PHYS 8120: Advanced Topics in Physics, 3 credits
Spring 2025, Mondays & Wednesdays, 9:30 - 10:45
In Person, 25 PP, Rm 628 (conference room)
Instructor: Piet
Martens
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Plasma Physics & MHD
Left: A soft X-ray image of the Sun taken by the Yohkoh satellite.
Dense and hot flare plasma emits brightly in the cusp in
the middle of the Northern hemisphere.
Right: Laser-plasma interaction during inertial
confinement fusion test at the University of Rochester. |
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Course Description
This is a course in the basic theory of plasma physics and magnetohydro-dynamics (MHD)
with applications
and examples from solar and stellar physics, neutron stars, accretion disks, galaxies,
magnetospheric physics,
magnetically controlled fusion, and
plasma experiments. The goal is to prepare the
students to apply plasma physics & MHD in their research.
Assignments
1) Presence, homework assignments after every class, and notes assignments,
together counting for 40% of the final grade,
2) Write an ApJL type paper on a subject of your choice from this class,
according to given instructions.
This will count for 60% of your grade.
Final Project: Instructions and Timetable.
Resources
The rules of the game:
Course Syllabus
The most useful booklet you'll ever have! Hardcopy also provided to students,
2023 NRL Plasma Formulary (latest version)
Textbook:
"The Physics of Fluids and Plasmas", by Arnab R. Choudhuri,
Inexpensive paperback on Amazon.
Frequently cited:
"Plasma Physics for Astrophysics", by Russel M. Kulsrud;
Not so expensive printed copy
"Plasma Physics: An Introduction
to the Theory of Astrophysical, Geophysical
and Laboratory Plasmas",
by Peter A. Sturrock.
"Magnetohydrodynamics of the Sun", by Eric R. Priest.
Gas Dynamics
13 January,
Subjects: Plasma versus gas. What is the main-free-path?
What is it in the Earth's atmosphere?
Gas dynamics: governing equations, co-moving
versus partial derivatives,
and static stellar corona.
Mean free path in
gases, short, useful read.
Notes Lecture 1 (Sanjib)
Homework: 1) Work out the derivation of the relation between local and co-moving
derivative for the momentum equation (Navier-Stokes), 2) work out the mass
conservation equation, 3)
solve for a static spherically symmetric solar corona with
constant temperature T=10^6 K, and
a particle density at the base of the corona of
n = 3x10^8 cm^-3. Compare with the pressure of the interstellar medium, at the
so-called heliopause, where the Sun's atmosphere/wind ends, is 3x10^-12 dyne/cm^2.
What do you conclude?
Assignment Equation
15 January
Subjects:
Static corona solution, Parker
solar wind, Voyager at the Heliopause
Notes Lecture 2 (Kisaru)
Homework: 1) At what coronal temperature would the pressure of the static solar corona
at infinity match that of the stellar medium?
2) How much difference does it make that the Sun's radius of influence does
not end at infinity, but at roughly 90 AU?
3) Mars has no magnetic field and the temperatur of its atmosphere is about
275 K. What is the pressure of a static Mars atmosphere at infinity?
And at ~ 4 Mars radii, where the solar wind impinges on it?
4) Work out the numerical values of the parameters in the static solar corona
and Parker wind, i.e. sound speed, pressure at infinity, and critical radius (in solar radii).
20 January
No Class: Martin Luther King Day
22 January
No Class: Weather Emergency
Basics of Plasma Physics
27 January
Subjects: Debye length, plasma parameter, start of MHD.
Note on Scale Height, and
note from previous year on Debye length
Notes Lecture 3 (Prachandra)
Homework:
1) Calculate the numerical value of the Debye length and plasma parameter in
a) the solar corona,
b) the Earth's magnetosphere,
c) the interior of the Sun,
d) the interior of a white dwarf,
e) the interior of a neutron star.
Look up the values of the parameters you need online and/or in the NRL Plasma Formulary.
Note: Verify whether you are indeed dealing with a plasma.
Magneto-HydroDynamics (MHD)
29 January
3 February
Subjects: Ohm's law revisited, Collisions, mean free path, resistivity.
Notes from previous year, and
my old write-up with figures.
No Notes Lecture 5
Homework: (1) Work though the algebra going from Eqs. (13) to (23) for yourself.
(2) For stellar coronae, the Sun in particular, compare the radius at which the
thermal
kinetic energy equals the electrostatic energy with the Debye length. What physical
conclusion do you draw from that?
(3) In solar coronal loops the mean free path (along the magnetic field) is ~ 100 km.
So what is then the (naive) value of the resistivity?
(4) With a magnetic field of ~ 30 Gauss, a typical length scale of 10,000 km,
and velocities ~ 10 km/sec, how do the first (inductive) and second (dissipative)
terms on the RHS of the MHD equation compare, using the resistivity from (3)?
5 February
Subjects: Coulomb logarithm, magnetic Reynolds number
Notes from previous year
Coulomb Logarith (my notes)
No Notes Lecture 6
Homework: 1)
Read the Wikipedia articles on Tokamak and Stellarator.
Write down the significant physical differences between the two.
Why was the stellarator design abandoned and later reconsidered?
10 February
Subjects: Frozen-in flux, Stokes' theorem, Gauss' theorem,
freezing in in Navier-Stokes
Notes Lecture 7 (Enosh)
Frozen-in plasma in coronal magnetic loops:
an iconic image.
Homework: 1) Calculate the resistivity and magnetic Reynolds
number for the solar corona,
and for a Tokamak, with input values you can look up,
2) Calculate the proton and electron gyro radii in a Tokamak and in the
solar corona;
3) Rederive vorticity preservation for an incompressible fluid decribed by the Navier-Stokes
equation, as shown in class.
4) What signals vorticity preservation in the Earth's
atmosphere in weather forecasting?
12 February
17 February
19 February
24 February
26 February
Subjects: Magnetic Reconnection
Basic reconnection animation.
Movie of an erupting limb filament/CME (1999),
Martens-Kuin (1989) cartoon for
erupting filament.
The Harris Current Sheet Analytical Model
Notes for Lecture 11 (Prachanda)
Homework: 1) Derive the current density, electric field, and inflow
velocity equations
for the Harris sheet, Eq. (12) in the notes. Graph those quantities.
Note: The electric field is assumed a constant, perpendicular to the plane of the figure;
not clearly explained in the notes.
2) For a typical inflow velocity of 10 km/sec,
magnetic field strength of 100 Gauss, and sheet
width of 100 km, what are the values
of electric field, current density at the center, and resistivity?
How does that compare with the Spitzer resistivity?
3 March
Final Project, Time-table
Simplest 2D Current Sheet; the Sweet-Parker Model,
(from Murphy, 2014)
Energy equations
The Biermann Battery Consider
a plasma without any magnetic field.
Using the expression for Ohm's law including all terms, except electron inertia.
Can be a magnetic field be generated, where there was none?
Notes for Lecture 12 (Enosh)
Homework: (1) Consider the Poynting flux in the ideal MHD approximation.
What is the physical interpretation of the expression for the Poynting flux in that case?
(2) What is the energy source of the magnetic field in the Biermann battery?
5 March
10 March
MHD Waves and Stability
12 March
Subjects: Magnetic Fields in Star Forming Regions, Orion Nebula
Magnetic Field Around the Black Hole at the Center of M87
Waves in action: Movie of solar tsunami, and
movie of coronal waves;
General theory of first order expansion in getting to the dispersion relation.
Compressional and Transversal Waves
Notes from a previous year
Homework: Done in Class, no need to submit
Derive shear Alfven waves in the simplest situation,
a constant magnetic field in one direction;
Derive sound waves in a situation with constant pressure and density,
while
the temperature does not fluctuate (T_1 = 0)
Derive the relationship between Alfven speed, sound speed, and plasma beta.
15-23 March
Spring Break, No Classes: Rest of Lecture Schedule TBD
20 March
One Page Proposal Due for Term Paper
23 March
Paper Proposal Returned With Comments
24 March
Subjects: 1)
Lecture on MHD waves by Rehka Jain.
2) Derivation of Brunt-Vaisala cut-off frequency and gravity waves;
Example of gravity waves in Earth's atmosphere.
Acoustic and gravity modes in stellar interiors
Read Kulsrud, pp.108
Friedrichs diagram sequence for Alfven and slow and
fast magneto-acoustic waves.
On y-axis phase velocity parallel to the magnetic field, and on x-axis perpendicular.
Alfven velocity increases from beginning to end, sound velocity is constant.
Stability and Waves
Homework: Start writing your final paper.
Transport Coeffficients and Energy Equation
26 March
31 March
Paper Preparation and Salient Subjects
2 April
7 April
9 April
14 April
Space Weather: Understanding and Forecasting, Abstract
Guest Lecture by Dr. Manolis Georgoulis,
Academy of Athens, former visiting professor at GSU
16 April
April 19
First Full Draft of Paper Due; Sent to Referees
April 23
I will be available to answer your questions via WebEx or email
April 26
Referee Reports Due to Editor
April 27
Referee Reports Back to Authors With Recommendations by Editor
April 29 to May 6
Final Exams Week: No Class
May 3
May 6
Final Paper Returned with Grade
May 8
Final Grade in PAWS by 5 pm EDT
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| Plasma discharge in the magnetic
reconnection experiment (MRX) of the Princeton Plasma Physics Laboratory.
The two flux cores and magnetic diagnostics are visible. |
Soft X-ray emission from hot plasma
in the Crab nebula observed by the Chandra observatory |
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