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It IS about physics. It ALL is.
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
A gas of charged particles with equal numbers of free positive and negative charge carriers... “4th state of
matter”
What is a Plasma?
Atoms or molecules have no electric charge
(neutral)
Strip off electron from atom (or molecule)
Ordinary Gas Plasma Add Energy (i.e. photon)
Ionized gas (ions & electrons)
Occurrence of plasmas: “exotic” under terrestrial conditions: ⇒ gas discharge, candle flame, electrons in metal,
ionosphere
solid liquid gas plasma
energy input
The Plasma State
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.
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!
Physics of a Plasma
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.
! Free particle -- potential energy from nearest neighbor << than the mean thermal energy <W>
ne ≈ nii∑
€
U << W
€
W = kBTwhere
n is number density
Some basic plasma properties A Quick Review: Force, Fields, Energy, Potential
€
F12 =q1q2
4πεor2
ˆ r 21
€
E12 =q2
4πεor2
ˆ r 21
€
φ12 =q24πεor
€
U12 =q1q24πεor
€
F12 = q1E12
€
E12 = −∇φ12
€
F12 = −∇U12
€
U12 = q1φ12
Vector Quantity
Relationship
Scalar Quantity
Particle Property
Relationship Field Property
+
Potential at 1 by 2
Force on 1 by 2 Electric field at 1 by 2
Potential Energy at 1 by 2
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
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.
Q: What if you added on extra
ion?
⇒ Process known as Debye Shielding
Some basic plasma properties How do we show that electric charge fields mutually cancel? ⇒ Now Semi-Quantitative
€
φC =q
4πεorCoulomb potential field
for each charge
€
φD =q
4πεorexp − r
λD
'
( )
*
+ ,
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.
€
λD =εokBTenee
2
$
% &
'
( )
1/ 2
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
€
λD =εokBTenee
2
$
% &
'
( )
1/ 2 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.
Debye shielding must be effective to remain a quasineutral plasma
⇒ Known as the Plasma Parameter €
ND =4π3neλD
3
€
Λ = neλD3
Some basic plasma properties What defines plasma response? ⇒ 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.
Q: What if we displace the electrons by a small amount in a fully ionized
plasma?
⇒ Known as the Electron Plasma Frequency
Some basic plasma properties What defines plasma response?
⇒ Now Semi-Quantitative
Q: What if we displace the electrons by a small amount in a fully ionized
plasma?
⇒ Known as the Electron Plasma Frequency
€
d2xdt 2
= −kmx
ω =km
ω pe =nee
2
meεo
Spring Analogy
Spring Force
Spring Frequency
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
• 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.
€
ω pe =nee
2
meεo
Plasma Frequency
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
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.
Physics of a Plasma: Recap
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.
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