1. BOUT++ Towards an MHD Simulation of ELMs B. Dudson and H.R. Wilson Department of Physics, University of York M.Umansky and X.Xu Lawrence Livermore National Laboratory, CA P.Snyder General Atomics, San Diego, CA

2. Outline BOUT++: motivation and philosophy ELM modelling: the approach and objectives Initial benchmarking results (work in progress), and future aims

3. BOUT++: Philosophy BOUT++ is a collaborative project between University of York and LLNL The code provides a framework for developing plasma fluid codes: – user defined magnetic geometry (in terms of metrics) – user-defined plasma model: Flexible, user-friendly code (small compromise on speed) – easy to adjust plasma physics model, and explore implications

4. Example of the code: Ideal MHD equations dndt = -n*Div(v) – V_dot_Grad(v,n) dpdt = –V_dot_Grad(v,p) - gamma*p*Div(v) dvdt = –V_dot_Grad(v,v) + ((Curl(B)^B) - Grad(p))/n dBdt = Curl(v^B)

5. Physics Objectives There are two main objectives: Edge turbulence modelling Edge MHD and ELMs – focus on the ELM modelling here

6. ELM modelling- the approach Two complementary approaches to tackle the ELM problem Full non-ideal MHD code, towards a model for the ELM crash – A range of codes being used: NIMROD, BOUT, JOREK, M3D, etc – Advantage: well-developed codes, some with 2-fluid effects – Disadvantage: difficult to pull out and and study the impact of specific physics elements without a detailed knowledge of the code; making contact with analytic theory is not easy Building up from simple ideal MHD model – Basic ideal MHD model eases comparison with analytic theory and linear codes (eg ELITE and non-linear ballooning theory) – The model can then be slowly built up, monitoring the impact of different physics effects BOUT++ is ideally suited to exploring the second approach – permits the user to add and subtract physics in a clear way

7. Initial benchmark studies (in progress) The Orszag-Tang vortex provides a “standard” test of 2D ideal MHD solvers: looks good, qualitatively Tests the ability to treat shocks (possibly important for ELMs) BOUT++, ideal MHD Athena, Roe solver

8. Quantitative Benchmark: linear ideal MHD We have begun to test the code against ELITE For initial tests, we have implemented a reduced ideal MHD model into BOUT++ – Valid for high-n ballooning modes Initial case: strong instability, with significant peeling component: – OK for intermediate n, but unable to reproduce higher n (yet) – Points to a problem with the kink/peeling drive (sensitive to plasma- vacuum boundary)

9. Produces “fingers” in non-linear regime Mode propagates radially Filamentary structures are produced in the non-linear regime Cannot take too seriously while there is disagreement in the linear regime – but encouraging first signs! n =10

10. New equilibrium to minimise coupling to vacuum Presently exploring a more ballooning case, with reduced coupling to vacuum (ELITE requires some edge interaction) ELITE predicts close to marginal stability:  /  A =0.01 ELITE Equilibrium mesh

11. The challenges of marginal stability Agreement has not yet been achieved (the BOUT++ runs take 12 hours, while ELITE is ~3 minutes, so comparisons are not trivial) It is necessary to work close to linear marginal stability – it is the experimentally relevant situation (p‘ increases slowly through marginal stability – modes that are strongly unstable linearly are likely to have different dynamics – existing non-linear theories are based on proximity to marginal stability One issue with proximity to marginal stability is resolution of fine-scale structures near rational surfaces – makes sense to use nq as the radial variable to improve resolution around rational surfaces (pack mesh there): presently exploring this When we go non-linear, an additional challenge will be the time taken to get into the non-linear regime – will need to make use of scaling of mode structure during linear phase to speed code up here

12. Future plans: the strategy Work to find a mesh and formalism that gives agreement with ELITE close to marginal stability with weak coupling to vacuum Extend/return to linear tests where mode couples to vacuum Extend to non-linear regime – compare non-linear evolution with and without kink- component Extend to include non-ideal physics (care: unphysical modes can be introduced when dissipation is introduced…diamagnetic effects will be an important first effect to include).