Nektar-1D-SOL

The Nektar-1D-SOL proxyapp models plasma transport in the scrape-off layer (SOL). The SOL is treated as a 1D flux tube, with mass being added continuously near the centre of the domain and flowing out to a divertor at either end. Neutral species are ignored and the plasma is assumed to have an ideal-gas equation of state.

The proxyapp was built using Nektar’s solver framework and is based on existing solver types that were designed for unsteady advection problems. It adopts a similar approach to that used in the soldrake code described in section 4 of the internal report ref. [77]. The starting point is a set of non-dimensionalised equations describing the evolution of SOL density, momentum and energy, which were derived in ref. [107]:

\begin{align} U_r \frac {\partial n}{\partial t} &= - \frac {\partial }{\partial s}(nu) + S^n, \label {eqn:n}\\ U_r \frac {\partial }{\partial t} (nu)&= - \frac {\partial }{\partial s} (nu^2) - \frac {\partial }{\partial s} (nT) + S^u, \label {eqn:u} \\ U_r \frac {\partial }{\partial t} \left ( (g-2)nT + nu^2 \right ) &= - \frac {\partial }{\partial s}(gnuT + nu^3) + \kappa _d \frac {\partial ^2 T}{\partial s^2} + S^E. \label {eqn:T} \end{align} The relative weight of time-dependent terms, \(U_r\), is set to unity and the diffusivity coefficient, \(\kappa _d\), to zero, yielding a system that closely resembles the compressible Euler equations. Source terms and boundary conditions are then chosen so as to simulate mass deposition at the domain centre due to cross-field-line transport, and sonic outflow at each end (see ref. [77] for a detailed description). The domain is discretised using the Discontinuous Galerkin method and time integration is performed using a 4\(^{\rm th}\) order Runge-Kutta scheme.

Running the proxyapp produces a number of output files containing the values of the \(n\), \(nu\), and \(E\) fields for each fluid element, which can be postprocessed using Nektar’s ‘FieldConvert‘ tool to produce equilibrium profiles for \(n\), \(u\), and \(T\). These profiles closely match the analytical solutions derived in ref. [107] and the results obtained using the soldrake code.

Nektar-1D-SOL is publicly available at https://github.com/ExCALIBUR-NEPTUNE/nektar-1d-sol.