magnetic ripple as a tool for elms mitigation

1ITPA Meeting. Kyoto, 18-21 April, 2005

Magnetic Ripple as a Tool for ELMs Mitigation

V. Parail, T. Johnson, J. Lonnroth, T. Kiviniemi, P. de

Vries, G. Saibene, Y. Kamada, N. Oyama, K. Shinohara, S. Konovalov, D. Howell


Outlook Evolution of plasma profiles between ELMs; Ways to maximise top-of-the-barrier plasma

pressure; Ways to avoid (mitigate) ELMs; Analytical theory of ripple transport; Predictive transport modelling of JET plasmas

with ripple transport; OFMC code ASCOT and simulation of thermal ion

ripple losses in plasmas with JET and JT-60U magnetic coils;

Summary.


Evolution of plasma profiles between ELMs (1)

Since

transport

within the ETB

is quite small,

plasma

develops

strong

pressure

gradient to

transmit heat

flux through

the ETB:

nTq


Evolution of plasma profiles between ELMs (2)As soon as edge parameters hit one or the other stability limit, an ELM develops, which throws away excessive pressure or current;


Evolution of plasma profiles between ELMs (3)How can we mitigate ELMs or remove them entirely (without sacrificing performance, which means keeping )?

Reduce the heat flux, which enters ETB (up to but not beyond the limit, which triggers transition to type-III ELMs):

Increase radiated power (extra impurities at the edge);

Increase CX losses (gas puffing?);

Increase the heat flux through the ETB between ELMs by increasing thermal conductivity:

Increase ion density ( );

Increase transport by magnetic ripples or ergodic magnetic limiter;

Induce quasi-continuous benign MHD (EDA, type-II ELMs, washboard modes, pellets ???)

nTq

2/ poliefficlneo

i BTZn

CRITnTnT


Evolution of plasma profiles between ELMs (4) Reduce the heat flux, which enters ETB (up to but not beyond the limit, which triggers transition to type-III ELMs):

Increase radiated power (extra impurities at the edge);impurity accumulation in plasma core; does not affect ions; difficult to optimise pressure within ETB; Increase CX losses (gas puffing?);it simultaneously increase losses between ELMs but it’s difficult to do it in a controlled way;

Increase the heat flux through the ETB between ELMs by increasing thermal conductivity:

Increase ion density ( );difficult to control , often triggers transition to type-III ELMs; pressure and current profiles might be far from optimum; Induce quasi-continuous benign MHD (EDA, type-II ELMs, washboard modes, pellets ???)We need much better understanding of these modes before we could reliably use them in a controllable way;

2/ poliefficlneo

i BTZn


Increase transport by ergodic magnetic limiter (controllable, but increases electron transport only) or by magnetic ripples;

Magnetic ripple as ELM mitigation tool

Follow B. Then |B|~B0[1+cos()+sin(N)] oscillate due to Toridicity Ripple

Particles can be toroidally trapped in magnetic wells caused by the ripple.

The ripple well depth

min

minmax

B

BB

Bmax

Bmin

Ripple well trapping


Ripple well trapping (2) Toroidal symmetry is

broken, so orbits are not confined.

The motion is a sum of: Oscillation between

turning points; Vertical drift

Detrapped by: Collisions; Moving towards smaller ;

Collisionality regimes: High: (these particles

oscillate between banana and ripple trapped state in a diffusive way)

Low: non-diffusive losses


Ripple Perturbations of Banana Orbits

Ripples perturb banana

orbits at their “banana tips”,

moving it across flux

surfaces.

[A.N. Boozer, Physics of

Fluids 23, 2283 (1980)]

If the “unperturbed tip”

appear at a ripple maximum,

then the reflection appear

earlier and vice versa.

This is a diffusive process


Total ripple-induced transport

Total ripple-induced

transport is a combination of:

convective/diffusive ripple losses (depending on collisionality), which are toroidally localised and

stochastic ripple-banana diffusion, which is toroidally uniform;

N. Oyama, K. Shinohara 2005


We use analytical formula for additional ion thermal transport due to ripple-induced thermal ion losses in our predictive simulations with JETTO

P. Yushmanov, Review of Plasma Physics, v. 16, New York, Consultants Bureau (1991).

Flux surface averaged additional ion thermal transport. Implemented into the JETTO transport code.

232/3

,

5.0~

BRe

TNq

i

i

ithi

Nq has to be satisfied for the extent of the region inside local mirrors on the outboard side of the torus with locally trapped particles. Please note that this inequality is actually NOT satisfied for most JT-60U plasmas!


Narrow edge-localised ripple: reduces performance and increases ELM frequency:

JETTO transport simulation.

The ripple-affected region is assumed to be significantly narrower than the pedestal width.

Bohm / gyro-Bohm transport model.

The density is low in this case.

no ripple-induced transportripple-induced transport


Narrow edge-localised ripple: reduces performance and increases ELM frequency (2)

Ripple-induced

edge-localised

transport

Flattening of the

pressure gradient

near the separatrix,

effective narrowing

of the pedestal.

Lowering of the

pedestal height.

Lowering of the

core pressure due

to profile stiffness.


Non-optimum pressuregradient


Narrow edge-localised ripple reduces performance and increases ELM frequency (3)The ELM frequency increases

with the introduction of ripple-induced transport because of: profile stiffness, which leads to increased transport inside the top of the pedestal in the case of lower pedestal height and faster replenishment of ETB; less energy loss during the ELM;

Might explain the higher ELM frequency at JT-60U.

Smaller, more benign ELMs.

Ripple losses can be an important tool used for ELM mitigation.

no ripple-induced transport

With ripple


Wide ripple at the edge: improved performance

JETTO transport simulation.

The ripple-affected region is assumed to be significantly wider than the pedestal width.

Bohm / gyro-Bohm transport model.

The density is high in this case.

no ripple-induced transportwith ripple-induced transport


Wide ripple at the edge: improved performance (2)

The ELM frequency decreases due to larger edge losses between ELMs with increased ripple transport.




Decreasing ELM frequency: The time-average

pressure at the top of the pedestal increases (even if max. pressure stays the same).

The time-average core pressure increases due to profile stiffness.

No ripple

less ripple more ripple



A reduction in the ELM frequency was occasionally seen in JET ripple experiments in 1995.

Resembles the improved performance obtained with a stochastic magnetic boundary in DIII-D [T. Evans, 2004 IAEA Fusion Energy Conference].

This mechanism is most pronounced in high density plasmas, which have the highest level of transport within the pedestal because of the temperature and density dependency of neo-classical transport.


Numerical simulation of ripple losses in realistic geometry (1)

#60856 belongs to JET/JT-60U identity plasma.

Ripple-induced transport in plasma with JET coils is outboard midplane localised.

Same plasma with JT-60U coils should have much larger ripple transport near x-point;

JT-60U coils JET coils I2/I1=0.5

After drawing general conclusions on what might be expected from magnetic ripples we decide to perform a detailed analysis of realistic plasmas



Orbit Following Monte Carlo code ASCOT was used for the simulations;

Code follows guiding centre orbits of thermal particles ensemble in a torus;

3D JET and JT-60U ripple model has been included as B=B0 +

B1cosN + B2cos2N , where Bn=Bn(R,Z), N- number of toroidal

coils;

Only collisions with a fixed background are considered;

Ensemble of particles can be initialised as:

delta-function in radius or

according to assumed ne(r) and Ti(r);



To speed up the simulations, can be calculated from the spreading of a “pulse” (with the radial electric field turned off):

f(t=0,r, v)=(r-r0)fMaxwell(v) If the process is diffusive the variance will grow at a constant rate

<(r (t,v)-<r (t,v)>)2> =V (t,v)=2Dv(v)t

Since the flow ~Dv, the transport coefficients are given by:

0 - relates pressure gradients and particles transport,

2 - relates temperature gradients and energy transport, and

1 - is the off-diagonal coefficient.

Accuracy ~ [Ntp -1/2 e-E/T Nmeasurements]-1/2 ~ 20%

)(2

5

22

1 23 vf

T

mv

dt

dVvd Maxwell

n

n



Rho=0.98, JET I2/I1=0.5 Rho=0.98, JT-60U coils


JT-60U coils

JET coils, I2/I1=0.5

JET coils, I2/I1=1.0

neo-classical CHI-I



Rho=0.98, JETcoils, I2/I1=0.5

Rho=0.98, JT-60U coils


Numerical simulation of ripple losses in JET geometry (1)

Four level of current imbalance between odd and even JET coils is being considered: I1/I2= 1.0; 0.66; 0.33 and 0.0 JAERI OFMC code is being used for the modelling of fast ion losses

I1/I2= 0.66 I1/I2= 0.33 I1/I2= 0.0

2 2 2


FULL ripple

66% ripple

33% ripple

Pmax~3.6MW/m2

2

2


Full ripple

Half ripple

No ripple

ASCOT code is being used to evaluate the role of magnetic ripple in thermal ion transport;

“Pulse propagation” technique is being used for first level of analysis;

Three levels of current imbalance are used: I1/I2= 0.0; 0.5 and 1.0;

JET shot #60856 (JET/JT-60U

identity plasma with Ip=1.15 MA)

is used as an example;



SUMMARY

Magnetic ripple, if carefully controlled, might serve as a valuable tool for ELM mitigation;

Magnetic ripple losses increase thermal ion transport only and it might be better to use it in combination with stochastic magnetic limiter;

Experiments on JET and JT-60U are under preparation to elucidate the role of controlled magnetic ripple in ELMy H-mode performance;

magnetic ripple as a tool for elms mitigation

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