Correlation between potential well structure and neutron production in inertial electrostatic confinement fusion

The electrostatic potential well in inertial electrostatic confinement (IEC) is studied using two approaches. First, the equilibrium potential profile is obtained by solving the charge neutrality condition, i.e. ni=ne, assuming the appropriate distribution functions for the ions and the electrons. The formation of a double well structure is demonstrated, with a depth depending upon the ratio between the focus radii of the electrons and the ions. The correlations between the well depth and the volume integrated neutron production due to deuterium-deuterium (DD) reactions are obtained. Second, in order to study the stability of the well, the dynamic behaviours of the potential well are calculated by performing time advancing numerical simulations on the basis of the particle in cell method. Single, double and triple wells, depending on the amount of injected ion current, are observed to be formed for ions with a monoenergetic distribution. The well in the centre of the multiwell structure is unstable and oscillates with a period much longer than the inverse ion plasma frequency. A double well structure can be formed even for ions with a spread out energy distribution when the ion current is larger than the threshold value. The time averaged neutron production by DD fusion events is proportional to a power of the ion current involved in forming the double well structure. The results strongly suggest that the high neutron production rate should be attributed to not only the well depth but also the unstable behaviour of the potential, i.e. the intermittent peaking of the density in the centre region. A numerical simulation reveals that IEC possesses a favourable dependence of fusion reactions on the injected ion current for the application to a neutron source or a fusion reactor