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M Romanelli 1 , F. Militello 1 , G. Szepesi 1,2 , A. Zocco 1PowerPoint Presentation

M Romanelli 1 , F. Militello 1 , G. Szepesi 1,2 , A. Zocco 1

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### Internal Transport Barriers and Improved Confinement in Tokamaks(Three possible trigger mechanisms)

1 EURATOM/CCFE Fusion Association, UK

2 University of Warwick, UK

Acknowledgments: F Crisanti, G Mazzitelli, F Zonca (ENEA),

J Hastie and J Connor (CCFE)

14th European Fusion Theory Conference, Frascati, Italy, September 26-29 2011

M Romanelli1, F. Militello1, G. Szepesi1,2, A. Zocco1

This work is funded by RCUK Energy Programme and EURATOM

CCFE is the fusion research arm of the United Kingdom Atomic Energy Authority

Introduction Tokamaks

Many different mechanisms can be responsible for improved confinement in tokamak plasmas.

In this presentation I will introduce three such mechanisms that could concur or play an independent role in the formation of an Internal Transport Barrier (ITB) or lead to improved confinement of particles and heat

- Fast ion induced alpha stabilization: the role of fast ion pressure in stabilizing the thermal-ion gradient driven modes is discussed in the context of e-m mode stability.
- Zonal perturbations: the interplay between drift-Alfvén wave turbulence and electromagnetic zonal perturbation is examined in the framework of a parametric instability analysis
- Impurities: improved electron confinement along with the expulsion of impuritiesis explained in terms of change in the turbulent spectrum and turbulent driven particle fluxes in the presence of a light impurity

Michele Romanelli – EFTC2011

Introduction Tokamaks

Discussion of triggering mechanisms:

- Fast ion induced alpha stabilization :the role of fast ion pressure in stabilizing the thermal-ion gradient driven modes is discussed in the context of EM mode stability.
- Zonal perturbations: the interplay between drift-Alfvén wave turbulence and electromagnetic zonal perturbation is examined in the framework of a parametric instability analysis
- Impurities: improved electron confinement along with the expulsion of impurities is explained in terms of change in the turbulent spectrum and turbulent driven particle fluxes in the presence of a light impurity

Michele Romanelli – EFTC2011

Fast ions Tokamaksα- stabilization

t

Flat region

2

3.5 m

3.5

Microstability analysis of a JET hybrid discharge with GS2 (EM)

JET #59137

Ti [eV]

20% of central temperature increase (same heating power) due to ITB

q

Ti @ 48.6 s - 49.6 s (1 s time evolution)

Michele Romanelli – EFTC2011

Fast ions Tokamaksα - stabilization

Thermal profiles corresponding to t=10s (gradients have been taken at R=3.5 m)

Density profiles of NBI+ICRH fast H minority

Michele Romanelli – EFTC2011

Fast ions Tokamaksα - stabilization (EM)

Change of the long wavelength spectra when increasing the temperature of the minority species

Increasing α -> complete ITG stabilization for Kρi≥0.6 -> EM modes

Michele Romanelli – EFTC2011

Fast ions Tokamaksα - stabilization (electrostatic)

Effect of changing Lnfast and s' in the electrostatic limit

In the electrostatic limit α-stabilization is less effective (requires much higher values of α to stabilize ITG at given s and Lnfast

Michele Romanelli – EFTC2011

Fast ions Tokamaksα - stabilization (EM)

At high TH micro tearing modes are found to replace ITG-TEM for Kρi≥0.6

- . Microtering arise the presence of wave particle interaction as can be seen from the parallel component of Ohm’s equation, given by the parallel gradient of equation:
- The drive of the instability is the gradient of the electron temperature.
- The mode is destabilized by increasing the ion pressure gradient, at constant electron temperature and density gradient.
- In general, the parallel electric field will be non-zero and will have a direct contribution from the parallel vector potential, second term on the LHS, and from the non-adiabatic part of the distribution functions.

[21] Zonca F et al 1999 Phys. Plasmas 6 1917

Michele Romanelli – EFTC2011

Fast ions Tokamaksα - stabilization (EM)

By increasing the energy of the hydrogen minority the short wavelength modes (μT) are stabilized however for α>0.4 the long wavelength AITG modes are destabilized.

Michele Romanelli – EFTC2011

Introduction Tokamaks

Discussion of triggering mechanisms:

- Fast ion induced alpha stabilization: the role of fast ion pressure in stabilizing the thermal-ion gradient driven modes is discussed in the context of e-m mode stability.
- Zonal perturbations: the interplay between drift-Alfvén wave turbulence and electromagnetic zonal perturbation is examined in the framework of a parametric instability analysis
- Impurities: improved electron confinement along with the expulsion of impurities is explained in terms of change in the turbulent spectrum and turbulent driven particle fluxes in the presence of a light impurity

Michele Romanelli – EFTC2011

Introduction Tokamaks

- The ITB can be caused by a region of plasma where the m=0, n=0 velocity shear is large, since there the correlation length of the turbulent eddies is reduced.
- Zonal Flows are m=0, n=0 secondary instabilities (i.e. they are linearly stable) which can arise from the interaction of drift waves.
- The generation of the Zonal Flows (and hence of the ITB) can be studied with a parametric instability approach.
Details in Militello, Romanelli, Connor and Hastie, Nuclear Fusion (2011).

Michele Romanelli – EFTC2011

We study the problem with a fluid model in a slab: Tokamaks

We assume Ti=0, Te=const, small finite b and negligible dissipation.

The time is normalized to the Alfven time and the length to a macroscopic size.

de is the electron skin depth and rs is the ion sound Larmor radius.

Modelradial profiles

Michele Romanelli – EFTC2011

Primary and secondary instabilities Tokamaks

- When density gradients are present, in the system appear:
- Drift-Alfven waves (primary “instability”, linear):
- Zonal perturbations (secondary instability coupled through sidebands, quasi-linear):

primary

secondary

Michele Romanelli – EFTC2011

Dispersion relation Tokamaks

- Linearizing the system around an equilibrium with a large primary instability leads to a (huge!) dispersion relation for the secondary instability (i.e. the Zonal Perturbation).

Normalized growth rate

of the Zonal perturbation

Normalized frequency

of the Zonal perturbation

Militello, Romanelli, Connor and Hastie, NF (2011)

Michele Romanelli – EFTC2011

Dispersion relation Tokamaks

- Linearizing the system around an equilibrium with a large primary instability leads to a (huge!) dispersion relation for the secondary instability (i.e. the Zonal Perturbation).

Normalized growth rate

of the Zonal perturbation

Normalized frequency

of the Zonal perturbation

Electromagnetic branch

Electrostatic Branch

Solid lines: Guzdar et al. PRL (2001)

Militello, Romanelli, Connor and Hastie, NF (2011)

Michele Romanelli – EFTC2011

Zonal magnetic fields (with Tokamaksde≠0) and zonal density can be generated as well (new result).

The zonal Fields can provide a drive for the Tearing mode. (Militello et al., PoP 2009)

Not only Zonal flowsZonal fields

Zonal density

Michele Romanelli – EFTC2011

ITB criterion Tokamaks

- As noted before, self-sustained Zonal Perturbations appear for >1.
- Around a resonant surface:
- We can define a width around the surface where the condition is always met:
- To shear the eddies, xcr must be larger than rs:

or equivalently:

Michele Romanelli – EFTC2011

The criterion is a Tokamaksnecessary condition but it is not sufficient (it does not say anything about the nonlinear evolution).

Assumption: a barrier survives if a sufficient amount of energy goes from the turbulence to the zonal perturbation.

Only the resonant modes transfer energy to the zonal perturbation.

Low order helicities have more resonant modes.

Conclusion:

an ITB forms and survives when a low order rational surface enters the palsma

and:

ITB criterion IIMichele Romanelli – EFTC2011

Introduction Tokamaks

Discussion of triggering mechanisms:

- Fast ion induced alpha stabilization: the role of fast ion pressure in stabilizing the thermal-ion gradient driven modes is discussed in the context of e-m mode stability.
- Zonal currents: the interplay between drift-Alfvén wave turbulence and electromagnetic zonal perturbation is examined in the framework of a parametric instability analysis
- Impurities:improved electron confinement along with the expulsion of impurities is explained in terms of change in the turbulent spectrum and turbulent driven particle fluxes in the presence of a light impurity

Michele Romanelli – EFTC2011

Impurity Tokamakstriggered inward e- pinch

- Turbulent particle fluxes (in the simplest case of electrostatic turbulence) arise from the phase shift between electrostatic potential fluctuations and density fluctuations
- In the presence of impurities the electron and deuterium fluxes are decoupled; the phase shift between electron-deuterium density fluctuations and electrostatic potential might become significantly different and inward pinches can appear.
- In strongly electron driven turbulence, impurities are expected to stabilise the ETG modes [Reshko M. and Roach C.M. 2008 Plasma Phys. Control. Fusion 50 115002]
- Impurity ions will change the turbulence spectrum moving the peak towardhigher

Michele Romanelli – EFTC2011

Plasma parameters Tokamaks

Plasma parameters have been taken from an FTU discharge where in the presence of Lithium Limiter improved confinement and strong density peaking was observed

Mazzitelli G. et al 2011 Nucl. Fusion 51 073006

- The effect of one light impurity (Li) species on (D-e-) plasma microstability has been investigated with the flux tube gyrokinetic code GKW.

A. Peeters et al, Computer Physics Communications 180 (2009) 2650–2672

Michele Romanelli – EFTC2011

Impurity effect on spectrum (GKW) Tokamaks

Michele Romanelli – EFTC2011

Linear particle fluxes Tokamaks

Michele Romanelli – EFTC2011

Linear particle fluxes Tokamaks

The change in sign of the fluxes coincides with the change of unstable mode from ITG to TEM

Extensive parametric scan is presented in

M Romanelli, G Szepesi et al Nucl. Fusion 51 (2011) 103008 (9pp)

Michele Romanelli – EFTC2011

Nonlinear particle fluxes at r/a=0.6, t=0.3s Tokamaks

Michele Romanelli – EFTC2011

Summary Tokamaks

Different triggering mechanisms can be responsible for the transition to improved confinement in tokamak plasmas. In this presentation three such mechanisms have been dsicussed

- Fast ions induced α - stabilization:
M Romanelli, A Zocco et al Plasma Phys. Control. Fusion 52 (2010) 045007

- Criteria for ITB formation in low shear plasmas:
F Militello, M Romanelli, J Connor and J Hastie, Nuclear Fusion (2011).

- Impurity induced inward deuterium and electron pinch:
M Romanelli, G Szepesi et al Nucl. Fusion 51 (2011) 103008 (9pp)

This work is funded by RCUK Energy Programme and EURATOM

Michele Romanelli – EFTC2011

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