EFFECT OF 3D FIELDS ON FLOWS

IN RFPs

L. Frassinetti, P. Brunsell, S. Menmuir, K.E.J. Olofsson and J.R. Drake

Association EURATOM-VR , School of Electrical Engineering, Royal Institute of Technology KTH, Stockholm

Experimental toolsExperimental tools:

- EXTRAP T2R - The feedback system - External magnetic perturbations

Plasma flow and Tearing Modes (TM) braking with - non-Resonant Magnetic Perturbations (non-RMP) (m=1, n=-10)(m=1, n=-10)

- Resonant Magnetic Perturbations (RMP) (m=1, n=-12)(m=1, n=-12) (m=1, n=-15)(m=1, n=-15)

TM dynamics on short time scale (0.1ms) with RMP and non-RMP

Modelling and viscosity profile estimation

0 0.5 1.0 1.5 2.0Te (keV)

100

75

50

25

0

flow

(km

/s)

RFX-modRFX-mod

EXTRAP T2REXTRAP T2RTM velocity 20-80 km/s

TM mainly wall locked

R/a=1.24m/0.183m Ip < 150kA tpulse≈ 0.1 s

-15

-12-13

-14

-16

(m=1 n<-12) are resonant

EXTRAP T2R safety factor

TM velocities: 4x64 local sensors for b

Plasma flow: Passive Doppler spectroscopy for OV, OIV, OIII, OII

-10-12

-15

shellshellshellshell≈≈13.8ms 13.8ms

(nominal)

active active coilscoils

sensor sensor coilscoils

The system is composed of:

- Sensor coilsSensor coils 4 poloidal x 32 toroidal located inside the shell

- Digital controller

- Active coilsActive coils 4 poloidal x 32 toroidal located outside the shell

0 10 20 30 40 50 60 70Time (ms)

1.0

0.8

0.6

0.4

0.2

0.0

br(

mT)

No Feedback

LCFS

(cm)

0 10 20 30 40 50 60 70Time (ms)

1.0

0.8

0.6

0.4

0.2

0.0

br(m

T)

Intelligent Shell

LCFS

(cm)

With the Intelligent Shell: - RWMs- RWMs - Error fields- Error fields are suppressedsuppressed

The LCFS is much smoother

It is useful to apply only a single external harmonic in order to have an easier interpretation of the results

0 10 20 30 40 50 60 70Time (ms)

1.0

0.8

0.6

0.4

0.2

0.0

br(m

T)

Measured spectrum at the plasma surface

Measured spectrum at t=25ms

(cm)

LCFSat t=25ms

0.15

0.10

0.05

0

-0.05

-0.10

-015

harmonic (1,-12)from 10ms to 30msamplitude 0.4mT

The feedback needs to: suppress error fields suppress RWMs apply the perturbation consider the plasma response to the external perturbation

The work done by the active coils is not obvious:

n

n

time (ms)

time (ms)

Measured br spectrum

Applied current spectrum

[Olofsson et al., Fus. Eng. Des. 2009][Olofsson et al., PPCF 2010][Frassinetti et al., IAEA 2010]

[Frassinetti et al., submitted to NF]

time (ms) 0 20 40 60

4

3

2

1

0

I 1,-

12 (

A)

br1,-12

I1,-12

time (ms) 0 20 40 60

phas

e (1

,-12

) br1,-12

I1,-12

flowTM velocity (1,-12) (1ms smoothed)

NO PERTURBATION

0 20 40 60 80time (ms)

60

40

20

0

velo

city

(km

/s)

br (

mT

)

1.0

0.8

0.6

0.4

0.2

0

flowTM velocity

60

40

20

0

velo

city

(km

/s)

br (

mT

)

1.0

0.8

0.6

0.4

0.2

0

0 20 40 60 time (ms)

WITH PERTURBATION (m,n)=(1,-12)

TMs rotate with velocities comparable to the flow

with the perturbation: - reduction of the TM velocity - reduction of the plasma flow

velocity profile (TM)

t=40mst=20ms

r/a

toro

ida

l vel

ocity

(km

/s)

(1,-15)

RMP (far from axis)

0.0 0.1 0.2 0.3 0.4 0.5 0.6r/a

0.10

0.05

0.00

q(r)

0.0 0.1 0.2 0.3 0.4 0.5 0.6r/a

v (

km/s

)

0

-5

-10

-15

-20

-25

RMP (far from axis)

(1,-15)

shot 22624

0.0 0.1 0.2 0.3 0.4 0.5 0.6r/a

v (

km/s

)

0

-5

-10

-15

-20

-25

0.10

0.05

0.00

q(r) (1,-12)

RMP (close to axis)

(1,-12)

Different RMP harmoniccDifferent RMP harmonicc produce different velocity brakingdifferent velocity braking

Maximum brakingMaximum braking located at the radius where theradius where the RMP harmonic is resonantRMP harmonic is resonant

RMP (close to axis)

0.0 0.1 0.2 0.3 0.4 0.5 0.6r/a

shot 22623

0.0 0.1 0.2 0.3 0.4 0.5 0.6r/a

v (

km/s

)

0

-5

-10

-15

-20

-25

(1,-10)

non-RMP

(1,-10)

non-RMP

shot 22668

0.10

0.05

0.00

q(r)

0.0 0.1 0.2 0.3 0.4 0.5 0.6r/a

n (harmonic of external perturbation)

v (

km/s

)MAX velocity variation

non-RMPRMP

Set of 13 shots with different harmonic of the perturbation n but same amplitude: br

n0.4mT

n (harmonic of external perturbation)

v (

km/s

)

TM velocity variation

non-RMPRMP

OV velocity variation

non-RMPRMP

n (harmonic of external perturbation)

v (

km/s

)

Set of 13 shots with different harmonic of the perturbation n but same amplitude: br

n0.4mT

flowTM velocity (1ms smoothed)ve

loci

ty (

km/s

)br

(m

T)

RMP

flowTM velocity (1ms smoothed)ve

loci

ty (

km/s

)br

(m

T)

non-RMP

0.1ms

TM velocity (not smoothed)

time (ms)

(mT

)(k

m/s

)

TM amplitude

With RMPRMP clear clear correlation correlation between velocity and TM amplitudevelocity and TM amplitude

0.1ms

[Frassinetti, NF 2010]

(mT

)(k

m/s

)

time (ms)

TM velocity (not smoothed)

TM amplitude

Island width: amplification and suppression Island velocity: acceleration and deceleration

depending of relative phase between TM and RMP

Static RMPStatic RMP

Rotating TMRotating TM

Island with RMP

LCFS(1,-12) island

0.1ms

• The island is not simplynot simply slowed downslowed down• It has strong strong velocity modulationsvelocity modulations

RMP n=-12RMP n=-12

n=-12 island

t=tt=t00

t=tt=t00+2µs +2µs t=tt=t00+4µs +4µs t=tt=t00+6µs+6µs

0.0 0.2 0.4 0.6r/a

TM

ve

loci

ty (

km/s

)

80

60

40

20

0

velo

city

(km

/s)

br (

mT

)

time (ms)

time (ms)

velo

city

(km

/s)

velocity variation

-10 -5 0 5 10 15 20time (s)

r/a

• The island is not simplynot simply slowed downslowed down• It has strong strong velocity modulationsvelocity modulations

RMP n=-12RMP n=-12

n=-12 island

t=tt=t00

t=tt=t00+2µs +2µs t=tt=t00+4µs +4µs t=tt=t00+6µs+6µs

0.0 0.2 0.4 0.6r/a

TM

ve

loci

ty (

km/s

)

80

60

40

20

0

RMP n=-15RMP n=-15n=

-15 island

t=tt=t00

t=tt=t00+2µs +2µs t=tt=t00+4µs +4µs t=tt=t00+6µs+6µs

0.0 0.2 0.4 0.6r/a

80

60

40

20

0TM

ve

loci

ty (

km/s

)

0.1ms

velo

city

(km

/s)

br (

mT

)

time (ms)

time (ms)

velo

city

(km

/s)

velocity variation

-10 -5 0 5 10 15 20time (s)

r/a

velocity variation

-5 0 5 10 15 20 25 30time (s)

• The island is not simplynot simply slowed downslowed down• It has strong strong velocity modulationsvelocity modulations

• The velocity perturbationperturbation is mainly located located at the island positionat the island position• But then it “spreads” to “spreads” to the surrounding plasmathe surrounding plasma

RMP n=-12RMP n=-12

n=-12 island

t=tt=t00

t=tt=t00+2µs +2µs t=tt=t00+4µs +4µs t=tt=t00+6µs+6µs

0.0 0.2 0.4 0.6r/a

TM

ve

loci

ty (

km/s

)

80

60

40

20

0

RMP n=-15RMP n=-15n=

-15 island

t=tt=t00

t=tt=t00+2µs +2µs t=tt=t00+4µs +4µs t=tt=t00+6µs+6µs

0.0 0.2 0.4 0.6r/a

80

60

40

20

0TM

ve

loci

ty (

km/s

)

[Frassinetti et al., IAEA 2010]

0.1ms

velo

city

(km

/s)

br (

mT

)

time (ms)

time (ms)

velo

city

(km

/s)

velocity profile with RMP n=-15

[Frassinetti et al., APS 2010]

SIMULATED DATA

time (µs)r/

a

,

3

1

4

m nEM

s

Tr r r

t r r r R r

Data are modelled using the torque balance equation. [Fitzpatrick et al. PoP 7, 3610 (2000)]

[Guo et al. PoP 9, 4685 (2002)]

Reasonable agreementReasonable agreementbetween modelled and

experimental data

velocity profile with RMP n=-15

EXPERIMENTAL DATA

time (µs)

r/a

,

3

1

4

m nEM

s

Tr r r

t r r r R r

exp. data

model

0( ) 1r cr

The viscosity profile is modelled using 3 free parameters

The free parameters are determined by comparing simulated and experimental velocity using a n=-15 RMP.

RMP n=-15

viscosity profile

10

-7 (

kg/m

∙s)

Viscosity is 1010-7-7kg/(mkg/(m∙∙s)s)

This corresponds to a momentum confinement time:

MM a a22 1ms 1ms

The observed plasma rotation braking is compared with simple empirical model:

[R.J. La Haye et al, PoP 9 (2002)2051]

- momentum confinement time

eff- effective frequency

Experimental data are well fitted with

3ms3ms and

eff = 4x106 s-1

2

0 2

1 reff

M

dV bV V V

dt B

br (

mT

)flo

w (

km/s

)

non-RMP (1,-10)

[Brunsell et al., EFDA MHD TG meeting 2010]

External magnetic perturbations produce plasma flow and TM brakingExternal magnetic perturbations produce plasma flow and TM braking

RMPs:RMPs: - The maximum braking is located in the position where the RMP is resonant - The island has phases with amplification-suppression and acceleration-deceleration - The estimated viscosity is approximately 10-7 kg/(m∙s) [M1ms]

Non-RMPsNon-RMPs

- The maximum braking is located in the core

- The estimated momentum confinement is M3ms

What happens if a RMP is applied to RFX-mod?

TMs are wall locked, do we still see a flow braking?

Do we see a transition in the flow braking from RMP to non-RMP?

TM velocity variation

n

v (

km/s

)

non-RMPRMP

?