1. Status of integrated core-edge modelling
V. Parail
Outline
Why do we need integrated CORE-ETB-SOL modelling?
What tools do we have at present;
What else is needed;
Summary.

2. What is integrated modelling (1)
Traditionally, plasma in tokamak is divided into two regions: CORE and SOL;
Indeed they have disparate time and space scales:
Plasma behaviour is controlled by different processes in CORE and SOL
FIRST WALL
CORE
SOL

3. What is integrated modelling (2)
Closer look reveals, however that these regions influence each other in many ways:
atomic physics penetrates into plasma core with neutrals and impurities;
profile stiffness makes core plasma dependant on the edge;
Edge transport barrier (which serves to separate core from SOL) is controlled by both;
MHD stability of ETB is influenced by the SOL;
FIRST WALL
CORE
SOL

4. Why do we need integrated core-ETB-SOL modelling (1)
If we start from the simplest task, which is to simulate plasma performance, then modellers should at least have boundary conditions for ne,I; Te,I and jz either on the top of ETB (ToB) for H-mode edge or on the separatrix for L-mode;
These parameters are needed because they influence plasma performance due to profile stiffness;
Traditionally boundary condition for plasma pressure is defined as a product of a critical pressure gradient (deduced from MHD stability analysis) multiplied by the ETB width (using a number of theory-based or heuristic models), see e.g.:
Onjun et al. PoP 9, 5018 (2002), Hubbard PPCF 42, A15, (2000); Guzdar IAEA_2004;

5. Why do we need integrated core-ETB-SOL modelling (2)
All models have quite big RMSE, at least due to involved experimental uncertainty;
On the top of that, modellers should use boundary condition for density (or use certain prescription for density profile in the core) and for one of temperatures;
The approach of using prescribed boundary is being actively used by a number of modellers to predict ITER performance:
Kritz et al, Kinsey et al, Janeschitz et al., Polevoi et al, Mukhovatov et al, Snowmass meetings;

6. Why do we need integrated core-ETB-SOL modelling (3)
This approach is definitely useful and bore some interesting results (particularly in assessing the role of profile stiffness in ITER performance);

7. Why do we need integrated core-ETB-SOL modelling (4)
However it does not allow simulation of the following important processes and situations:
Self-consistent modelling of L-H transition and formation of the ETB;
G. Janeschitz et al., M. Tokar, P. Guzdar, B. Scott…
Evolution of plasma profiles within the ETB even with a prescribed width;
Plasma parameters are not necessarily uniform within the ETB (pressure gradient, current) and MHD stability depends sensitively on these profiles;

8. J. Lonnroth et al., 2003

9. Predictive Modelling of ELMs (1)
J. Lonnroth et al., 2003

10. Why do we need integrated core-ETB-SOL modelling (5)
Modelling of ELM dynamics (even inside separatrix) as well as evolution of plasma parameters between ELMs require an inclusion of the ETB into computational domain (many techniques, used for ELM mitigation, require a controlled increase in heat and particle transport within the ETB between ELMs);
T. Evans, 2004, M. Becoulet, V Parail (this meeting),..
Simulation of impurity penetration through the ETB relies on computational domain extended even over the separatrix:
W. Houlberg, P. Belo, J. Hogan,...

11. V. Parail, 2003
Convective velocity changes sign from positive to negative after the change of the boundary conditions (ELMs keep =const:

12. Why do we need integrated core-ETB-SOL modelling (6)
Since ETB is positioned between core and SOL it is influenced by both these regions;
It is therefore very important to include simulation of the SOL (at least 2D in nature) into modelling domain;
ELM dynamics involves SOL (propagation of the heat and particle flux along the field lines (A. Loarte, J. Lonnroth, D. Coster…)
Role of the gas puffing in ELMy H-mode, including ETB formation (R. Groebner,
A. Kukushkin+A. Polevoi, J. Lonnroth, A. Loarte, A. Kallenbach, J. Hogan…);
Modelling of plasmas with radiating mantle, ELM mitigation by impurity seeding (all impurities come from the SOL!);

13. What do we have already and what we must have (1)
To simulate ETB and transport between ELMs:
there is a couple of theory-based/heuristic models for L-H transition and evolution of ETB (Janeschitz/Sugihara et al., Guzdar, Tokar), who use magnetic shear, density gradient and shear in plasma rotation to stabilise mainly drift Alfven instability. Note that there is a strong opposition from other theoreticians, notably Bruce Scott; Available models for L-H transition and ETB width are far from completion;
GLF23 has been recently used to generate ETB with an externally induced shearing rate. Its outstanding feature is that it has short wavelength turbulence (ETG mode) in it, which is not suppressed by the shearing rate; As far as I know, there is no EM modes in it (drift Alfven Bruce Scott);
There is no attempt yet to take into account turbulence spreading effect (T.S. Hahm, P. Diamond, Z. Lin et al.);

14. What do we have already and what we must have (2)
To simulate ETB and transport between ELMs (cont.):
even neo-classical transport is not well known near the separatrix (within few banana widths from it);
To simulate ELMs:
Linear MHD stability theory is probably well-developed, particularly for “standard” situations. However theory of EDA, type-II ELMs, washboard modes are much less known (BOUT is probably the best-known tool to use);
There are attempts to use linear eigenfunction of unstable modes to simulate radial extend of ELM or at least to associate ELM size with the amplitude of losses during ELM (P. Snyder, H. Wilson, S. Saarelma, J. Lonnroth). Note that this correlation is being disputed by a number of experimentalists;

15. What do we have already and what we must have (3)
To simulate ELMs:
Non-linear MHD for ELMs practically does not exist (at least in approximation, which can be used in transport codes). BOUT is being actively used at present to generate this knowledge (P. Snyder, H. Wilson, S. Cowley, G. Huysmans & M. Becoulet use quasi-linear approximation)
It’s a very long way before we will be able to use non-linear ELM model in predictive modelling (we need 3D picture of ELM and its time evolution, we need to know how it influenced heat and particle transport as well as current re-distribution both inside and outside separatrix!);

16. What do we have already and what we must have (4)
Self-consistent modelling of the core and SOL:
there are attempts to link 1D core transport codes with 2D SOL codes (COCONUT) or to extend 2D into core (beyond ETB: B2/EIRENE, BOUT);
longitudinal transport in the SOL is treated in fluid approximation (though quite sophisticated like 21 moments approximation with flux limiters, but still an approximation…). Kinetic effects should be included in a much more comprehensive way (PIC simulations?);
Drift effects are being taken into consideration by major codes but the task of its full implementation is far from being completed. Note that OFMC codes are frequently used to simulate radial electric field distribution near the separatrix (might play a role in L-H transition);
perpendicular transport used in 2D SOL is very primitive (usually ~D~1m2/sec);
There is a very interesting work to simulate large scale anomalous transport in the SOL: so called blobs (M. Greenwald, S. Krasheninnikov, T. Rognlien et al., P. Snyder…)

17. X.Q. Xu et al, IAEA 2004 using BOUT

18. What do we have already and what we must have (4)
Plasma-wall interaction:
if we discuss just how plasma-wall interaction influences plasma performance then we should mention wall and target plates sputtering by plasma flows in the SOL and wall recycling;
physics and chemistry of C wall and tiles is reasonably well known, however heavy metal W wall or Li or Be wall are much less studied.