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YQ Liu, Peking University, Feb 16-20, 2009 Introduction to the Resistive Wall Mode (RWM) Yueqiang Liu UKAEA Culham Science Centre Abingdon, Oxon OX14 3DB,

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Presentation on theme: "YQ Liu, Peking University, Feb 16-20, 2009 Introduction to the Resistive Wall Mode (RWM) Yueqiang Liu UKAEA Culham Science Centre Abingdon, Oxon OX14 3DB,"— Presentation transcript:

1 YQ Liu, Peking University, Feb 16-20, 2009 Introduction to the Resistive Wall Mode (RWM) Yueqiang Liu UKAEA Culham Science Centre Abingdon, Oxon OX14 3DB, UK

2 YQ Liu, Peking University, Feb 16-20, 2009 Outline 1.What is RWM? 2.Why important? 3.Approaches/tools to study RWM  Analytical  Numerical  Experimental 4.Status-quo in RWM research  What is known?  Partially understood?  Not understood? 5.Plans for following lectures

3 YQ Liu, Peking University, Feb 16-20, 2009  External ideal kink instability (time scale = microseconds)  Normally pressure-driven (above no-wall beta limit)  Resistive wall slows down kink instability to time scale of wall eddy current decay time  RWM (typically milliseconds)  At high pressure, mode located towards low-field side (kink-ballooning)  Low toroidal mode number n=1,2,3  Similar to vertical instability (RWM with n=0)  Three consequences of slowed down  Still unstable  eventually causes disruption  Time scale feasible for feedback control  Kinetic effects become important What is RWM ?

4 YQ Liu, Peking University, Feb 16-20, 2009  Important for advanced tokamaks, aiming at steady state, high bootstrap current, high pressure operation  Good microscopic property (internal transport barrier), rather bad macroscopic MHD (low pressure limit due to RWM)  Stabilization of RWM essential for increasing fusion power production of advanced tokamaks  MHD modes in ITER  Causing disruptions  RWM (advanced scenario)  NTM (conventional scenario, mode locking)  Degrading performance  ELM (H-mode)  AE/TAE (alpha-particle destabilized), sawteeth, etc  Possibly stable or not so important  TM, Interchange mode, etc Why important ?

5 YQ Liu, Peking University, Feb 16-20, 2009  The key for success of AT is to increase normalised plasma pressure by stabilising RWM  Example: for ITER advanced scenario (Scenario-4), successful stabilization of n=1 RWM can increase from 2.5 to 3.5 e.g. fraction of plasma self-generated current In more detail...

6 YQ Liu, Peking University, Feb 16-20, 2009 The other way to look at it …

7 YQ Liu, Peking University, Feb 16-20, 2009 Outline 1.What is RWM? 2.Why important? 3.Approaches/tools to study RWM  Analytical  Numerical  Experimental 4.Status-quo in RWM research  What is known?  Partially understood?  Not understood? 5.Plans for following lectures

8 YQ Liu, Peking University, Feb 16-20, 2009 Analytic approaches  According to ideal MHD description, RWM is ideal kink mode, whose free energy largely dissipated by eddy currents in the wall.  In cylindrical theory, growth rate determined by combining andand vacuum solution  Let’s go through a simple analytic example: cylindrical Shafranov equilibrium

9 YQ Liu, Peking University, Feb 16-20, 2009 Analytic approaches  Consider single fluid, ideal, incompressible plasma, no flow  Perturbed momentum equation  With perturbed quantities  Faraday’s law gives  The z-component of curl of momentum equation (toroidal torque balance) gives …

10 YQ Liu, Peking University, Feb 16-20, 2009 Analytic approaches  Assuming a step density function, we have vacuum-like field everywhere  … and a jump condition across  Vacuum solution + jump condition result in the dispersion relation for ideal (current-driven) external kink

11 YQ Liu, Peking University, Feb 16-20, 2009 Analytic approaches  Adding a jump condition across a (thin) wall  … together with the plasma & vacuum solution, we arrive at the dispersion relation for the RWM  Neglecting plasma inertia

12 YQ Liu, Peking University, Feb 16-20, 2009 Analytic approaches  There are enormous literatures covering various analytical aspects of RWM  Probably one of the finest is offered by [Betti PoP (1998)] (as far as analytics can go)  A very useful dispersion relation, valid in toroidal geometry, has been derived by several authors [Haney PF B1 1637(1989), Chu PoP (1995)]  … representing also the energy principle inertia plasmavacuum+wallkinetic

13 YQ Liu, Peking University, Feb 16-20, 2009  Basic is system of ideal MHD equations  Additional terms/equations for RWM modeling:  Vacuum equations  Equation for resistive wall  Equation for feedback coils  Flow terms  Kinetic terms  Full toroidal codes that are used for RWM study  MARS-F [Liu PoP (2000)], CarMa [Albanese COMPUMAG 2007]  VALEN [Bialek PoP (2003)]  NMA [Chu NF (2003)]  KINX [Medvedev PPR (2004)]  CASTOR_FLOW, STARWALL [Strumberger NF (2005)]  AEGIS [Zheng JCP (2006)]  MARG2D [Tokuda IAEA FEC08]  MARS-F is so far the only code including both feedback and advanced rotational damping physics Modelling tools

14 YQ Liu, Peking University, Feb 16-20, 2009  Not always easy from experiments. However, several possibilities do exist:  Check beta limit – unstable only if beta exceeds no-wall limit  Use ideal stability code to compute beta limit  Use experimental li-scaling  Resonant field amplification (RFA routinely used on DIII-D and JET)  If possible, measure mode growth rate and frequency  Both proportional to inverse wall time  RWM frequency normally between 0-100Hz, unlocked island a few KHz  RWM growth rate sensitive to plasma-wall separation [JT60-U], unlike internal modes  Mode structure  Global field perturbation and displacement within plasma (ELM, TM)  Ballooning structure at plasma surface  MHD spectroscopy [DIII-D, JET]  Measure resonant field amplification by (marginally) stable RWM  Using either a dc-pulse excited error field  Or traveling/standing waves field perturbation Experimental approaches: identify RWM

15 YQ Liu, Peking University, Feb 16-20, 2009  Not easy by local modification of plasma equilibrium profiles, largely determined by transport requirements and properties of AT:  Reversed or flat central q profile  broad current profile  low li  Strong pressure peaking  Stabilization by plasma flow (passive way)  Various damping mechanisms (MHD, kinetic)  Still active research area  Feedback stabilization of RWM (active way)  Using magnetic coils to suppress the magnetic field produced by RWM  Very similar to vertical stability control of elongated plasmas  Difference is helical field perturbation  Also possible to apply feedback + plasma flow Experimental approaches: stabilise RWM

16 YQ Liu, Peking University, Feb 16-20, 2009 Active control: one more point …  The fundamental reason that a magnetic feedback system, by suppressing the field perturbation, can stabilise the plasma instability, is that …  for an ideal plasma, the field lines are frozen into the plasma  This is the underlying assumption of many magnetic control of plasmas (vertical instability control, RWM control, etc.)  For this to be successful, plasma  must generate external field perturbations to interact with coil fields  can be treated as ideal (field line frozing)  For the above reasons, tearing mode (TM or NTM) or internal kink (sawteeth) cannot be stabilised by magnetic feedback (fortunately there are other means to stabilise them)  How about ELMs ?

17 YQ Liu, Peking University, Feb 16-20, 2009 Outline 1.What is RWM? 2.Why important? 3.Approaches/tools to study RWM  Analytical  Numerical  Experimental 4.Status-quo in RWM research  What is known?  Partially understood?  Not understood? 5.Plans for following lectures

18 YQ Liu, Peking University, Feb 16-20, 2009  Understanding damping physics of the mode  Requires comparison of experiments with theory and simulations  Alfven continuum damping [Zheng PRL (2005)]  Sound wave continuum damping [Bondeson PRL (1994), Betti PRL (2005)]  Parallel sound wave damping [Chu PoP (1995)]  Damping from plasma inertial and/or dissipation layers [Finn PoP (1995), Gimblett PoP 7 258(2000), Fitzpatrick NF 36 11(1996)]  Particle bouncing resonance damping [Bondeson PoP (1996), Liu NF (2005)]  Particle precession drift resonance damping [Hu PRL (2004)]  Effect of error field – experiments show mode stability very sensitive to error field  Nonlinear coupling of mode stability, error field, and plasma momentum damping  A metastable RWM amplifies external error field, causing toroidal torque which damps plasma flow  Plasma flow below threshold results in unstable RWM Status-quo: critical issues in mode physics

19 YQ Liu, Peking University, Feb 16-20, 2009  Two essential components in feedback 1)Plasma dynamics (P) 2)Controller (K)  Constructing plasma response models (PRM) describing the mode dynamics [Liu PPCF (2006), Liu CPC (2007)]  Realistic control design  3D conducting structures (walls, coils)  Noise (v,w,n), ac losses for superconducting coils (ITER)  Power supply constraints (voltages, currents, time delays, etc.)  Controller design = normally solving nonlinear optimization problem with constraints [Fransson PoP (2000)]  Choice of active coils (u): high priority topic in ongoing ITER design review  Ideally coils should be placed as close as possible to plasma  Physical constraints on space  Choice of sensor signals (pick-up coils) (y) [Liu NF (2007)] Status-quo: critical issues in mode control

20 YQ Liu, Peking University, Feb 16-20, 2009 Status-quo: mode physics  MHD physics  Ideal kink + resistive wall (well understood)  Fluid continuum resonance damping (understood)  Resistive-viscous damping (understood)  Kinetic physics  Parallel sound wave damping (understood)  Particle bounce resonance (part. understood)  Particle precession drift resonance (part. understood)  Resonant field amplification (RFA) (part. understood)  Coupling to momentum confinement (poor understood)  Coupling to other MHD modes (not understood)

21 YQ Liu, Peking University, Feb 16-20, 2009 Status-quo: mode control  Resembles vertical stability control of elongated plasmas (n=0 RWM)  Magnetic feedback works because of:  External mode magnetic structure  Slow growth rate to allow feedback system to react  Important aspects:  Plasma (RWM) dynamics (part. understood)  Controller design and optimisation (PID, H-infinity, SISO, MIMO, …) (part. understood)  Choice of active coils (understood)  Sensor signal optimisation (well understood)  3D conductors for modelling (part. understood)  Practical issues: noise, power saturation, ac-losses (for SC), … (not well understood)

22 YQ Liu, Peking University, Feb 16-20, 2009 Summary: issues to be resolved

23 YQ Liu, Peking University, Feb 16-20, 2009 Plans for following lectures: topics 1.Active control of RWM 2.Damping physics of RWM 3.Resonant field amplification (RFA) 4.3D conductor effects on RWM

24 YQ Liu, Peking University, Feb 16-20, 2009 Plans for following lectures: structure  On each topic, try to show three aspects of research:  Analytic theory  Toroidal modelling  experiments  Basic analytic theory (not a comprehensive coverage)  Systematic modelling results  Brief description of some experimental results (to compare with modelling)


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