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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 Add Energy (i.e. photon) Plasma Atoms or molecules have no electric charge (neutral) Strip off electron from atom (or molecule) Ionized gas (ions & electrons)

Occurrence of plasmas: The Plasma State 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. n e i! Free particle -- potential energy from nearest neighbor << than the mean thermal energy <W> U << W W = k B T where n i n is number density

Some basic plasma properties A Quick Review: Force, Fields, Energy, Potential + Vector Quantity Particle Property Relationship F 12 = q 1q 2 r 4πε o r ˆ 2 21 F 12 = q 1 E 12 E 12 = Field Property Force on 1 by 2 Electric field at 1 by 2 q 2 4πε o r 2 ˆ r 21 Relationship F 12 = U 12 E 12 = φ 12 Potential Energy at 1 by 2 Potential at 1 by 2 Scalar Quantity U 12 = q 1 q 2 4πε o r U 12 = q 1 φ 12 φ 12 = q 2 4πε o 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 φ C = q 4πε o r For collective behavior Debye potential form. Here for distances r > λ D the potential rapidly falls off, and the Debye length, λ D, characterizes the length where thermal particle energy balances with the electrostatic potential energy. φ D = q 4πε o r exp ' ) r ( $ λ D = ε ok B T e ' & ) % n e e 2 ( 1/ 2 λ D *, +

Some basic plasma properties Example: Calculate the Debye Length for a typical space plasma (in the Earth s magnetosphere) with k B T = 10,000 ev, n e = 1 cm -3 $ λ D = ε ok B T e & % n e e 2 ' ) ( 1/ 2 k B = 1.38 x 10-23 J / K ε o = 8.9 x 10-12 F / m T is the temperature of the plasma n e 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 R E

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 λ D, therefore N D >> 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 λ D, therefore N D >> 1. Debye shielding must be effective to remain a quasineutral plasma N D = 4π 3 n eλ D 3 Λ = n e λ D 3 Known as the Plasma Parameter

Some basic plasma properties What defines plasma response? Start Qualitative Q: What if we displace the electrons by a small amount in a fully ionized plasma? 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? Q: What if we displace the electrons by a small amount in a fully ionized plasma? Now Semi-Quantitative Spring Analogy Spring Force Spring Frequency Plasma Frequency d 2 x dt 2 ω = ω pe = = k m x k m n e e2 m e ε o Known as the Electron Plasma Frequency

Some basic plasma properties What defines plasma response? Things to note: m e is << m i, therefore the electrons are more mobile and characterize the response of the plasma as a whole to disruptions to quasineutrality Plasma Frequency ω pe = n e e2 m e ε o 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 >> λ D 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 ω pe τ n >> 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.