Description
The geometric structure of space-charge-confined plasmas is examined. Particle motion in electrostatically confined plasmas depends on the spatial structure of the equilibrium potential. Relaxed space-charge confinement equilibria based on the configuration of Pacheco, Ordonez, and Weathers (Phys. Plasmas 19, 102510, 2012) are analyzed using the curvature of the electrostatic potential. Both single-species and two-species plasmas are considered while varying plasma size, density, and the edge electric field.
The configuration provides a reference geometry in which the equilibrium field and particle motion are examined using the local Hessian of the potential, and parameter changes modify the potential profile and the curvature distribution in the plasma region. The geometry of the system is described by the Hessian of the electric potential. This is found by taking the second spatial derivatives of the electric potential at each point in order to create a map of particle confinement or loss throughout the system.
In the single-species configuration the potential minimum is located near the system center and increases toward the boundary, the second spatial derivatives are calculated and the eigenvalues followed along the principal directions in the domain. Regions of positive curvature correspond to bounded motion, while regions with negative curvature correspond to particle loss. Mixed signs restrict motion to selected directions. Mapping these regions produces extended confinement volumes separated by narrow escape channels whose position shifts as the equilibrium parameters vary and determines whether trajectories reach the wall.
When a second species is introduced the interior potential becomes flatter over a large fraction of the radius, near the interface between the species the gradient changes more rapidly and localized curvature structure develops. These regions correspond to directional transport, with confinement and escape depending on the direction of motion.