| New results in kinetic theory are found and applied to antimatter synthesis and confinement. The first Penrose-like stability criterion with boundary conditions is found. The resulting stability boundary is found for two drifting Maxwellians with any temperatures, densities and masses. Previous results are for a neutral Maxwellian electron-proton plasma. A perturbed-contour method is found for computing the stability of any system with a perturbed dispersion relation. A topological result is used to find the number of unstable electrostatic modes of a plasma; boundary conditions, discrete spectra of wave numbers, and very large or very small magnetic fields may be included. Various theorems follow.; Seven collision operators are found. Three Balescu-Guernsey-Lenard (BGL) analogs are found using a trick permitting derivation in one easy line. Three corresponding Landau analogs follow. The multiple-species generalization of O'Neil's operator is found. For the first time the wavenumber integral is removed from a BGL analog, which is the spatially localized generalization to multiple species and perpendicular velocities of the Dubin-O'Neil operator [Phys. Rev. Lett., 78, 3868 (1997)]. The corresponding Landau analog, which has a new collision frequency, is found not to fully thermally equilibrate most plasmas. A perturbatively collisional linear stability analysis of counter-streaming Maxwellian positrons and antiprotons shows that stability improves as the antiprotons become hotter or less dense, as coupling parameters decrease, or, overall, as mixing velocities decrease.; Multiple-scale analysis is used to study colliding particles many gyroradii apart. Resonant exchange of perpendicular kinetic energy is found. The resulting equations of motion have an error proportional to the fourth power of either gyroradius in units of the impact parameter, and permit numerical temporal steps much greater than the cyclotron periods. Accordingly, the equations of motion are exceptionally useful in 'molecular' dynamics simulations. The dynamical response of any guiding-center plasma to a charged particle of any non-relativistic velocity is found for the first time at all spatial points. In contrast, Oberman's result [Interactions Onde Electromagnetique-Plasma, edited by F. Troyon et al., 40 (1970)] applies very far from a non-relativistic super-thermal particle in a thermally equilibrated ion-electron plasma without a magnetic field. |
