Chapter 10
Past exam papers
,184
Plasma Physics C17 1993: Final Examination
Attempt four questions. All six are of equal value. The best four marks will be
considered, but candidates are discouraged from answering all six questions because
it is unlikely that there will be sufficient time.
Show all working and state and justify relevant assumptions briefly.
Question 1 (10 marks): (answer both parts, illustrate with appropriate equa-tions)
a List three quantitative criteria for a plasma and explain each in a few lines.
b Describe three out of four of the following phenomena, and their relation to
adiabatic invariants.
i adiabatic compression
ii Fermi acceleration
iii ion cyclotron heating
iv transit time magnetic pumping
Question 2 (10 marks): Discuss one of the following: answers are not re-stricted to
material from the specialist lectures
a Plasma fusion and magnetic confinement devices
b Extraterrestrial plasma and plasma phenomena
c Plasma diagnostics using laser radiation
d Describe the process of electrical breakdown between electrodes in gas at
pressures near 1 Torr, including relevant equations. Explain why secondary
emission is important, and at which electrode.
Question 3 (10 marks): Derive an expression for the Debye length in planar (1-D
slab) geometry taking into account both Te and Ti. Assume time scales long enough
so that both species have equilibrium (Maxwellian) distributions. Discuss the validity
of your treatment of the ions.
Question 4 (10 marks):
(5/10) aUsing the single fluid MHD equations and Fick’s law (Γ = −D∇n), obtain
the coefficient of diffusion perpendicular to magnetic field lines.
(2/10) b Explain how and why this diffusion depends on plasma resistivity.
, Past exam papers 185
(3/10) c In a few sentences, explain neoclassical diffusion qualitatively with the aid
of a few sketches.
Question 5 (10 marks): Consider a high frequency plane transverse elec-tromagnetic
wave in an unmagnetized plasma. (B0 = 0)
a From the two fluid electron equation, show that
2
ie n0E1
j 1
=
mω
b and continue, by considering Maxwell’s equations, to derive the dispersion
relation.
c Calculate the group velocity and sketch both the group and phase velocities on
graphs with labels and numerical scales for ne = 1 × 1018 ± 3.
Question 6 (10 marks): Consider the plasma sheath region near a wall in planar
geometry.
a Write down Poisson’s equation including both electron and ion terms, explain-ing
and justifying your assumptions.
b Justify under what conditions the electron contribution in (a) can be ignored, and
solve the equation for those conditions to obtain a relation between V (or Φ)
the sheath width d, and J.
, 186
Plasma Physics C17 1994: Final Examination
Attempt four questions. All are of equal value. Candidates are discouraged from
answering all six questions because it is unlikely that there will be sufficient time.
Show all working and state and justify relevant assumptions briefly.
Question 1 (10 marks): (answer both parts, illustrate with appropriate equa-tions)
a List three quantitative criteria for a plasma and explain each in a few lines.
b Describe three out of five of the following phenomena.
i Debye shielding.
ii Boltzmann’s relation for electrons.
iii Energy transfer from a plasma to a conducting wall.
iv Mechanisms for plasma generation, confinement, and loss.
v Discuss an example of a plasma heating scheme that relies on conserva-tion
of an adiabatic invariant, and one that relies on the breaking of an
adiabatic invariant.
Question 2 (10 marks): Discuss one of the following: answers are not re-stricted to
material from the specialist lectures
a Plasma fusion and magnetic confinement devices
b Low temperature plasma, and its use in materials processing.
c Plasma diagnostics - measurements of density, temperature etc.
d Discuss Coulomb collisions, explaining the basic properties of the collisions, the
range of the interaction, the effect on plasma resistivity, runaway electrons,
indicating scaling (e.g. with n, T etc.) where appropriate.
Question 3 (10 marks):
a Show that the electrical resistivity of a fully ionized plasma can be expressed
in the form ν m
ei e
η= 2
nee
where νei is the electron-ion collision frequency. Do not attempt to find an
expression for νei or derive Coulomb scattering!
Past exam papers
,184
Plasma Physics C17 1993: Final Examination
Attempt four questions. All six are of equal value. The best four marks will be
considered, but candidates are discouraged from answering all six questions because
it is unlikely that there will be sufficient time.
Show all working and state and justify relevant assumptions briefly.
Question 1 (10 marks): (answer both parts, illustrate with appropriate equa-tions)
a List three quantitative criteria for a plasma and explain each in a few lines.
b Describe three out of four of the following phenomena, and their relation to
adiabatic invariants.
i adiabatic compression
ii Fermi acceleration
iii ion cyclotron heating
iv transit time magnetic pumping
Question 2 (10 marks): Discuss one of the following: answers are not re-stricted to
material from the specialist lectures
a Plasma fusion and magnetic confinement devices
b Extraterrestrial plasma and plasma phenomena
c Plasma diagnostics using laser radiation
d Describe the process of electrical breakdown between electrodes in gas at
pressures near 1 Torr, including relevant equations. Explain why secondary
emission is important, and at which electrode.
Question 3 (10 marks): Derive an expression for the Debye length in planar (1-D
slab) geometry taking into account both Te and Ti. Assume time scales long enough
so that both species have equilibrium (Maxwellian) distributions. Discuss the validity
of your treatment of the ions.
Question 4 (10 marks):
(5/10) aUsing the single fluid MHD equations and Fick’s law (Γ = −D∇n), obtain
the coefficient of diffusion perpendicular to magnetic field lines.
(2/10) b Explain how and why this diffusion depends on plasma resistivity.
, Past exam papers 185
(3/10) c In a few sentences, explain neoclassical diffusion qualitatively with the aid
of a few sketches.
Question 5 (10 marks): Consider a high frequency plane transverse elec-tromagnetic
wave in an unmagnetized plasma. (B0 = 0)
a From the two fluid electron equation, show that
2
ie n0E1
j 1
=
mω
b and continue, by considering Maxwell’s equations, to derive the dispersion
relation.
c Calculate the group velocity and sketch both the group and phase velocities on
graphs with labels and numerical scales for ne = 1 × 1018 ± 3.
Question 6 (10 marks): Consider the plasma sheath region near a wall in planar
geometry.
a Write down Poisson’s equation including both electron and ion terms, explain-ing
and justifying your assumptions.
b Justify under what conditions the electron contribution in (a) can be ignored, and
solve the equation for those conditions to obtain a relation between V (or Φ)
the sheath width d, and J.
, 186
Plasma Physics C17 1994: Final Examination
Attempt four questions. All are of equal value. Candidates are discouraged from
answering all six questions because it is unlikely that there will be sufficient time.
Show all working and state and justify relevant assumptions briefly.
Question 1 (10 marks): (answer both parts, illustrate with appropriate equa-tions)
a List three quantitative criteria for a plasma and explain each in a few lines.
b Describe three out of five of the following phenomena.
i Debye shielding.
ii Boltzmann’s relation for electrons.
iii Energy transfer from a plasma to a conducting wall.
iv Mechanisms for plasma generation, confinement, and loss.
v Discuss an example of a plasma heating scheme that relies on conserva-tion
of an adiabatic invariant, and one that relies on the breaking of an
adiabatic invariant.
Question 2 (10 marks): Discuss one of the following: answers are not re-stricted to
material from the specialist lectures
a Plasma fusion and magnetic confinement devices
b Low temperature plasma, and its use in materials processing.
c Plasma diagnostics - measurements of density, temperature etc.
d Discuss Coulomb collisions, explaining the basic properties of the collisions, the
range of the interaction, the effect on plasma resistivity, runaway electrons,
indicating scaling (e.g. with n, T etc.) where appropriate.
Question 3 (10 marks):
a Show that the electrical resistivity of a fully ionized plasma can be expressed
in the form ν m
ei e
η= 2
nee
where νei is the electron-ion collision frequency. Do not attempt to find an
expression for νei or derive Coulomb scattering!
