 1.
Debye shielding must
be effective to remain
a quasineutral plasma
Some basic plasma properties
What defines a plasma?
⇒ Now Semi-Quantitative
In order for Debye shielding
to be effective you need to
have a large number of
particles inside the Debye
sphere prescribed by λD,
therefore ND >> 1.
4π
3
N D = n e λD
3
Debye shielding must
be effective to remain
a quasineutral plasma
Λ = n e λD
3
⇒ Known as the Plasma Parameter
€
Some basic plasma properties
What defines plasma response?
Q: What if we displace the electrons by
a small amount in a fully ionized
plasma?
⇒ Start Qualitative
A: The electrons will feel a
restoring force that pulls
them back to the original
(‘equilibrium’) position,
analogous to the motion of a
mass on a spring. The
electrons will oscillate with a
characteristic frequency
related to the density of the
plasma.
⇒ Known as the Electron Plasma Frequency
Some basic plasma properties
What defines plasma response?
⇒ Now Semi-Quantitative
Spring Analogy
Spring Force
Spring
Frequency
Q: What if we displace the electrons by
a small amount in a fully ionized
plasma?
Plasma
Frequency
d2 x
k
=− x
2
dt
m
k
ω=
m
ω pe =
nee 2
meεo
⇒ Known as the Electron Plasma Frequency
€
Some basic plasma properties
What defines plasma response?
Things to note:
•  me is << mi , therefore the electrons
are more mobile and characterize the
response of the plasma as a whole to
disruptions to quasineutrality
Plasma
Frequency
€
ω pe =
nee 2
meεo
•  In a partially ionized plasma (the
ionosphere for example), the plasma
frequency must be much higher than
the collision frequency with neutrals
in order to respond as a plasma to
electric and magnetic perturbations.
Some basic plasma properties
So to Recap:
Three Main Criterion for Defining
Plasma Properties:
•  Physical dimensions of the system
must be large relative to the Debye
length ⇒ L >> λD
•  Must have high enough densities to
enable Debye shielding ⇒ Λ >> 1
•  The time between collisions with
neutrals must be large relative to the
reciprocal of the plasma frequency
⇒ ωpeτn >> 1
Now Quantitative:
Whiteboard Derivations of Plasma
Frequency and Debye Length
Physics of a Plasma: Recap
Preliminary definition:
•  A plasma consists of free positive and negative
charges (e.g., protons, electrons, …). It may also
contain neutral particles.
•  The properties of the plasma are mainly determined
by the charged particles.
•  On average, the plasma is electrically neutral.
Quasi-neutrality:
On average, a plasma is electrically neutral.
⇒  average over both, spatial scales and time scales!
•  size of averaging volume defines a characteristic
length scale (Debye length)
•  length of averaging time interval defines typical time
scale (inverse plasma frequency)
Below these length and time scales: No neutrality!
Collective behavior:
•  The dynamics of the plasma are not controlled by the
interactions between individual particles (e.g., binary
collisions)
•  The dynamics of the plasma are determined by the
particle system as a whole!
Examples of Plasmas
Homework 1
Handed out Friday, and also on the course website.
Due next Friday (1/20) in class.