1. Space Physics and Space Weather
Space: “empty” volume between bodies (solid bodies are excluded)
Space physics: space within solar system (astrophysics is not space physics)
Solar-terrestrial relations: space physics focused on solar wind and terrestrial space
Space plasma physics: application of plasma physics to space
Space physics: Coriolis force and gravity not important (unless noted)
Space weather: space physics applications. Space phenomena that endanger space assets and applications and human in space
Space physics: electromagnetic field + charged particles
Require significant math:
Working on but not solving partial differential equations in this class
Vector operations
Require: electromagnetics (additional reading may help)
Reiterated space physics involves studying plasmas, that electromagnetic fields are important, and that coriolis force and gravity are not important (unless noted).

2. Here’s an example where gravity and coriolis force are important
Here’s an example where gravity and coriolis force are important. Currents in Earth’s interior are significantly driven by coriolis force, and give rise to an intrinsic dipolar field. The dipole is not perfectly centered on the earth’s axis, and the dipole axis is not aligned with the spin axis. The dipole axis is moving. The Earth polarity undergoes reversals that paleontologists have found (students knew a lot about that).

3. The Sun also has a magnetic field, but it is not dipolar
The Sun also has a magnetic field, but it is not dipolar. The sun has a wind of particles constantly being blown outward. The particles flow away from the sun radially, and due to the sun’s rotation it forms an Archimedian spiral like a lawn sprinkler. The particles carry the magnetic field with them. The planets are orbiting in the solar wind.

4. The Earth’s dipolar field would continue forever if space were empty
The Earth’s dipolar field would continue forever if space were empty. But the Sun’s magnetic field interacts with the Earth’s field and the fields superpose. The Earth’s field carves out a cavity or bubble in the solar wind. The Earth’s field is stretched to form a tail on the night side, and is compressed on the dayside. The solar wind has about 3 to 6 particles per cc (hope that’s right) and is traveling about 450 km/s. Sometimes the Sun outputs a magnetic cloud of particles that travels up to 1000 km/s. The solar wind is supersonic and the Earth’s field forms a shock called the bow shock and a region called the magnetosheath – much like a boat wake. For a long time people thought that nothing interesting happened in the magnetosheath, but more recent measurements have shown that there are turbulent processes that are not well understood so it is a place for active research. The magnetosheath is the region between the magnetopause, where the magnetic field of the Earth disappears and the bow shock which is the boundary to the solar wind. We’ll be talking about other regions in the magnetosphere as well.

5. Magnetic clouds http://geo.phys.spbu.ru/~tsyganenko/modeling.html
The Solar wind impacts the Earth’s magnetosphere in two ways. The first is the interaction of the magnetic field with the Earth’s magnetic field. There are always changes due to Earth rotation on the left, and the speed and direction of the solar wind also contribute to the wind socking of the tail. Occasionally a magnetic cloud will pass by causing a geomagnetic storm – the changes to the magnetic field are substantial and measured by ground magnetometers near the equator.

6. The other way that the solar wind impacts the magnetosphere is that particles enter. Most particles are deflected around the sides, as shown in the top image. But particles do enter the magnetosphere and from the tail travel along field lines even into the ionosphere forming the aurora. Dangerous energetic particles can enter directly. They mess up the electronics on satellites. Astronauts on the International Space Station say they can detect particles with their eyes closed – they see occasional bright flashes when the particles interact with their eyes. In fact, during one of the Apollo missions, the astronauts were on the Moon when the Sun had a major solar flare with dangerous levels of energetic particles. If they had been travelling from between the Earth and Moon at the time, they would have died from the exposure. We were lucky.

7. Regions in Space
Solar wind (sun’s atmosphere, but not bonded by gravity): plasma (ions and electrons in equal number but not attached to each other) stream flows out continuously, but with variations, from the sun with extremely high speeds into the interplanetary space. Note: in space, all ions are positively charged.
Formation of the magnetosphere: the solar wind deflected by the geomagnetic field.
Magnetopause: the boundary separates the magnetosphere from the solar wind (crucial for any solar wind entry).
Bow shock: standing upstream of the magnetopause, because the solar wind is highly supersonic.
Magnetosheath: the region between the bow shock and the magnetopause.
We’ve already talked about these regions in space, but we’ll read through the list once again. These are important to know… (reading though these – sometimes going back to point to them). Discussing again the bow shock, magnetosheath, and magnetopause. The magnetopause is about 10 to 12 Earth radii towards the Sun with the Bow Shock another 2 to 5 Earth radii beyond that. The dipole field is compressed on the dayside, and sometimes during periods of intense geomagnetic activity the magnetopause is inside the geosynchronous orbit of 6.6 Earth radii.

8. Regions in Space, cont.
Magnetotail: the magnetosphere is stretched by the solar wind on the nightside.
Radiation belts: where most energetic particles are trapped, (major issue for space mission safety).
Plasmasphere: inner part of magnetosphere with higher plasma density of ionospheric origin.
Ionosphere: (80 ~ 1000 km) regions of high density of charged particles of earth origin.
Thermosphere: (> 90 km) neutral component of the same region as the ionosphere. The temperature can be greater than 1000 K.
The magnetotail is created when the earths dipole is stretched – it extends to about 100 earth radii and the Moon is about 60 earth radii away so sometimes the Moon is inside the magnetosphere and sometimes it is outside. The radiation belts are here – show on next image – and energetic particles get trapped there. Dr. Song is working on ways to mitigate them and protect space assets. The plasmasphere is here – on picture – and an area where the plasma is denser and it suddenly drops off at the plasmapause. The ionosphere you know about from meteorology – the boundary layer, then the troposphere, stratosphere, mesophere, then ionosphere. The thermosphere is co-located with the ionosphere. The charged particles make up the ionosphere, and the neutral particles make up the thermosphere. UML does a lot of research about the ionosphere, and developed Digisonde a way to do soundings to determine the composition of the ionosphere from the ground – even spun off a company.

9. This picture shows the regions that we already talked about
This picture shows the regions that we already talked about. Changes in magnetic fields give rise to electric fields and current systems. Changes in currents give rise to magnetic fields. It’s complicated, but by the end of today’s lecture, we’ll have explained how the and magnetopause current here on the dayside and the cross tail current here in the tail are formed. We’ll also be discussing the ring current.

10. Space Weather Phenomena
Magnetic storms (hurricanes in space)
Global-scale long-lasting geomagnetic disturbances
Magnetic substorms (tornadoes in space)
Impulsive geomagnetic disturbances
Auroras (rains from space)
Enhanced energetic particle precipitations associated with storms/substorms
Ionospheric plasma density disturbances (fog?)
Destruction of the layered structure of the ionosphere.
Enhanced extremely high-energy particle fluxes (hails?)
Changes in the solar wind cause changes in the magnetic field and currents in the magnetosphere. Dr. Song has analogies of space weather that results to weather in the troposphere. The magnetosphere extends 100 Earth radii and a geomagnetic storm impacts the magnetic field everywhere, and we measure a storm in ground magnetometers near the equator. Substorms are smaller scale, intense, and last only about a half an hour whereas the storms last for days. Substorms are analogous to tornados which are highly localized events. These are seen in ground magnetometers at high latitudes. Aurora are created when particles precipitate into the ionosphere, and this precipitation is analogous to rain. There are also density structures in the ionosphere akin to fog. We also talked about the dangers of high energy particles, and that is like hail.

11. These movies didn’t play well on the UML equipment
These movies didn’t play well on the UML equipment. The one on the left shows the STEREO mission and follows a CME from Sun to Earth and we talked about how doing this is relatively new. CMEs are one cause of geomagnetic storms. The one on the right is an artist conception of a substorm. Substorms typically occur in context of storms. The model at the bottom shows a substorm – pointed out the stretching and dipolarization that occurs.

12. Here are the links to the movies - just used to illustrate not with their audio - but I think the class might like them:
New Slide 11
(Left)
Title: STEREO Tracks Solar Storms From Sun To Earth
(Right)
Title: Substorms
The point being not the accuracy of the depiction
but that substorms are localized events and lead to aurroa
New Slide 12
Title: Aurora from Orbit Sept. 17, 2011
The 5 min movie of aurora from ISS but it is too big to
Aurora from Earth
The other movies on New Slide 23 just show the 3 ways of describing plasma.

13.
These movies didn’t play well either. The one on the left was the 4 minute movie but has been replaced with a smaller one because the longer one is over 70 Mbytes and won’t . They show the aurora from space (left) and from ground (right), and put a good perspective on how small the ionosphere is compared to earth. We talked about how aurora are different colors depending on the energy of the particles and what part of the ionosphere is auroral based on knowledge of light emitted by different atomic and molecular species and our knowledge about the ionosphere composition – and that spectroscopy can be used to identify O, O+, O2, O2+, N, N2, N+, N2+, H, OH, NO, etc. But most of it is oxygen and nitrogen.

14. Evidence for Space Processes
Aurora: emissions caused by high energy charged particle precipitation into the upper atmosphere from space.
Geomagnetic field: caused by electric currents below the earth’s surface.
Geomagnetic storm/substorm: period of large geomagnetic disturbances.
Periodicity of magnetic storms: ~ 27 days.
Rotation of the Sun: 26 ~ 27 days.
Read through this – talked about the 27 day rotation.

15. Space physics started with observations of the aurora.
Old Testament references to auroras.
Greek literature speaks of “moving accumulations of burning clouds”
Chinese literature has references to auroras prior to 2000BC
Read through this.

16. Descartes thought they are reflections from ice crystals.
Galileo theorized that aurora is caused by air rising out of the Earth’s shadow to where it could be illuminated by sunlight. (Note he also coined the name aurora borealis meaning “northern dawn”.)
Descartes thought they are reflections from ice crystals.
Halley suggested that auroral phenomena are ordered by the Earth’s magnetic field.
In 1731 the French philosopher de Mairan suggested they are connected to the solar atmosphere.
Can read later.

17. By the 12th century the European records mention the compass.
By the 11th century the Chinese had learned that a magnetic needle points north-south.
By the 12th century the European records mention the compass.
That there was a difference between true north and the direction of the compass needle (declination) was known by the 16th century.
William Gilbert (1600) realized that the field was dipolar.
In 1698 Edmund Halley organized the first scientific expedition to map the field in the Atlantic Ocean.
Can read later about the history of the understanding of the Earth’s magnetic field.

18. Model Si Nan (Pointing to South) of Han Dynasty (206 BC–220 AD).
South pointing Fish of Northern Song Dynasty (960–1127).
The evolution of the compass – all in China. First ladles were made of magnetic rock. These were used for fortune telling and feng shui lifestyle decisions. Then needles of magnetic rock were embedded in wood carvings of fish then floated in a water. Then the needles of magnetic rock were embedded in carvings of turtles and suspended so they were dry. Finally, compasses were designed and used for navigation. Shortly thereafter Europeans used compasses for navigation in years of nautical exploration.
South pointing Turtle of Southern Song Dynasty (1127–1279).
Compass for navigation

19. Again the Earth’s dipole field is compressed on dayside and stretched on nightside by the solar wind. But the field is very close to being a dipole even to 4 or 5 Earth radii. Modelers have been able to show that this dipole comes from currents inside the earth that arise from the Coriolis and gravity forces on molten iron. Field reversals have been modeled and the pole is moving – students knew more than I do about all that. Then we talked about the Wiki dipole field formula and how the field falls off as 1/r^3. Something to keep in mind is that the formula look different if expressed in terms of the spherical polar coordinate vs. the latitude – do get mixed up.

20. Plasma A plasma is an electrically neutral ionized gas.
The Sun is a plasma
Interplanetary medium: the space between the Sun and the Earth is “filled” with a plasma.
The Earth is surrounded by plasmas: magnetosphere, ionosphere.
Planetary magnetospheres, ionospheres
A stroke of lightning forms plasma
Over 99% of the Universe is plasma.
Although neutral, a plasma is composed of charged particles- electric and magnetic forces are critical to understand plasmas.
Plasma physics: three descriptions
Single particle theory
Fluid theory
Kinetic theory
Two things that Dr. Song wants everyone to know are 1) A plasma is an electrically neutral ionized gas and 2) there are three ways to describe plasmas. We talked about examples of plasmas – and that a plasma is neutral but because of the charged particles magnetic and electric forces are critical to understanding them whereas gravity and coriolis forces are not generally important.

21. The Sun's mass makes up over 99
The Sun's mass makes up over 99.85% of the Solar System, and since it is nearly all in the plasma state, over 99.9% of the mass of the Solar System is in the plasma state.
The universe is mostly plasma – we can figure that out just from considering the solar system where space physics takes place. By volume this picture shows the relative sizes of the Sun and planets. By mass, the relative portion of the Sun is even greater. The Sun is mostly plasma and so is the solar wind. The gas planets are mostly plasma. The rings of Saturn are a ‘dusty’ plasma. It is easy to see that 99.9% of the solar system is plasma.
The Solar System edited by Thérèse Encrenaz, Published 2004 Springer, ISBN Page 1
Introduction to Plasma Physics: With Space and Laboratory Applications, by Donald A. Gurnett, Published 2005 Cambridge University Press, ISBN , Page 2

22. A plasma is an electrically neutral ionized gas.
Definition of a Plasma
The plasma approximation: Charged particles must be close creating collective behavior.
Bulk interactions: Electrical screening lengths are short compared to the physical size of the plasma.
Quasineutrality: The electron plasma frequency is large compared to the electron-neutral collision frequency, so they can quickly shield externally applied electric fields.
Degree of Ionization α = ni/(ni + na)
Temperature
Densities
Electric Potential (fields and circuits)
Magnetization (anisotropic)
Filaments
Shocks
A plasma is an electrically neutral ionized gas – that’s all you need to know. But I’m going to clarify that a little – there are three criteria for defining a plasma. (blah, blah, blah) You don’t need to know all this now, but plasmas are characterized by degree of ionization, temperature (although there is no requirement that it be in thermal equilibrium we define it this way), density can be found from boltzmann, and turning that around we can find an electric potential and taking the gradient the field – the gradients in density result in an electric field, magnetization creates anisotropies because it affects particle motions differently, and magnetization can become organized into filaments that we saw in that last picture of the Sun and in the aurora, and shocks are supported they will be talked about later in this class. Many different plasmas are on these different density and temperatures but mostly this class is about solar, solar wind, and magnetosphere here on this plot.

23. Gas vs. Plasma A plasma is an electrically neutral ionized gas.
Property
Gas
Plasma
Electrical Conductivity
Very Low
Very High
Independently Acting Species
All gas particles behave the same (gravity and collisions)
Electrons, Ions, and Neutral particles behave differently.
Velocity Distribution
Maxwellian
May be Non- Maxwellian
Interactions
Primarily Two-Particle Collisions
Each particle interacts simultaneously with many others (collective behavior)
Again a plasma is an electrically neutral ionized gas. Although that definition calls a plasma a gas, a plasma is different from gases you studied in thermodynamics and chemistry. We read through this table – people had questions about what a Maxwellian distribution is – we said it is a distribution of velocities of particles and you learned about it in physics 3 and how to get the average velocity, expected velocity, and root mean square velocity – but most students didn’t take physics 3 – so I told them you discuss this later in the course.

24. Plasma physics: three descriptions Single particle theory Fluid theory
Kinetic theory
Dr. Song wants you to know that there are 3 descriptions of plasmas. The first is single particle theory (playing upper left movie) and it deals with the motion of a charged particle in the electric and magnetic fields. The others are fluid theory and kinetic theory. Today, we’ll be using single particle theory to explain a few currents. But later in the class you’ll learn about fluid and kinetic theories and here are some examples where these descriptions are applied to modeling a solar ejection and magnetic reconnection – where magnetic fields superpose.

25. Forces on charged particles (single particle theory)
Electric force FE = qE
Magnetic force FB = qvxB (like coriolis force)
Lorentz force F = qE + qvxB
Neutral forces Fg =mg,
This is something you need to know. These are the forces on a single particle. We talked about how the magnetic force is like the coriolis force because the force is in a direction perpendicular to the field and the velocity. All the field can do is change the direction of the particle.

26. A commonly used smaller unit is the Gauss. 1 T = 104 G
The units of B are N/(C.m/s) or N/(A.m) in SI units(MKS). This is called a Tesla. One Tesla is a very strong field.
A commonly used smaller unit is the Gauss. 1 T = 104 G
(Have to convert Gauss to Tesla in formulas in MKS)
Just an FYI – I wish I had memorized that a Tesla is N/Am sooner! It is important to keep track of units and that a Telsa is 10^4 G. You can find this in Wikipedia.

27. Single Particle Motion
We read through this. I asked if they were taking E/M with Egan, and they aren’t but are seniors – so they have only E/M from Physics 2 and seemed generally unfamiliar with vector calculus.
SI Units
mass (m) - kg
length (l) - m
time (t) - s
electric field (E) - V/m
magnetic field (B) - T
velocity (v) - m/s
Fg stands for non-electromagnetic forces (e.g. gravity) - usually ignorable.

28. Electric Field Added to a Plasma (B=0)
This is important to understand. Here at the bottom is an externally applied electric field and no magnetic field. But when you apply the field because, as we said, it is a conductor, the charged particles quickly rearrange to make it zero. Here we get the charges at the edges and an induced field cancels the external field. Maybe you remember from E/M class, but the field inside a conductor is zero. If there were an electric field, the particles would quickly move to cancel it. When a field is applied to a conductor, the charges on the surface. If you put charge on a conductor, it all moves to the outer surface to make the internal field zero. You can’t externally induce a field in a conductor and you can’t on a plasma. There is charge built up on the sides, but the bulk of the plasma in here is neutral so that quasineutrality condition is maintained. The bulk of the plasma behaves as required in spite of those polarization charges.
Eexternal

29. Electron Plasma Frequency
Eexternal
We can use that picture to derive the electron plasma frequency we talked about as fundamental to being a plasma – this derivation is shown just for your information and you don’t need to know it – just added for clarifying what a plasma is. Talked about wave equation and they knew it from stability analysis.

30. If q is positive particle gyrates in left handed sense
Now we have a magnetic field and no electric field. I fumbled to derive this on the white board – ugh – was running out of time.
If q is positive particle gyrates in left handed sense
If q is negative particle gyrates in a right handed sense

35. Use right hand rule to find the direction of F. F=q v x B
Negative Charge
Positive Charge
So we saw that it creates uniform circular motion, and now need to consider the direction of motion depending on the charge being positive or negative. This is confusing, so I just remember that when the magnetic field is out of the board or paper then with thumb in direction of field, my right hand fingers curl in the direction of electron motion and left hand in direction of ions/protons. Generally, doing these hand gymnastics, especially during a test, is problematic. It is better find a way to remember it, or to use cyclic components – so nobody knew what that was and we talked about x-hat – y-hat – z-hat being cyclic and kept in that order X x Y = Z, Y x Z = X, Z x X = Y, and other way Z x Y = -X and so on for r-hat, phi-hat, z-hat in cylindrical coordinates. Expressing in terms of components is less problematic.

36. So we’ve derived the equations of motion, and how to find the direction of motion for positive/negative charges. Putting together the circular motion and the motion along the field line forms a helix. The ratio of energy in the parallel direction to the perpendicular direction defines the pitch of the helix coils. The pitch angle is defined here – talk and show – and it is important to know. If the pitch angle is 90 degrees all the motion is in the perpendicular direction so the particle just gyrates around one point. If the pitch angle is 0 degrees, all the motion is along the field line and the particle doesn’t gyrate.

37. Example: If a proton moves in a circle of radius 21 cm perpendicular to a B field of 0.4 T, what is the speed of the proton and the frequency of motion? 1 v r x 2
Here’s an example, but there isn’t time to go through it but you can see how to solve this sort of problem and to keep track of the units.

38. We saw that the particle undergoes a helix trajectory along the z-axis which is along the magnetic field. But magnetic field lines are not straight in the dipolar field. So the z-axis is a local axis. The particles will travel along the field line. They travel along the field line and then mirror since the field lines form magnetic bottles like in this picture. The point where they mirror depends on the pitch angle. As you can see from the plot, if the pitch angle is 90 degrees, then the motion is entirely in the perpendicular direction so it never leaves the plane of the equator. If the pitch angle is 0 degrees the particle only has motion along the field line and doesn’t mirror but precipitates into the ionosphere. You’ll learn how to figure out the mirror point later in the course and it is in the book, so you can make that plot. You’ll also learn about what they call a loss cone, a range of pitch angles which precipitate into the ionosphere and don’t mirror.

39. Two other quantities you need to know how to derive the Larmor radius and the period of the orbit. These depend on the mass of the particle so the radius is much bigger for protons than for electrons. I’ll show a different way to derive this on the board if you start with knowing it is uniform circular motions – showed vector calculus to find that a=v^2/r then equated mv^2/r = qvB -> r = mv/qB (with v being v-perpendicular). The main point being that the derivative of the vector r is not zero even though the radius r is a constant.

40. Here’s what I wrote on the board – but I didn’t have a slide of it then.

41. This picture is also in the book – showed that page on the camera
This picture is also in the book – showed that page on the camera. This one is very important figure. We talked about the fact that an externally applied electric field will not induce an internal electric field. But changes in currents give rise to changes in magnetic fields, and a change in a magnetic field gives rise to an electric field. So there are fields in the magnetosphere. The odd thing is that electric fields do not result in a current - here we see that the electric field results in both electrons and protons moving in the same direction. Other forces, even gravity which we say is not that important, will give rise to a current. Wrote on board that current is the product of density, charge, and difference in velocity of ions and electrons.

42. The circular motion does no work on a particle
Gyro motion
The gyro radius is a function of energy.
Energy of charged particles is usually given in electron volts (eV)
Energy that a particle with the charge of an electron gets in falling through a potential drop of 1 Volt- 1 eV = 1.6X10-19 Joules (J).
Energies in space plasmas go from electron Volts to kiloelectron Volts (1 keV = 103 eV) to millions of electron Volts (1 meV = 106 eV)
Cosmic energies go to gigaelectron Volts ( 1 geV = 109 eV).
The circular motion does no work on a particle
Oh but before we do that it this is important – magnetic forces do no work on charges. The work is F dot x. Take the time derivative – the change in work energy in time is F dot v – and by the work energy theorem that is equal to the change in kinetic energy – but that is the dot product of v and a vector perpendicular to v so the shows that the magnetic force does no work on a charged particle. It is important to know that and be able to derive it.
Only the electric field can energize particles!
The magnetic force does no work on a particle

43. Now we’re ready to explain two currents in the magnetosphere
Now we’re ready to explain two currents in the magnetosphere. The first is that current on the magnetopause – back up and show again on the picture.

44. The second you get by taking a cross section of the middle of the tail and looking down the tail …

45. The both have a step gradient
The both have a step gradient. The tail current looking down the tail looks like this with a region of field coming towards the earth above and a region of field going away from earth below. The magnetopause is similar, the region inside could be regarded as the lower section of field into the paper, and above is no field. Both are gradients in field. On the board… show the motion of electrons and protons – these are in opposite directions and therefore create a current. Go back two slides to show the magnetopause current. Also show where the cross tail current is.

46. This is the current that arises from a gradient in the magnetic field
This is the current that arises from a gradient in the magnetic field. It is the situation we have with the the two step gradients. I hoped to derive that today but will not have time, basically you can get the force by doing a Taylor expansion of the magnetic field.

47. Here are the currents.

48. The magnetic moment is an important concept and what you need to know is that it is the product of the current and area it encloses and that it is the ratio of the kinetic energy of perpendicular motion and the field strength. Here are some iron filings in the presence of currents. The induced field opposes the ambient field. This other integral you should have learned in classical mechanics – it is the action integral – when a system that undergoes periodic motion changes very slowly compared to the period of the motion, it is invariant - this is called an adiabatic invariant – adiabatic processes of thermodynamics, pendulum motion angular momentum, and even the Bohr atom quantization are all adiabatic invariants. It is easily shown that the magnetic moment is a constant of the motion.

49. Pitch angle and magnetic moment
The pitch angle is relatied to the magnetic moment. Here are the definitions again.

50. This is the motion that you get when there is a force that creates a current – the ring current. The particles drift in opposite directions, while they are gyrating. The basic concept is that of guiding center motion. It’s in the book – so we looked at the book pages on the camera. The motion of the guiding center can be separated from the gyration around the guiding center and the motion along the field line.

51. Single particle theory: guiding center drift
The electric field can modify the particles motion.
Assume but still uniform and Fg=0.
Frequently in space physics it is ok to set
Only can accelerate particles along
Positive particles go along and negative particles go along
Eventually charge separation wipes out
has a major effect on motion.
As particle gyrates it moves along and gains energy
Later in the circle it losses energy.
This causes different parts of the “circle” to have different radii - it doesn’t close on itself.
Drift velocity is perpendicular to and
No charge dependence, (electrons and ions move in the direction and speed) therefore no currents
When there is an electric field, we can use the concept of a guiding center motion to figure out the drift velocity. The lorenz force on the guiding center is set to zero since it is free to move – and the factor of q is divided out. Now just take these two terms and cross them into B, and using a vector identity for (v x B) x B and since v dot B is zero, find the u=ExB/B^2. A lot of students had to leave and there were a lot of questions still – students were confused about it not resulting in a current and then not sure about it at all.

52. This is what I tried to write on the board – but it wasn’t going well – the class was ending and there were a lot of questions about what directions things moved.

54. Drift Motion: General Form
Any force capable of accelerating and decelerating charged particles can cause them to drift.
If the force is charge independent the drift motion will depend on the sign of the charge and can form perpendicular currents.
Some students had to leave before this could be discussed. You just replace the E in the previous derivation with F/q. Here the motion depends on charge, and will result in an electric current.

55. Homework 2.13, 2.15 (no (d) for under), 2.16, 2.18, 2.4*
Errors in the book.
2.4, gamma => 1/gamma
2.13, page 32, line 2 above the figure, delB=-3B/r
2.15, alpha is a constant, not pitch angle.
2.18, 10^6 km, not used.
2.18: assume parallel for curvature drift and perpendicular for gradient drift
2.18, Hint: radius of curvature: calculus.
This is the assignment – there is no due date yet – sometime in a couple weeks. Take a look at the problems and be sure to ask Dr. Song about questions you have.

56. Lecture II

57. Electric and Magnetic Fields: Simple situations
Single electric charge (monopole):
Positive charge
Negative charge
Net charge
E field (intensity): + => -
Electric dipole
No magnetic monopole.
Magnetic field (magnetic dipole)
Magnet: N and S (pointing to), geomagnetic poles: located oppositely,
B (mag flux density, including magnetization): N=>S
(H: mag field intensity)
current loop
E and B are chosen in plasma physics because of the Lorentz force.

58. Maxwell’s Equations Maxwell’s equations
Poisson’s Equation (originally from Coulomb's law)
E is the electric field
 is the electric charge density
0 is the electric permittivity (8.85 X Farad/m)
Positive charge starts electric field line
Negative charge ends the line.
Gauss Law (absence of magnetic monopoles)
B is the magnetic field
Magnetic field line has neither beginning nor end.

59. Maxwell’s Equations (II)
Faraday’s Law
Ampere’s Law
c is the speed of light.
0 is the permeability of free space, H/m
J is the current density
00 = 1/c2

60. Integral Form of Maxwell’s Equations
Gauss’ integral theorem
Maxwell’s equations in integral form
A is the area, dA is the differential element of area
n is a unit normal vector to dA pointing outward.
V is the volume, dV is the differential volume element
n’ is a unit normal vector to the surface element dF in the direction given by the right hand rule for integration around C, and is magnetic flux through the surface.
ds is the differential element around C.

61. Nonuniform B Field: Gradient B drift

62. Centrifugal Force: Curvature drift

65. Adiabatic Invariants

66. Magnetic mirrors The two components are related as required
by the divergence-free of the magnetic field

69. The force is along B and away from the direction of increasing B.
If and kinetic energy must be conserved
a decrease in must yield an increase in
Particles will turn around when

70. Magnetic bottle bounce period

71. In general, the second adiabatic invariant
The integral of the parallel momentum over one complete bounce between mirrors is constant (as long as B doesn’t change much in a bounce).
Using conservation of energy and the first adiabatic invariant
If the field is a dipole their trajectories will take them around the planet and close on themselves.

72. The third adiabatic invariant
As particles bounce they will drift because of gradient and curvature drift motion.
As long as the magnetic field doesn’t change much in the time required to drift around a planet the magnetic flux inside the orbit must be constant.

74. Limitations on the invariants
 is constant when there is little change in the field’s strength over a cyclotron path.
All invariants require that the magnetic field not change much in the time required to one cycle of motion
where  is the orbit period.

75. The Concept of the Guiding Center
Separates the motion (v) of a particle into motion perpendicular (v) and parallel ( v||) to the magnetic field.
To a good approximation the perpendicular motion can consist of a drift (uD ) and the gyromotion ( vc)
Over long times the gyromotion is averaged out and the particle motion can be described by the guiding center motion consisting of the parallel motion and drift.