Implementation of a fluid model for the non-linear interaction - - PowerPoint PPT Presentation

Fluid model for post-disruption runaway electrons Summary Fluid model for post-disruption runaway electrons

Implementation of a fluid model for the non-linear interaction between runaway electrons and background plasma

1Max-Planck-Institute for Plasma Physics, Garching, Germany 2Max-Planck-Institute for Plasma Physics, Greifswald, Germany 3ITER Organization, Saint Paul Lez Durance, France

• V. Bandaru1, M. Hoelzl1, G. Papp1, P. Aleynikov2, G. Huijsmans3

EFTC, Athens, Oct-2017

Fluid model for post-disruption runaway electrons Summary Fluid model for post-disruption runaway electrons Vinodh Bandaru Introduction RE fluid model Tests on pseudo-quenches

Runaway electrons – basic overview

• 𝑤𝑑 ≈ 6𝑤𝑈𝑓 in a normal Tokamak discharge
• Runaway of only distribution tails
• Further,
• At 𝐹 > 𝐹𝑑, runaway of thermal electron population*,
• Typical 𝐹/𝐹𝑑~10−2

*Dreicer, 1959

• Rapid fall of collision frequency at high energies,

Free acceleration or “runaway” of electrons

Larger E-fields necessary for significant runaway electron generation

Fluid model for post-disruption runaway electrons Summary Fluid model for post-disruption runaway electrons Vinodh Bandaru Introduction RE fluid model Tests on pseudo-quenches

Scenario in a disruption

Field stochastization Large radial transport Thermal quench Large toroidal E RE generation JET

Wesson et al. 1989

Implications for large tokamaks (like ITER)

• Up to 70% conversion to RE current
• If unconfined => potentially severe localized surface damage*

*Hollmann PoP 2015

Fluid model for post-disruption runaway electrons Summary Fluid model for post-disruption runaway electrons Vinodh Bandaru Introduction RE fluid model Tests on pseudo-quenches

Runaway confinement and MHD

• RE confinement depends on flux-surface restoration timescale
• Plasma stability is strongly affected by REs
• RE  MHD is hence important and is also highly non-linear

Larger aim: Understand the coevolution of disruption and runaway electrons using a fluid model Scope of this talk: A fluid model for REs in the MHD code JOREK, tested with artificial thermal quenches

Fluid model for post-disruption runaway electrons Summary Fluid model for post-disruption runaway electrons Vinodh Bandaru Introduction RE fluid model Tests on pseudo-quenches

Non-linear MHD code JOREK*

• Single fluid reduced-MHD code
• Realistic toroidal X-point geometries
• Includes 3D resistive wall effects

Numerics

• Flux-aligned 2D Bezier finite-elements
• Fourier decomposition in the toroidal direction
• Full implicit time-stepping
• Preconditoning + GMRES iterations
• MPI + OpenMP parallelized

Routinely used to simulate ELMs and disruptions

*Huijsmans et al., NF 2007

Flux-aligned 2D Bezier finite elements

Fluid model for post-disruption runaway electrons Summary Fluid model for post-disruption runaway electrons Vinodh Bandaru Introduction RE fluid model Tests on pseudo-quenches

RE fluid model

Total current density: Runaway current density: Integrating the drift-kinetic equation over the velocity phase-space yields REs considered as a separate fluid species Dreicer source (small angle Coulomb scattering)

* Connor et. al., NF (1975)

*

Fluid model for post-disruption runaway electrons Summary Fluid model for post-disruption runaway electrons Vinodh Bandaru Introduction RE fluid model Tests on pseudo-quenches

*

RE fluid model

* Rosenbluth et al., NF (1997)

Other governing equations (full form) Avalanche growth (large angle knock-on collisions)

Fluid model for post-disruption runaway electrons Summary Fluid model for post-disruption runaway electrons Vinodh Bandaru Introduction RE fluid model Tests on pseudo-quenches

Test cases with pseudo thermal quenches

Equilibrium plasma quenched by sudden step-up of perp. thermal conductivity

Circular plasma

𝑆 = 1.65𝑛, 𝑏 = 0.6𝑛, I = 0.67MA (sim. to ASDEX-U) RE source triggering thresholds *

* Stahl et. al., PRL (2015)

Fluid model for post-disruption runaway electrons Summary Fluid model for post-disruption runaway electrons Vinodh Bandaru Introduction RE fluid model Tests on pseudo-quenches

Runaway conversion

Case A Case B RE Conversion = 29.4% RE Conversion = 39.5%

Qualitatively similar behaviour observed experimentally

Fluid model for post-disruption runaway electrons Summary Fluid model for post-disruption runaway electrons Vinodh Bandaru Introduction RE fluid model Tests on pseudo-quenches

Peaking of RE profiles

Case A Case B

Reduced peaking for larger conversions

Fluid model for post-disruption runaway electrons Summary Fluid model for post-disruption runaway electrons Vinodh Bandaru Introduction RE fluid model Tests on pseudo-quenches

Growth rates

Case B

RE current growth saturates when E-field diffusion dominates

Fluid model for post-disruption runaway electrons Summary Fluid model for post-disruption runaway electrons Vinodh Bandaru Introduction RE fluid model Tests on pseudo-quenches

Preliminary comparison with GO*

* Pokol et al., EPS conf. (2017)

Much slower quench

* GO: Existing 1D RE code

Fluid model for post-disruption runaway electrons Summary Fluid model for post-disruption runaway electrons Introduction RE fluid model Tests on pseudo-quenches

Outlook

• Improved near-threshold treatment*
• Investigate the non-linear interaction of resistive-kink modes with peaked RE

beams

• Simulate the interaction of REs with a real disrupted plasma
• Detailed comparison to ASDEX-U and other machines

* Embreus et al., REM talk. (2017) Nardon et al., PPCF (2017)

Fluid model for post-disruption runaway electrons Summary Fluid model for post-disruption runaway electrons Vinodh Bandaru

Backup

Fluid model for post-disruption runaway electrons Summary Fluid model for post-disruption runaway electrons Introduction RE fluid model Tests on pseudo-quenches

References

1.

• P. Helander, D. Grasso, R.J. Hastie, A. Perona, Resistive stability of a plasma with runaway electrons,
• Phys. Plasmas 14, 122102 (2007).

2. J.W. Connor, R.J. Hastie, Relativistic limitations on runaway electrons, Nucl. Fusion 15, 415 (1975). 3. M.N. Rosenbluth, S.-V. Putvinski, Theory for avalanche of runaway electrons in Tokamaks, Nucl, Fusion 37, 1355 (1997). 4.

• P. Helander, L.-G. Eriksson, F. Andersson, Suppression of runways electron avalanches by radial

diffusion, Phys. Plasmas 7, 4106 (2000). 5.

• P. Aleynikov, B.N. Breizman, The theory of two threshold fields for relativistic runaway electrons,
• Phys. Rev. Lett. 114, 155001 (2016).

Fluid model for post-disruption runaway electrons Summary Fluid model for post-disruption runaway electrons Introduction RE fluid model Tests on pseudo-quenches