HIGHLY PRECISE APPROXIMATION OF FREE SURFACE GREEN FUNCTION AND ITS HIGH ORDER DERIVATIVES BASED ON REFINED SUBDOMAINS

The infinite depth free surface Green function (GF) and its high order derivatives for diffraction and radiation of water waves are considered. Especially second order derivatives are essential requirements in high-order panel method. In this paper, concerning the classical representation, composed of a semi-infinite integral involving a Bessel function and a Cauchy singularity, not only the GF and its first order derivatives but also second order derivatives are derived from four kinds of analytical series expansion and refined division of whole calculation domain. The approximations of special functions, particularly the hypergeometric function and the algorithmic applicability with different subdomains are implemented. As a result, the computation accuracy can reach 10-9 in whole domain compared with conventional methods based on direct numerical integration. Furthermore, numerical efficiency is almost equivalent to that with the classical method

Electron positron pair production in strong electric fields

This work covers electron positron pair production in spatially homogeneous electric (and magnetic) fields. Different field configurations are looked at in order to study various phenomena including multiphoton pair production, Sauter-Schwinger pair production and dynamically assisted pair production. The main focus lies on pulsed, rotating fields with one main frequency component which are called rotating Sauter pulses. The results are obtained via different numerical methods, that rest on different theoretical approaches. A generic method is derived from the Dirac-Heisenberg-Wigner (DHW) formalism which entails a modified quantum kinetic equation. We call the numerical solution of this equation the Wigner method. Other types of equations are derived from the DHW formalism as well and numerically solved with the aim to include magnetic fields. In the case of rotating Sauter pulses a completely different numerical method is developed, which is based on a semiclassical approach and therefore called the semiclassical method. A number of parameter studies are conducted to understand pair production in these rotating Sauter pulses. In those studies the Wigner method and the semiclassical method are compared exhaustively and found to complement each other. This makes it possible to cover the complete range of parameters of the rotating Sauter pulse, which helps to calculate the pair production rates for experiments involving counter-propagating circularly polarized laser light. An interpretation of the resulting pair production spectra is given. Due to the general nature of the Wigner method it is possible to study more general field configurations which include pulses with elliptic polarization, chirped pulses or bichromatic rotating Sauter pulses. Each of these exhibit interesting features, including the dynamically assisted Schwinger effect in bichromatic pulses, which could be useful in planning high-intensity laser experiments

Electron positron pair production in strong electric fields

This work covers electron positron pair production in spatially homogeneous electric (and magnetic) fields. Different field configurations are looked at in order to study various phenomena including multiphoton pair production, Sauter-Schwinger pair production and dynamically assisted pair production. The main focus lies on pulsed, rotating fields with one main frequency component which are called rotating Sauter pulses. The results are obtained via different numerical methods, that rest on different theoretical approaches. A generic method is derived from the Dirac-Heisenberg-Wigner (DHW) formalism which entails a modified quantum kinetic equation. We call the numerical solution of this equation the Wigner method. Other types of equations are derived from the DHW formalism as well and numerically solved with the aim to include magnetic fields. In the case of rotating Sauter pulses a completely different numerical method is developed, which is based on a semiclassical approach and therefore called the semiclassical method. A number of parameter studies are conducted to understand pair production in these rotating Sauter pulses. In those studies the Wigner method and the semiclassical method are compared exhaustively and found to complement each other. This makes it possible to cover the complete range of parameters of the rotating Sauter pulse, which helps to calculate the pair production rates for experiments involving counter-propagating circularly polarized laser light. An interpretation of the resulting pair production spectra is given. Due to the general nature of the Wigner method it is possible to study more general field configurations which include pulses with elliptic polarization, chirped pulses or bichromatic rotating Sauter pulses. Each of these exhibit interesting features, including the dynamically assisted Schwinger effect in bichromatic pulses, which could be useful in planning high-intensity laser experiments