QSH, what comes next ?

M. Zuin RFX–mod 2009 Programme Workshop Padova, 20/01/2009

QSH,

what comes next ?

Matteo Zuin


QSH in RFX-mod

MHD control has allowed high-current operation up to 1.6MA ( target 2MA)

Spontaneous transitions to Quasi-SH

m=1,n=-7

[ n=8-15(m=1, n)2 ]1/2


What do we know? (experimentally)

The choosen parameter to interpret experimental data is the Lundquist number

S = R / A =

QSH pureness is observed to depend on S

but:

is, actually, S ruling the MH-QSH transitions?


Comparison to numerical modeling

Numerical simulations use and as parameters. The transition from MH to QSH is ruled by the Hartmann number: H=(

S = R / A

1/H = P1/2 S-1

dominant mode

secondarymodes

secondary modes

dominantmode

Specyl – 3D viscoresistive nonlinear MHD

S S

which is the role played by viscosity?

Experiment


QSH persistence

QSH persistence is observed to depend on Ip (and S)

Which is the mechanism ruling QSH dynamics and duration?


From ”oscillating“ to long lasting QSH

Ip=1560 kA

Ip=930 kA

b n=

-7/B

(a)

[%]

b n=

-7/B

(a)

[%]

The increase of the plasma current produced longer, purer QSH phases with almost constant mode amplitude and no clear regular time behaviour

• What is at the origin of QSH crashes?


QSH crashes and reconnection events

Each QSH crash is associated to a discrete relaxation event (DRE): rapid variation of F, due to spontaneous magnetic reconnection

• Does QSH crash induce F variation or viceversa?

b n=

-7/B

(a)

[%]

F



b n=

-7/B

(a)

[%]

At intermediate plasma current, DREs occur both in MH and QSH phases, with the same properties

The dynamics of F seems not to depend on plasma helicity

F

Ip=1560 kAIp=930 kA



Ip=1560 kAIp=930 kAIp=450 kA

b n=

-7/B

(a)

[%]

F

At low plasma current and deep F, DREs occur nearly-periodically, with high frequency and large amplitude, in MH discharges.

No QSH is observed


QSH crashes in detail

Magnetic reconnection is toroidally localised

(current sheet formation)

The m/n 1/-7 pattern persists

Large region of the plasma is still unperturbed!


QSH maximum duration

Shallow FDeep F (<-0.1)

The longest QSH are observed in shallow F discharges.

At deeper F, relaxation events are more frequent and large, thus preventing long lasting QSH states


What determines QSH persistence

Ip= 1.5MA F= -0.1

Ip= 1.5MA F= -0.03

The intensity and the probability of the reconnection process is strictly related to Ip and F

A role may be played in the reconnection process by the ratio between the guide field: B(a) and the reconnecting field: B(a)

24936 ( record)

To observe very long lasting QSH, high current and F0 seem mandatory


QSH on the Electrostatic field

Mode analysis on ISIS electrostatic sensors reveals the appearance of QSH also on Floating potential.

Comparison with magnetic component


QSH on the Electrostatic field

Magnetic signals Electrostatic signals

Is this electrostatic field pattern due to plasma–wall interaction ?

or

Is it the helical electrostatic dynamo field observed in SH simulations ? (Bonfiglio

PRL2005)


Te profiles in SHAx

?

SHAx states have flat electron temperature profiles in the core:

- role of m>1 modes and residual chaos ?- power balance in the helical core ?- microturbulence ?- flat helical q profile ? (see L. Marrelli, this

afternoon)


“Conclusion”

A number of open issues was presented:

• Physical parameters governing MH to QSH transitions

• Dynamics of QSH crashes

• QSH Electrostatic field pattern

• Te profiles during SHAx state


Comparison with nonlinear MHD simulations

MH SH transition found in 3D viscoresistive nonlinear MHD codes (e.g. SpeCyl and NIMROD) by reducing the Hartmann number below a threshold value

During the transition, the secondary modes decrease and the dominant one first increases and then saturates, which is qualitatively similar to the experiment.

An agreement between simulations and experiment is possible ONLY IF the experimental viscosity is assumed to be strongly increasing with S: (Paolo, nota che è normale che P cresca con S!)

S=R/A; R= V/A; P=S/RH=(SR)1/2=S/(P)1/2

Simulations: bsecdH0.8=S0.4R0.4

Experiment: bsecdS-0.3

Assuming experimental bsecdH0.8 estimate for experimental R & P:RS-1.75; PS2.75.

Dominantm=1 mode

Secondarym=1 modes


Lundquist number scaling

The mode saturation amplitude should not depend on S, but the linear growth rate does (see D. Biskamp, Nonlinear magnetohydrodynamics, Cambridge Univ. Press, pag. 107)

Both predictions consistent with experiment


SH dynamo - edge

Dominant mode (1,-7)Magnetic field perturbation

b/B

(%)

S

Dominant mode (1,-7)Electric field perturbation

S

Eloop + < v 1,-7 b 1,-7 > = j ~ S-1 E1,-7 BB2

v 1,-7

Laminar helical flow


The SHAx occurrence allows an enlargement of the hot region to the other side of the chamber geometrical axis, thus inducing an increase of the plasma thermal content.

QSHi

SHAx

Dominant mode amplitude (%)

The

rmal

str

uctu

re w

idth

(m

)

MH

SHAx

QSHi

Te

(ev)

r (m)

QSHi = QSH with island


SHAx are more chaos-resilient

QSHiSHAx

Dominant mode only

All modes

More remnanthelical fluxsurfaces +broad region ofsticky magneticfield lines


Helical flux surfaces

We have a developed a relatively simple, yet effective, procedure to reconstruct the helical flux surfaces.

This involves starting with an axisymmetric equilibrium, and reconstructing the dominant mode eigenmode as a perturbation, using Newcomb’s equation supplemented with edge B measurements.

(r) given by

= m0 – nF0 + (mmn-nfmn)exp[i(m-n)]

- 0 and F0 poloidal and toroidal fluxes of the axisymmetric equilibrium

- mn and fmn poloidal and toroidal fluxes of the dominant mode

- and are the flux coordinates

B· = 0

The resulting helical flux function can be used as an effective radial coordinate.

Temperature and soft X-ray (and density) emissivity measurements can be mapped on the computed helical surfaces in order to validate the procedure.


Mapping of Te on helical flux function

• The profile is asymmetric with respect to the geometric axis, strong gradient regions (shaded) different on the two sides.

• The two half profiles collapse when plotted as a function of = (/0)1/2 (0=helical flux at the plasma boundary)


Mapping of line-integrated soft X-ray emissivity

• The X-ray emissivity measured by silicon photodiode along 78 lines of sight in 4 fans

• Measurements (red) are reconstructed using a simple three-parameter model of the form () = 0(1 - ) (black).

• Resulting emissivity plotted as a function of

• 2D emissivity map resulting from the reconstructions


Energy confinement time doubles

After the separatrix disappearance the energy confinement time doubles

assumingTe = Ti


The single helicity RFP

Spontaneous transitions to Quasi – Single Helicity observed in experiment

(m=1, n=-7)

q, s

afet

y fa

ctor

r/a

(1, -8)(1, -9)

(1, -10)

low amplitudem=1 secondary modes

Good confinement inside the remnant helical flux surfaces

P. Martin et al., PPCF 49, A177 (2007)

QSH, what comes next ?

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