Resonant Field Amplification Yueqiang Liu UKAEA Culham Science Centre Abingdon, Oxon OX14 3DB, UK

YQ Liu, Peking University, Feb 16-20, 2009

Resonant Field Amplification

Yueqiang Liu

UKAEA Culham Science Centre

Abingdon, Oxon OX14 3DB, UK


Outline

1. Introduction1) What is resonant field amplification (RFA)?2) Why interesting and important?3) How to measure RFA?

2. Basic analytic theory

3. Toroidal modelling vs. Experiments


What is RFA ? RFA: plasma amplifies an external field, which has the same

resonant component (same field helicity) as one of the stable eigenmodes present in plasma


Why important ?Error fields strongly affect plasma stability and confinement

Plasma can amplify external (static or LF ac) error fields due to resonance with (meta-) stable MHD modes (RFA).

Known example is RFA due to stable RWM

Causes magnetic braking of plasma rotation, modification of mode stability, etc.

Can also be useful to probe plasma stability boundary (active MHD spectroscopy)

Will be a significant issue for ITER with regard to momentum damping and RWM stability [Hender NF 47 S128(2007)]


Apply fields with external saddle coils

Measure plasma response

)coil to0(

)coil to90(o

r

or

B

BRFA

Measurement of RFA in JET using saddle loops

How to measure RFA in experiment ?


Outline





Basic theory RFA was first proposed by Boozer [Boozer PRL 86 5059(2001)]

As linear response of plasma (stable eigenmode) to external fields

With strongest amplification near stability margin

Theory can be understood from solution of a general ODE, without involving plasma physics

The full solution is


Basic theory Special case A: steady-state linear response to a travelling wave

Special case B:

A marginally stable mode does not give an “infinite” RFA response !


In our notation

Basic theory RFA amplification factor for RWM normally defined as

[Reimerdes NF 2005, PPCF 2007]

where

is the vacuum field in the presence of walls but in the absence of plasma

RFA determined by the eigenvalue (damping rate and real frequency) of the stable mode

Maximum amplification if external frequency matches intrinsic frequency of the mode

Experimentally measurable amplification factor helps to deduce the mode eigenvalue (active MHD spectroscopy)


Outline





Toroidal modelling vs. Experiments MHD spectroscopy

No-wall ideal kink beta limit Stable RWM spectrum

Low-n peeling mode induced RFA

RFA measurements test RWM damping physics

RFA inter-plays with NTV-caused momentum damping


Resonant field amplification (RFA) Observed in high-pressure plasmas, where low-frequency

error fields are amplified by the plasma response, due to meta-stable low-frequency MHD modes (RWM)


RFA as MHD spectroscopy RFA can be used as a tool to determine

Troyon beta limit Damping rate and frequency of stable RWM …

… Using an empirical formula [Reimerdes NF 2005, PPCF 2007]


Toroidal modelling vs. Experiments



JET


RFA mode structure


RFA induced by peeling mode Some of the RFA peaks in experiments correlated

with ELM-free period prior to the first ELM, before reaching the RFA threshold [Gryaznevich PPCF 50 124030(2008)]


Equilibrium reconstructed from shot 70200

Among other parameters, peeling mode stability sensitive to edge current density, which is somewhat arbitrarily chosen here

Our goal is to reach qualitative understanding. Quantitative prediction requires extremely accurate knowledge of the plasma equilibrium

Choose two rotation profiles, differing slightly at the plasma edge

Equilibrium and rotation profile


Stability of peeling mode, as an edge current driven mode, is largely controlled by proximity of edge q to an integer number

Unlike the external kink mode, which is mostly driven by beta in advanced tokamaks

For our equilibrium, m=6 is the most unstable peeling mode (in SFL coordinates)

Eigenmode structure


Effect of rotation on peeling stability


With fixed field and total current, scaling plasma pressure leads to change of edge q-value, hence stability of ideal peeling modePeeling mode becomes stable for qa just above 6 for these equilibriaCompute RFA response from both stable peeling and RWMRatio of contribution from two modes varies with simultaneous increase of betan and qa

RFA response from stable modes


A better way to track the peeling response is to keep a low beta, and scale qa only.

This requires slight scaling of total plasma current at a fixed magnetic field

RFA response from peeling mode


RFA tests damping model

semi-kinetic damping

sound-wave damping


Stability also tests damping model


RFA & momentum damping


RWM couples to momentum confinement Meta-stable RWM amplifies plasma response via RFA,

creating large helical field perturbation inside plasma. Plasma particles, going through these 3D fields, experience

a viscous force (NTV) [Shaing PoP 10 1443(2003)]

[Zhu PRL 96 225002(2006)]


Coupling to other MHD modes DIII-D observes triggering

of stable RWM by ELMs or fishbones Triggering is sporadic, and

criteria for ELM not known Hypothesis: plasma

generated n=1 perturbation increases effective rotation threshold, similar to magnetic breaking

Strong evidence in JET and DIII-D suggesting coupling of RWM to tearing modes


Summary Error fields play a key role in stability and

performance of fusion plasmas

RFA response by (meta-)stable modes in plasma complicates the matter, and requires re-thinking when designing error field correction coils

Good news is that RFA can be used as an active MHD spectroscopy tool to detect damping rate and frequency of stable RWM validate mode damping physics (examples of other such tool: using TAE cascad to predict q-

profile evolution)

RFA due to low-n, stable MHD modes can be modelled using codes such as MARS-F (MARS-K), IPEC, ...

Resonant Field Amplification Yueqiang Liu UKAEA Culham Science Centre Abingdon, Oxon OX14 3DB, UK

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