5 September
Handout: Chapter 2 of P.A. Sturrock, "Plasma Physics"
Questions: Calculate
the Debye length and plasma parameter for the following situations (the
numbers in brackets
are the temperature in K and density per cubic cm): Corona (10^6, 10^9),
geotail (10^6, 10^-1),
MRX experiment (10^5, 10^14), atmosphere of a neutron star (10^7, 10^12),
ionosphere (10^3,
10^6), metal (10^2, 10^23). Which does not qualify as a plasma?
7 September
Questions:
- What is the relation
between the Debye length and the plasma frequency?
- Assuming a constant
coronal temperature of 1 million K, calculate from the linear part of Fig.
2.1
the velocity of the particle beam that causes the type III burst
12 September
Handout: Sections 1.7 & 1.8 of A. Hasegawa and T. Sato, "Space Plasma Physics"
Question: Given the following typical magnetic field strengths (in Gauss): Corona (10^1), geotail (10^-4), MRX experiment (10^3), atmosphere of a neutron star (10^12), ionosphere (10^-2), and the temperatures and densities given above, calculate for each of these plasmas the following quantities: (1) mean interparticle distance, (2) electron plasma frequency, (3) sound velocity, (4) gyro frequency, (5) mean gyro radius
14 September
No handout
Questions: (1) In a magnetic mirror a particle will reverse its course along the magnetic field. Hence there must be a physical force acting upon it. Where does this force come from? (2) In the derivation of the conservation of magnetic moment a sign change occurs in comparison with the standard formulation of Stokes' law. What is the origin of this sign change?
19 September
Handout: First set of grade assignments, Section 10.3 of P.A. Sturrock, "Plasma Physics"
Questions: none
21 September
Handout: Sections 10.2 & 10.4 of P.A. Sturrock, "Plasma Physics"
Questions: Find the solution to the eqs. of motion for an impact parameter b=0. Are these solutions consistent with the limit b -> 0 for the general case?
26 September
Handin: First set of grade assignments, no handout
Questions: (1) Calculate the value of the Coulomb logarithm for the plasmas we considered earlier, i.e. corona, geotail, MRX experiment, atmosphere of a neutron star, ionosphere. (2) Derive the expression for the second moment of the parallel velocity, i.e. <(dv//)^2>
28 September
No handout
Question: Calculate <(dv//)> from integration over the impact parameter
3 October
Handout: Second set of grade assignments
Question: Calculate the expectation value of x and x^2 as a function of time for the normalized Gaussian probability distribution P(x,t) = (1/sqrt(4 pi c t)) exp(-x^2/4ct)
5 October
Handouts: notes on derivation grad(B) X B drift, collision integral in terms of impact parameter, and naive derivation of resistivity
Question: calculate the e-e collision contribution to <(Dv//Dt)>, the first term on the right hand side of the Fokker-Planck equation
10 October
Handout: Note on thermal conductivity, Sections 13.4, 13.6, 13.7, 14.1, & 14.2 from "The Physics of Fluids and Plasmas" , by A.R. Choudhuri
Question: Read handout from Choudhuri's book
12 October
Handout: Note on shear viscosity,
Question: Calculate the collision frequency and mean free path for the five plasmas we considered before, i.e. solar corona, geotail, ionosphere, neutron star atmosphere and MRX.
17 October
Handout: Revised note on grad B X B drift. Chapter 11 of P.A. Sturrock, "Plasma Physics". Third set of grade assignments.
Question: Calculate the Reynolds number for the five plasmas we considered before. Justify your assumptions for the length scales and typical velocities.
19 October
Handout: None
Question: Read chapter 11 of P.A. Sturrock, "Plasma Physics".
24 October
Handout: Note on Poynting flux and energy conservation
Questions: (1) Carry out the steps in the derivation of eq. 11.5.2 of Sturrock, (2) For a Maxwellian velocity distribution, derive the gas law by calculating the second moment of the velocity <(v_r*v_s)>
26 October
Handout: Chapter 13 of P.A. Sturrock, "Plasma Physics".
Questions: 1. Calculate the plasma beta for corona, MRX, neutron star,
ionosphere, and geotail.
2. (new) For the constant alpha sheared arcade treated in class,
calculate (a) the potential magnetic field energy (alpha=0)
in a slab with x between 0 and pi/k, and z between 0 and plus
infinity, and no integration over y. (b) calculate the magnetic
energy for arbitrary value of alpha. (c) Find the free magnetic
energy for arbitrary value of alpha, i.e the energy that can be
dissipated without changing the normal boundary component at the
photosphere (B_z(z=0)). Note that the fieldline connectivity
will be changed as this free energy is dissipated.
31 October
Handout: Chapters 9 and 10 of Priest and Forbes, "Magnetic Reconnection". Fourth grade assignment.
Question: None
2 November
Handout: Sections 3.1.1, 4.1, 4.2.1., and 4.3 of Priest and Forbes, "Magnetic Reconnection".
Question: None
7 November
9 November
14 November
Handout: Chapter 4, "Magnetohydrodynamic Waves" of "Plasma Astrophysics", J.G. Kirk, D.B. Melrose, and E.R. Priest (eds.). Fifth set of grade assignments.
Question: None
16 November
Handout: None
Question: None
21 November
Handout: Section 7.6 of "Classical Electrodynamics", by J.D. Jackson. Course evaluation forms (hand in to Margaret). "Magnetic Reconnection: Sweet-Parker versus Petschek", draft paper by Russel M. Kulsrud, Princeton University.
Question: Read Kulsrud paper prior to 11/29
23 November
28 November
Handout: Write-up on MHD stability and Coronal Heating, Sixth and final set of grade assignments.
Question: None
29 November
Note: this meeting replaces the lecture of November 30.
5 December
Handout:
Question: Show that the terms containing the magnetic field cancel in the example of the interchange instability derived through the energy method treated in class.
7 December
Handout: Chapter 8, "Two Stream Instability" of P.A. Sturrock, "Plasma Physics"
Question: None
12 December
Handout: None
Question: None
14 December
Handout: (1) "Magnetic Helicity in Space Physics", by M.A. Berger, in "Magnetic Helicity in Space and Laboratory Plasmas", M.R. Brown, R.C. Canfield, and A.A. Pevtsov, eds., (2) Note on basics of magnetic helicity.
Question: None
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