1

Anomalous phenomena Anomalous phenomena in ECRH in ECRH experiments at experiments at toroidaltoroidal devices and devices and

low threshold parametric decay low threshold parametric decay instabilitiesinstabilities

Gusakov E.Z., Popov A.Yu.

Ioffe Institute of RAS, SPb, Russia

17th Joint Workshop on Electron Cyclotron Emission and Electron Cyclotron Resonance Heating 07.05.2012

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• Common theoretical understanding of parametric decay instability role in ECRH experiments at toroidal machines

• Resent observations of anomalous phenomena at ECRH experiments in toroidal devices (non local electron transport, fast ion generation and induced backscattering phenomena)

• New theoretical approach – to look for conditions when at least one of the daughter waves is trapped in plasma and therefore its convective losses are suppressed

• Drastic decrease of the decay instability threshold in the presence of non-monotonic density profile and magnetic field inhomogeneity leading to Bernstein wave trapping across and parallel to the magnetic field

• Induced Backscattering convective PDI threshold at Textor• Anomalous reflection absolute instability threshold and growth rate • Anomalous absorption and absolute

instabilities threshold and growth rate• Possible PDI role in the energy budget• Conclusions.

OUTLINEOUTLINE

IBt t l

EB IBt l l UH UHt l l

3

The PDI thresholds in ECRH experiment The PDI thresholds in ECRH experiment

• Parametric decay instabilities (PDI) leading to anomalous reflection or

absorption of microwave power are believed to be deeply suppressed in

tokamak MW power level ECR O-mode and second harmonic X-mode heating

experiments utilizing gyrotrons. According to theoretical analysis of PDI

thresholds [1-3], the typical RF power at which these nonlinear effects can be

excited at tokamak plasma parameters is very high (around 1 GW for induced

backscattering), which is only possible with free electron laser application

planned in late 80th at MTX.

[1-3]: M. Porkolab et al. Nucl. Fusion 28 (1988) 239; B. Cohen et al. Rev. Mod. Phys. 63,

(1991) 949; A. Litvak et al. Phys. Fluids B 5, (1993) 4347

• The high PDI threshold is due to strong convective losses of daughter waves

from the decay region both along magnetic field and plasma inhomogenuity

direction.

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Convective losses along plasma Convective losses along plasma inhomogenuityinhomogenuitydirectiondirection

• Three-wave resonance (decay) conditions

• Interaction coherence length

• Spatial amplification coefficient

1

0 1 220

dx

d k x k x k xl

dx

0 0 1 1 2 2, , ,d d dk x k x k x

0 1 2

2

2

20 0

1

expv

lv

S

(A.D. Piliya 1971, M. Rosenbluth 1972)

PDI were only observed in 100 kW power range EBW heating experiments (M. Porkolab et al. @ Versator, 1983; M. Larionov et al. @ FT-1, 1986; G. Batanov @ L-2, 1989, H. Laqua et al. @ WVII-AS, 1997, V. Shevchenko et al.

MAST, 2006), where the backscattered and pump wave group velocity is reduced and the pump electric field is increased by the presence of the UHR thus decreasing the PDI power threshold

(E.Z. Gusakov et al. 2007 Plasma Phys. Control. Fusion 49, 631)

is the maximal PDI growth rate in homogeneous plasma, proportional to the pump wave amplitude0

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The parametric decay instabilities in ECRH experimentThe parametric decay instabilities in ECRH experiment

• Present day understanding – wave propagation and absorption

in O-mode and 2nd harmonic X-mode ECRH experiments where

no UHR exists is well described by linear theory and thus

predictable in detail. No anomalous reflection or absorption

are expected.

• However during the last decade a “critical mass” of observations

has been obtained evidencing presence of anomalous

phenomena in ECRH experiments at toroidal devices.

(a) Non local electron transport

was shown to accompany ECRH in some devices indicating that the RF power is not deposited in the regions predicted by standard theory, but is rather quickly redistributed all over the plasma.

Andreev V.F. et al. Plasma Phys. Control. Fusion. – 2004. – V.46. – P.319-335The ballistic jump of the total heat flux after ECRH switching on (observations on T-10)

(a) Non local electron transport

Strong nonlocal power redistribution in LHD ECRH

experiments just after pellet injection

K. Ida et al., Multiple states of electron heat transport inside an internal transport barrier in LHD, 3rd EFDA Transport Topical Group Meeting )

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(b) Ion acceleration accompanying ECRH experiments at TJ(b) Ion acceleration accompanying ECRH experiments at TJ--IIII

D Rapisarda, B Zurro, V Tribaldos, A Baciero and TJ-II team, Plasma Phys. Control. Fusion 49 (2007) 309–324

Conditions of 2Conditions of 2ndnd harmonic ECRH at TJharmonic ECRH at TJ--IIII

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Hollow profile typical for ECRH in TJ-II at low density

TJ-II magnetic configuration and 54 GHz 2nd harmonic ECRH scheme

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-0.2 0 0.2 0.4 0.6 0.8 1

ne(rho)(1150.0ms)-25326ne(rho)(1090.0ms)-25331ne(rho)(1074.0ms)-25333ne(rho)(1074.0ms)-25335

rN

e10

13cm

-3

(b) Ion acceleration accompanying ECRH (b) Ion acceleration accompanying ECRH experiments at TCVexperiments at TCV

Christian Schlatter Turbulent Ion Heating in TCV Tokamak Plasmas THÈSE NO 4479 (2009)

Conditions of 2Conditions of 2ndnd harmonic ECRH at TCVharmonic ECRH at TCV

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Hollow profile typical for 82.4 GHz ECRH in TCV at low densityTCV magnetic configuration

and 2nd harmonic ECRH scheme

0,85 0,90 0,95 1,00 1,05 1,10

1,00E+019

2,00E+019

n (m

-3)

R (m)

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(c) TEXTOR backscattering observations(c) TEXTOR backscattering observations

E. Westerhof et al. PRL 103, 125001 (2009)

Finally the first observations of the backscattering signal in the 200 – 600 kW 2nd harmonic ECRH experiment at TEXTOR tokamak were reported. This signal down shifted in frequency by approximately 1 GHz, which is close to the lower hybrid frequency under the TEXTOR conditions, was surprisingly strongly modulated in amplitude at the m=2 magnetic island frequency.

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(c) TEXTOR backscattering observations(c) TEXTOR backscattering observations

E. Westerhof et al. PRL 103, 125001 (2009)

This observations performed at the modest RF power under conditions when no UHR was possible for the pump wave provides an indication that probably a novel low threshold mechanism of the PDI excitation is associated with the presence of a magnetic island.

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• Backscattered wave - X-mode

• Low frequency wave – lower hybrid or high harmonic ion Bernstein wave

sv c

Ion Bernstein (IB) wave turning point

The candidates for the role of decay waves The candidates for the role of decay waves

si

i sk kk

2

2

20 0

1

expv

lv

S

Though the convective losses are Though the convective losses are supressedsupressed in a vicinity of in a vicinity of turning pointsturning points…….. Still high threshold of PDI (500 MW) at a

single turning point due to small size of decay region

t t l

2D IBW localization2D IBW localization

-0.35 -0.3 -0.25 -0.2 -0.152

2.2

2.4

2.6

2.8

3

3.2

3.4

3.6

3.8

4x 10

19

z, m

ne, m

-3

Shot 107128: q=2 island phases

x-bottomo-topo-bottomx-top

b

M. Yu. Kantor et al. 2009 Plasma Phys. Control. Fusion 51 055002

20 22 24 26 28 30 32

40

60

80

100

20 22 24 26 28 30 32

1

2

3

ki,xks,x qx

k i,xk

s,xq

x (c

m-1)

n

n (1

013

cm-3)

x (cm)

IBW localization In the radial direction due tolocal density maximum at O-point of the island

E.Z. Gusakov, A.Yu. Popov PRL105 (2010) 115003The polidal phase portrait qy(y) showing IBW poloidal localization

(Ray tracing procedure)

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• The ion Bernstein daughter wave equationThe coupled wave equationsThe coupled wave equations

3

, / 2 4

, , exp ;2 2 2

dr D r r r r r

r r r r dqD r r D q iq r r

D D

2 2 22 2

2 2 2

21 1 cotpe pe pi

ce ti ti ti ci

iD

D q q X Yq q

2exp tX iY dt

t io

(A.Piliya and A. Saveliev 1994 PPCF 36 2059)

The nonlinear charge density responsible for coupling of low and high frequency waves is provided by a

ponderomotive force2

2 2

14

iyi

spe

e

ys

ceyy

i

EE

x xE

xEe

m

22

2 2

2 2

2 2

4

4

ssx sy

pei

s

sye s ce

y

y iyn

k i

u

jx c

jm x

E

Eee

The high frequency daughter wave equation

17

22 2

0202 2 2

2 2 22 2

00

2 2 200

2s 4 ,in pe

xxx nx b

x yq D D b b x yxD q

y Lq x L

perturbations

In the vicinity of magnetic island O-point situated in the equatorial plane of the torus and coincident to the IB wave turning point the above system can be reduced to differential equation

Solution of the unperturbed equationSolution of the unperturbed equation……

2

0

2

0( , ) e2

x2

pkk l lyx x y

x x xb x y x H H xyy y

1 21/ 41/ 2 1/ 22 20 00 0

/ / / 2 ; sin / /x nx x x y b x peL q D q L q

1 22

0 0, 2 2

0 0 0

2 1 sin 2 12

pex xk l

x nx b

q qD D k lq L L

18

04 exp 0k l k l k l xx y D x y x y iq x dydx

……. & waveguide perturbation theory. & waveguide perturbation theory

243 2 2

02 2 2 2, exp exp ,

16

xpe ix

syi ce

aq y zb x y i ik y dx i K x x b x yH

2 3 2 2 2 2

2 3 2 2 2 2 2 200

1 2 34sin

z

x x x x x x

D q D D Diq q q

Dq x q q y

i

0 , ,x i x s xK q k k

dampingcorrection due to

decay instability for the IB waveguide

2 2 22 20 0 00 3 2 2 2

0 0

2 20 0

2 2 20 0

20

2 2

2 exp sec

2 ex 1 expp

pe pix

ce ti x ti x ti ci ci

p cici

m tit

ei ii

i

ti x ti x t ii

qq q

q q q

D

mq

The convective PDI threshold

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2 cot 1y zq 2

5/2 3/20 ,

2sin2

pe iz x x k l

i ce

aq qH

2

20,0 223 2

3 2 2 2

0

2 exp

2 3 1

x

yxx

x y x

K

D Dqq q

The imaginary q|| correction due to decay instability for the IBW cavity

The IBW gain coefficient &PDI power threshold

2 2 22

2 4 2 5 3, 0

12 2 1

i ceth

k l pe y x x

cHPl q

IBt t l

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The convective The convective PDI PDI powerpower thresholdthreshold in TEXTORin TEXTORTEXTOR experimental parameters

13 -319 kGs, 140 GHz, 3 10 cm ,

600 eV, 1 cmi

i

H f n

T

for the fundamental IB mode

45 kWthP

0

0,0

/ 2 0.92 GHz,

/ 2 10 MHz, 0.8 cm, 0.6 cmy x

Dependence of frequency corresponding to maximal IB wave gain on plasma density. (triangles-Ti=300eV,

circles- Ti=600eV, stars- Ti=900eV)

density variation in a magnetic island 0.1n n

a magnetic island width 3w cmDependence of the IB wave gain on the radial mode number at P = 400 kW,

Circles – n = 2·1013 cm-3, Stars - n = 3·1013 cm-3

exp , 1

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AbsoluteAbsolute PDI threshold for PDI threshold for toroidaltoroidal IBW cavity IBW cavity parametric excitationparametric excitation

20 0

PDIIB E

damtC

ph VP

V

APDI threshold in hollow density profile tokamak:

1

0

,IB ECx

D cD

damp

2

2PDI

pol

VV R

APDI threshold in homogeneous plasma:

20 0

thIB ECP

2 2 020 0 i

PP E

IBt t l

Threshold and growth rate of reflective absolute PDIThreshold and growth rate of reflective absolute PDI

For JET-like tokamak parameters

/ 2 1.35GHz 0 170f GHz

IBt t l

3 keVD eT T 14 -31 10 cmn

23 kGsH

22ndnd harmonic EBW trapping and harmonic EBW trapping and possibility of anomalous absorptionpossibility of anomalous absorption

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Radial trapping of EBW satisfying decay condition for the process

EB IBt l l

For the typical conditions of TCV ECRH experiments

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Radial and poloidal trapping of second harmonic EBW

22ndnd harmonic EBW trapping and harmonic EBW trapping and possibility of anomalous absorptionpossibility of anomalous absorption

For the typical conditions of TCV ECRH experiments

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Instability threshold and growth rateInstability threshold and growth rate

For the typical conditions of TCV ECRH experiments

350iT eV 3600eT eV0 / 2 82.4GHz 14200 ,H Gs13 32.2 10mn cm

/ 2 0.55I GHz 194 ,EBxq cm 177 ,IBxq cm

UH wave trapping by density maximum and UH wave trapping by density maximum and lowlow--threshold twothreshold two--plasmonplasmon decaydecay

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22 20

4pe ce UH UHt l l

Trapping of UH waves in radial direction in the vicinity of density maximum for

Textor magnetic island

2D localization of UH waves by the pump beam at high enough power corresponding

to absolute instability onset

Absolute PDI growth rate and threshold for two-UH-plasmon decay

The dependence of the growth rate on the pump wave power for Textor

magnetic island parameters.

0 0

1, 500 , 1 ,

/ 2, 0, 13, 160 .e y z

thy

s p T eV w w cm

q k l P kW

The dependence of the growth rate on the waist of the beam along the magnetic field.

0 600P kW

See A. Popov On possibility of low-threshold two-plasmon decay instability in second harmonic ECRH experiments at toroidal devices P1-01 at EC-17

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Possible role of PDI in energy balance in ECRH Possible role of PDI in energy balance in ECRH experimentsexperiments

D Rapisarda, B Zurro, V Tribaldos, A Baciero and TJ-II team, Plasma Phys. Control. Fusion 49 (2007) 309–324

Up to 38 kW absorbed by ions is needed at TJ-II to explain observed ion heating at ECRH power of 400 kW which is a lot because energy is

distributed in PDI proportionally to wave frequency

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Possible role of PDI in Possible role of PDI in non local electron transport

Nonlocal Transport Phenomena is observed when the electron density profile becomes hollow!

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• Drastic decrease of parametric decay instability power threshold is provided by non monotonous profile of plasma density, which is routinely observed at the discharge axis, in the vicinity of magnetic islands or blobs and at the plasma edge due to electron pump out effect or pellet injection.

• Acting in parallel with poloidal magnetic field inhomogeneity it makes possible localization of Bernstein decay waves and suppression of their convective losses. The typical backscattering convective parametric decay instability pump power threshold is estimated at the level of less than 100 kW.

• Based on the convective PDI the absolute decay instability can be excited for hollow density profile in tokamak.

• The non monotonous density profile can lead to trapping of decay EBWs as well, thus making possible the low-threshold anomalous absorption at ECRH

• Trapping of the UH waves at the non monotonous density profile leads to low-threshold excitation two-plasmon absolute decay instability

ConclusionsConclusions--11

UH UHt l l

EB IBt l l

IBt t l

IBt t l

31

• The low threshold anomalous absorption and reflection most likely play a role in anomalous backscattering at TEXTOR and ion acceleration and heating at TJ-II and TCV accompanying ECRH.

• The low threshold anomalous absorption and reflection can, in principle, lead to reduction of ECRH efficiency and quick change of its localization which is interpreted in terms of so called “non local electron transport effect” .

• The low threshold PDIs are potentially dangerous for ECRH in ITER therefore their excitation and consequences should be studied in the present day experiments.

• The physical reasons of density peaking in the magnetic island and electron-pump-out effect deserve systematic investigation as well.

ConclusionsConclusions--22

PDI and non local electron transportPDI and non local electron transport in ECRH in ECRH experimentsexperiments

Local maximum of the density profile

Threshold of the PDI decreases drastically

Excitation of the backscattered EC wave with downshifted frequency,which is then reflected from the wall and absorbed diffusively

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Power deposition profile of daughter EC waves differs from the one predicted by linear theory

Quasi-linear saturation of absolute PDI

,cit

1/3

0

0 0 04ct i

x x

h Bq q c

Strong stochastic damping of the IBW

C.F.F. Karney and A. Bers Phys. Rev. Lett. 39, 550 (1977)

Quasi-linear saturation of absolute PDI2 2

0 02 2 2

0 0

22

12 exppiQ

thth

Lti x ti x ti

Dq q

H

-Heaviside functionthH For JET-like parameters

When the PDI pumping exceeds the “perpendicular” Landau damping the quasi-linear saturation fails. Above this “second” threshold ion tails generation, spectral cascades and significant modification of power

deposition profile can occur.