Equations (8), (9), (10) in the Course Notes, the ideal fluid equations, were derived in
class. Manipulate these to:
1. Obtain the alternate form for Eq (9), Eq (9a).
2. Obtain the alternate form for Eq (10), Eq (10a).
Due Sep 21 2010
Solve for f(r,) correct to 2nd order in the small parameter 1/ < 1 if f is single valued
2f/2 + r f/r = - r (1+cos)f.
Solve it assuming r ~ O(1). Your solution to f2(r,) should be determined upto
At t=0, a neutral gas is configured so that
f(x,v,0) = (2vth2)-3/2 exp[-v2/2vth2] [n0 + n1sin(2x/L)],
where vth is the thermal speed and n1 < n0. Assuming that L < , where is the mean
free path, and that gravity can be neglect
Phys 761 Making and sustaining a Plasma 9 November 2010
Prof. Derek Boyd
We function in a relatively low temperature and high density environment so most
of the matter around us is in a molecular state.
To make a plasma and sustain it we need to ionize th
7.1 Rederive the convective cell linear normal modes, as was done in class
and in the notes, from the Navier Stokes equations. Thus, you will not
obtain omega = 0 any more. Does the mode oscillate? damp?
7.2 Rederive the sound wave dispersion us
In this problem, we wish to obtain, by using an expansion in large k, the lower frequency
g-mode normal mode in the coupled oscillator problem for the case where k/m > g/l.
This will show you the technique to extract low frequency information fr
Long wavelength limit of the Rayleigh-Taylor Instability
In this problem, we obtain the growth rate of the RT instability in the long wavelength
limit, ie, for kL < 1. The opposite limit was done in class. Proceed as follows:
All the equations g
This problem is to calculate the flow pattern around a sphere. Consider a sphere of
radius a, situated at the origin of a spherical coordinate system. At infinity, there is a
uniform flow, u, in the positive z-direction given by u = z^u0. In ge
Alfven waves and resistivity
14.1 Consider a homogenous equilibrium with constant B0 pointing in the z^ direction.
Derive the dispersion relation for ideal Alfven waves, with B~ polarized along x^ and the
k vector lying in th
Derive the plasma wave dispersion relation from kinetic theory. That is, use the
collisionless Boltzmann Equation with Gauss' Law (magnetic perturbations are zero).
Assume exp[ikz - it]. In doing the integral, ignore the singularity for when =
Rederive the plasma wave from the 2-fluid equations as was done in class, except this
time do not assume that the ions are relatively immobile; ie, keep the ion response. This
will answer some of the questions that came