# NEO Overview

NEO is a $\delta f\,\!$ Eulerian code which provides first-principles based numerical calculations of the neoclassical transport (particle flux, energy flux, bootstrap current, poloidal flows, etc.). NEO solves a hierarchy of equations derived by expanding the drift-kinetic equation in powers of $\rho_{*i} \,\!$, the ratio of the ion gyroradius to the system size. NEO includes the self-consistent coupling of electrons and multiple ion species via complete cross-species collisional coupling, the calculation of the first-order electrostatic potential via coupling with the Poisson equation, general geometry effects, and rapid toroidal rotation effects (including centrifugal effects). NEO has recently been upgraded to include the full linearized Fokker-Planck collision operator. Various reduced collision models are also implemented (Hirshman-Sigmar, zeroth-order Hirshman-Sigmar, and the Connor model) for comparison with analytic theory and testing. NEO has been extensively benchmarked and compared with analytic neoclassical theory, for example as shown here.

Figure 1: Ion energy flux and bootstrap current versus collision rate. NEO results using various collision models are shown, along with predictions from the Hinton-Hazeltine theory, Chang-Hinton theory, Taguchi theory, and the Sauter model.

The NEO user manual can be found here.

## Publications

E. Belli and J. Candy, Kinetic Calculation of Neoclassical Transport Including Self-Consistent Electron and Impurity Dynamics. Plasma Physics and Controlled Fusion, vol. 50, 095010 (2008).

E. Belli and J. Candy, An Eulerian Method for the Solution of the Multi-Species Drift-Kinetic Equation. Plasma Physics and Controlled Fusion, vol. 51, 075018 (2009).

E. Belli and J. Candy, Full Linearized Fokker-Planck Collisions in Neoclassical Transport Simulations. Plasma Physics and Controlled Fusion, vol. 54, 015015 (2012).