xkcd.com It IS about physics. It ALL is.

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1 xkcd.com It IS about physics. It ALL is.

2 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 EAS 4360/6360 2:1

3 The Plasma State A gas of charged particles with equal numbers of free positive and negative charge carriers... 4th state of matter Ordinary Gas What is a Plasma? 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) EAS 4360/6360 2:2

4 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. EAS 4360/6360 2:3

5 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 n i n is number density Free particle -- potential energy from nearest neighbor << than the mean thermal energy <W> U << W W = k B T where EAS 4360/6360 2:4

6 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 EAS 4360/6360 2:5

7 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? EAS 4360/6360 2:6

8 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 EAS 4360/6360 2:7

9 How do we show that electric charge fields mutually cancel? Now 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 *, + EAS 4360/6360 2:8

10 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 J / K ε o = 8.9 x 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 EAS 4360/6360 2:9

11 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 EAS 4360/6360 2:10

12 What defines a plasma? Now 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 EAS 4360/6360 2:11

13 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 EAS 4360/6360 2:12

14 What defines plasma response? Now Quantitative Spring Analogy Q: What if we displace the electrons by a small amount in a fully ionized plasma? 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 EAS 4360/6360 2:13

15 What defines plasma response? Now Quantitative 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. EAS 4360/6360 2:14

16 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 EAS 4360/6360 2:15

17 Examples of Plasmas EAS 4360/6360 2:16

18 Homework 1 Handed out today, and also on the course website. Due next Friday( 1/18 ) in class. Next lecture will cover single particle motion in a magnetic field EAS 4360/6360 2:17

19 Single Particle Motion in a Magnetized Plasma Magnetized Plasma Plasmas in a magnetic field have special properties since charged particles execute 3 distinct types of motion in a non-uniform magnetic field: gyromotion: circular motion about a magnetic field line bounce motion: motion up and down along (parallel to) the magnetic field drift motion: motion perpendicular to the field line and to the magnetic gradient EAS 4360/6360 2:18

20 Single Particle Motion in a Magnetized Plasma Magnetized Plasma Unlike neutral gases and fluids, plasmas are coupled to electromagnetic fields due to their charge. They also generate electromagnetic fields due to their relative motion. Maxwell s Equations For more detailed review see the Appendix (A.5) EAS 4360/6360 2:19

21 Single Particle Motion in a Magnetized Plasma Maxwell s Equations -- Quick Review Ampère-Maxwell Equation Maxwell-Faraday Equation Gauss s Law for Magnetism Gauss s Law B = µ o j + ε o µ o E t E = B t B = 0 E = ρ ε o EAS 4360/6360 2:20

22 Single Particle Motion in a Magnetized Plasma Maxwell s Equations -- Quick Review B = µ o j + ε o µ o E t E = B t B = 0 E = ρ ε o Since ε o µ o = c -2, where c is the speed of light, the time variable electric field term is relatively small in the absence of very rapidly varying electric fields. j is the current density, or difference in flux of ions and electrons. No divergence of the magnetic field essentially indicates no magnetic sources, i.e. no magnetic monopoles. ρ is the charge density, and the divergence of E comes from the fact that the field is sourced at charged particles. EAS 4360/6360 2:21

23 Single Particle Motion in a Magnetized Plasma div, grad, curl, etc reminders F = F x x + F y y + F z z % f = f x, f y, f ( ' * & z ) Divergence, div Gradient, grad F = i j k x y z Curl F x F y F z & = F z y F ) y & ( + i + F x ' z * z F z ( ' x ) & + j + F y * x F x ( ' y ) + k * Leibniz vs. Newton df vs. F dt EAS 4360/6360 2:22