- Derive the dispersion relation (8.28) from Equations (8.23)-(8.27).
- Show that the dispersion relation (8.28) can be written
- Show that, when combined with the Maxwellian velocity distribution (8.24), the dispersion relation (8.23) reduces to
- Show that, when combined with the Maxwellian velocity distribution (8.24), the dispersion relation (8.49) reduces to
- Derive Equation (8.74) from Equations (8.69) and (8.73).
- Derive Equation (8.82) from Equations (8.74) and (8.79).
- Derive Equations (8.89)-(8.91) from Equation (8.82).
- Derive Equations (8.94)-(8.96) from Equation (8.82).
- Derive Equations (8.102)-(8.105) from Equation (8.82).
- Derive Equation (8.119) from Equation (8.118).
- Derive Equation (8.120) from Equations (8.79) and (8.119).
- Derive Equation (8.124) from Equation (8.123).
- Demonstrate that the distribution function (8.131) possesses a minimum at
when
, but not otherwise.
- Verify formula (8.133).
- Consider an unmagnetized quasi-neutral plasma with stationary ions in which the electron velocity
distribution function takes the form

where . Assuming that is real and positive, and that lies in the upper half of the complex plane, show that when the integrals are evaluated as contour integrals in the complex -plane (closed in the lower half of the plane), making use of the residue theorem (Riley 1974), the previous dispersion relation reduces to - Derive Equation (8.137) from Equations (8.134)-(8.136).
- Derive Equations (8.160) and (8.161) from Equations (8.154), (8.155), and (8.159).