Homework 2: Understanding the paper by Young et al. [1974] (JGR, pg. 1082):

1. Show that the differential energy flux, $G$, as a function of energy in Fig. 1 is correctly mapped to the distribution function, $f$, as a function of velocity space. Does this electron distribution function agree with other observations of electron distribution functions measured in the plasma sheet?

2. Is the assumption that the distribution function is seperable in terms of $v_{\parallel}$ and $v_{\perp}$ (Eqn. 2) a reasonable assumption? Why?

3. Review the Nyquist Method and Penrose Criterion on pages 97-105 of the book: ``Introduction to Plasma Theory'' by D.R. Nicholson (John Wiley and Sons, NY, 1983) to understand Young's stability criteria of the ECH dispersion relation. Write a quick synopsis of why the Penrose Criterion is the necessary and sufficient condition for the linear instability of a Vlasov-Poisson equilibrium.

4. What wave frequencies are most likely to be excited by the flute mode ($k=0$) and by the more general mode ($k\neq0$)?

5. Of the two modes, with $k=0$ or $k\neq0$, which one does Young et. al [1974] believe is the one most likely to be excited in the central plasma sheet and what conditions does he give to support this conclusion?