Novel integration method for calculating generalized plasma dispersion function with applications to non-Maxwellian incoherent scatter spectra and nonlinear instability analysis

Kinetic plasma studies, such as nonlinear instability coupling or calculating incoherent scatter spectra, often require computing integrals of a velocity distribution function over a set of complex poles. Previous methods have invoked the Plemelj theorem and struggled with higher order poles, computational inefficiency, and numerical inaccuracy. We forego the Plemelj contour and have developed a novel, efficient, accurate, and simple to implement direct integration method that can perform the calculation for an arbitrary number of arbitrary order poles. Multiple discretization schemes are provided to work with a variety of numerical plasma simulation methods (e.g., Vlasov, PIC, Monte Carlo). The method is used to develop a forward model for calculating the incoherent scatter spectra of arbitrary non-Maxwellian, collisional, magnetized plasmas. We provide example spectra for kappa and toroidal distributions which are found in space plasmas. We also provide a framework for studying plasma waves and instabilities in the magnetosphere.