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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

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.