This thesis presents work on two topics related to nuclear fusion in plasmas.
The first topic is the energy spectrum of products of fusion reactions in plasmas,
called the production spectrum. The second is an investigation of the fusion reaction
processes in high energy density Z pinch plasmas and the feasibility of ignition of
such plasmas.
A method is presented for the derivation of production spectra for plasmas with
various distributions of ion velocities. The method is exact, requiring the solution of
a 5 dimensional integral and is suitable for both isotropic and anisotropic distributions.
It is shown that many of the integrals can be solved analytically. The solutions
are used to study the spectra of neutron energies produced by deuterium-deuterium
and deuterium-tritium reactions. It is found that for maxwellian distributions of ions
the neutron spectrum is asymmetric with a longer high energy tail when compared
with gaussian approximations of the spectrum.
Deuterium and deuterium-tritium Z pinch plasmas are studied computationally
using a hybrid code in which the fuel is modelled as a magnetohydrodynamic (MHD)
fluid and fast ions are modelled as discrete particle-in-cell (PIC) particles. Using
a Z pinch model in which the magnetic and thermal pressures are in equilibrium
it is found that significant energy gain can be achieved for currents greater than
50MA. Deuterium gas puff experiments with a 15MA current are also analysed
computationally in order to determine the reaction mechanism. The results of MHD
simulations in 3 dimensions are post-processed with a PIC code to model reactions
occurring due to the acceleration of deuterium ions by large electric fields. It is
found that reactions due to this beam-target mechanism represent a small fraction
(0.0001) of the number of thermonuclear reactions.