ECE AND ECH APPLICATION FOR INVESTIGATION OF PLASMA SELF-ORGANIZATION

IN T-10 TOKAMAK

V.I. Poznyak, T.V. Gridina, V.V. Pitersky, G.N. Ploskirev, E.G. Ploskirev, O. Valencia

RRC “Kurchatov Institute”, IFT, Moscow, Russia

Plasma self-organization is put into effect only by accidentally emergent wave processes which possess by a fast far-ranging transport.

The best mechanism of the plasma self-organization is potential electron plasma waves. They are capable to carry an electron momentum to a long distance but do not leave the plasma volume. Those waves exist in any plasma, in any conditions. Their velocities are maximal among all kind of the potential waves. The wave transport of the electron momentum leads to alteration of the holding magnetic field structure.

The connection between micro and macro plasma parameters appears. Spontaneous wave generation is more active under an influence of the internal and external forces. This process, into frames of probability theory, is described in term of electron distribution function.

Goal is to investigate the regularity of electron distribution function dynamics and its connection with the internal self-optimizing structural peculiarities of the plasma system.

Main tool of analysis in this work is electron cyclotron emission of high energy electrons.

2

f, GHz40 50 7060

Trad, keV

0

4

8

12

Thermal ECEО-mode

80 100 120 140 f, GHz0

1

2

Trad, keV

Thermal ECEХ-mode

5

6

40

50

60

70

f, GHz

0

12

18

24

30

100 300 500 700 900

t, ms ECH

0

4

10

2

6

8

№36057

100300

500700

900

t, ms

100

120

140

160

f, GHz

80

Trad, keV

ECH

Trad, keV

EMISSION IN LOW FREQUENCY PARTS OF SPECTRA (P1-17)

Every discharges is accompanied by similar spectra. Necessary condition

for observation – density on LFS must be smaller than critical value

for low frequencies

NATURE OF LOW FREQUENCY ECE (P1-17)

600

001800

ce 22pece

22)2/(2/ pecece

1200pe

We can observe on 1st ECE resonance only O-mode ECE with k//v// < 0 from small area (2 – 3 сm) near equator on LFS.

Regime with increasing density

ECE spectrum does not depend on antenna position and polarization filter.

6

LFSHFS

00

)(LFSpe

Local resonance

zones

ωminωmax

MAIN DISCHARGE CHARACTERISTICS

B = 24.8 KGs, I = 250 kA,ne = 1.7·1013cm-3

On-axis 1 - 3 gyrotrons 140 GHz,Off-axis1 – 2 gyrotrons 129 GHz

The eigen frequencies of oscillations of m/n=1/1 mode in central plasma area - f11/1 ~ 6.3 kHz, f2

1/1 ~ 12.5 kHz, f2

1/1 ~ 23 kHz are discovered by disturbance velocity around torus. They coincide with eigen frequencies of plasma current oscillations in plasma periphery (by magnetic probes)

№36058

№36057

3

COMMON ANALISIS BY ECE IN 2nd X- AND 1st O-MODE (τ ~ 8-10)1 GYROTRON

140 ГГц.Phase shift40 – 45 μs

1 – Х-mode2 – О-mode3 – plasma oscillations

4

Te

Te

Te

Te

Variations of longitudinal velocity can be comparable with its average value for period of “saw” instead of continuous pumping of ECH energy to perpendicular degree of freedom (high electric

field into central area). Periodical kinetic instability takes place into central plasma area

2 gyrotrons 140 GHz, 1 gyrotron129 GHz

1 – 16 GHz

O-mode

X-mode

Periodical pumping-over of energy from longitudinal to perpendicular degree of freedom

Quasineutralitycondition

r)T(Tne4

TTD

ei2

ei

π

10-3 t, s

10-4

10-5

1010

109

V//, cm/s

10-1 100 101 102 103

W//, keV

Primary electron flows (> 1 MeV) relaxes by plasma waves. Consequence of relaxation is secondary flow (<W> ~ 200 keV). Amount of slow electrons increases fast. Avalanche-like ionization happens. Rotation transformation arises in the plasma center. Secondary beam ECE spectrum persists its form up to end of discharge.

Rotation transformation

Uloop, V

I, kA

ne, 1013cm-3

O-ЕСЕ, 43 GHz

O-ЕСЕ, 45 GHz

O-ЕСЕ, 50 GHz

O-ЕСЕ, 52 GHz

X-ЕСЕ, 134 GHz

X-ЕСЕ, 126 GHz

Dalfac

CIII

HXR

Gas

100 110 120 130

020

500

a.u

.

0.50

Contbk

Dbetlm

7

№36058

Probe

HF, 1-16 GHz

t, ms

20

0

0

0

0

0

0

0

0

0

0

0

0100 11

0120 t, ms

a.u. f, GHz

10

4

5

5

10

2

1

2

1

1

0.5

2

4

6

8

10

12

14

16

18

20

22

24

FORMING OF ECE SPECTRUMINITIAL STAGE OF DISCHARGE

j = en<v//>

0

1

2

Trad, keV

3

3

3

3

1

2.5

0

0

0

0

0

0

100 200 400 600 800 t, мс

GHz1

2

4

6

8

HF: 0.5 – 16 GHz

a.u.

3

t, мс

f, ГГц

500300

12

8

4

0100

Trad, кэВ

46

38

50

42

8

1

1

5

2

34

5

1211

ОН 1 – 5110 – 200 msafter 10 ms

ОН 1 – 12200 –310 msafter 10 ms

38 42 46 50 54 58 62 66 70 f, GHz

Trad, кэВ

0

4

0

8

4

2

6

2

1

2

ОН 1 – 5310 – 550 msafter 60 ms

ECH 1 – 6560 – 680 msafter 20 ms

1

6

ECH 1 – 5690 – 790 ms after 20 ms

ECH 1 – 4800 – 880 ms after 20 ms

15

14

1234-5

2

38 42 46 50 54 58 62 66 70 f, GHz

Trad, кэВ

0

0

0

0

2

2

2

4

2 3

4

5

6

In first stage position of spectral maximum ~45 GHz serves. Spectrum relaxation up to ~53 GHz (drop of energy) begins just before sawtooth process in plasma center. With ECH start, electrons brief accelerates. Spectrum serves its form during all discharge. New peculiarity – 56 GHz (under on-axis ECH).

Plasma current, кА

FEATURES OF PERIPHERAL ECEBACKGROUND OF O-ECE SPECTRUM.

0

250No direct correlation with loop voltage, plasma current,

electron density and temperature

PECULIARITIES OF PERIPHERAL ECE9

“Saw” Spikes№36055RELAXATION PART OF FIRST O-ECE

Frequency ~112 ГГц is multiple to frequency on first resonance ~56 GHz.Appearance of powerful O-ECE spikes in the boundary corresponds to phase of the hard internal disruptions. Oscillations of distribution function under ECH rise up to the limit energy.Strong spikes on 2nd harmonic happen only one-two period of saw after ECH start. All subsequent spikes have essentially lower amplitude as during so called “fan instability”.

№36057

Trad, keV

0

1

2

3

80 90 100 110 120 130 140 150 160 f, GHz

1 – 2 ОН

3 - 53 – 5ECH

3 Gyr. - 140 GHz

0

1

2

Trad, кэВ

80 90 100 110 120 130 140 150 160 f, GHz

1 - 2

3 - 4

1 – 2ECH 1 Gyr. - 140 GHz

3 – 4ECH 1 Gyr. - 129 GHz

BACKGROUND OF SECOND HARMONIC

10DYNAMICS OF HIGH ENERGY ELECTRON SPECTRUM

Strong longitudinal deformation of main part electron distribution in plasma center. Period of saw is two times shorter. Powerful spikes during every tooth of saw.

№ 36057

Ценральный ЭЦН

Нецентральный ЭЦН

Start of spike generation in plasma boundary only after hard disruptions

t, ms

1.1

Tra

d,

keV

0.95

t, ms

1.1

Tra

d, k

eV

0.95

1st harmonic

Start of saw after beginning of relaxation. m/n=1/1 oscillations before every disruption

It should to take into consideration the persistence of “screen” (life time of high energy electrons on q=3 is several periods of saw)

X-mode

Distribution function accomplishes strong periodical longitudinal oscillations near certain equilibrium position: compression in the time of current pinch and broadening with fast temperature rise by ECH. Total spectrum can be sum of local that emitting by several layers (here q=3 and 2). All dynamical changes in peripheral spectra fully correspond to changes in central plasma with mode m/n=1/1 and sawtooth oscillations.No dependence of spectrum on electron temperature and density.

23 24 25 260,15

0,18

0,21

0,24

0,27

0,30

B, kGs

Width of spectrum is proportional to value of magnetic field

lim

lim

ω

*ωω

Longitudinal electron energy oscillates: in thermal part ~Te, in superthermal part – no less then 20 keV - that is obvious consequence of periodical kinetic instability. Electric field which is necessary for electron acceleration during half of period frequency f1

mod: under action in all pass – 0.03 V/cm, under action in small part of trajectory – 0.3 V/cm. This can be only result of periodical relaxation of current. Frequencies of oscillations in central and peripheral plasma are identical but Emin >>> Uобх/ 2πR.

PULSATORY ELECTRIC FIELD

Periodical oscillations of electron energy in the column border is result of wave transport initiated by kinetic instability in central plasma area (mode m/n=1/1 and internal disruptions)

500 520 540

50 GHz

ОН

461 462 463 t, мс

48 GHz

134 GHz

5 1015 20 25

f11/1

f21/1

f41/1

ECE-ОН

f, kHz 5 10 15 20 25

Probe-ОН

f21/1

f11/1

№34429a.u..

a.u..

t, мс

5 10 15 20 25

f21/1

f41/1f1

1/1

Probe-ECHECH

42 GHz

595 600t, ms

42 GHz

580 600 620 640 t, ms

f1mod

f2mod

f, kHz2 104 6 8

ECE-ECH134 GHz

a.u.

a.u.

11

V.V. Parail, O.P. Pogutse. Problems of plasma theory, v. 11, p. 5. 1982. (Soviet plasma physics, 1976)

V.D. Shapiro, V.I. Shevchenko. JETP, v. 54, p. 1187, 1968

COMMENTARY12

constv)k

ω(v 22

////

constv

ωlowωlow~ωpi

ELECTRON DISTRIBUTION FUNCTION AND PLASMA WAVES

////2

cek vkβ1nωω n ≤ 0

Resonance conditions

Propagation under – ωk < ωpe

13

pe

cecrD ω

ωvvD EEvvC Dtecr

e

e3D T

nΛ4E πe

e

2e

pe m

en4ω

π

cm

eBω

ece

e

ete m

2Tv

p. 1087

C D

p. 1187 dv)vf(v2f

2D

2

v

B~E

E

B~vD D

14

Conductivity depends on parameters σ = σ(E, Ne, B, Te, Zeff)

А – “classical” conductivity under Erun/ED < 0.03. Observation of high energy electrons is impossible.

В – “runaway” regime under Erun/ED > 0.03. Amount of high energy electrons is than more than plasma density is lower.

С – «abnormal» dependence on electric field (positive feedback between electric field and plasma current), that is current disruption under critical electric field Ecr/ED ~ 0.1. Amount of high energy electrons decreases fast just before disruption.

PLASMA ELECTRIC CONDUCTIVITY

ωpe/ωce: 1 – 0.5, 2 – 0.7, 3 – 0.9

Eru

n/E

D

ELECTRON DISTRIBUTION FUNCTION IN ELECTRIC FIELD

Poznyak V.I. at al. // Proc. of 15th Intern. Conf. on Plasma Phys. and Contr. Nuclear Fusion Research // Seville, Spain,

1994. Nuclear Fusion. 1995. V. 2. p. 169. EC9, Borrego Springs, California, USA, 1995

ГE ~ exp (- ED / 4E) ~ nr

γw~ nГ

Гw ~ - exp γw ~

~ exp (exp(- ED / 4E))

1

lnf

- 5

E/ED

0.20

0.15

0.10

0.05

0

0-5 5 v//

ωpe/ωce= 0.9

fеvcrkC

kD

0 5 10 15 20 25 301

10

100

E,m

V/cm

Ecr

Erun

Uloop/2πR

№36057 ОН

r, cm

15

1

1

2

34

5

1211

ОН 1 – 5110 – 200 msafter 10 ms

ОН 1 – 12200 –310 msafter 10 ms

38 42 46 50 54 58 62 66 70 f, ГГц

Trad, кэВ

0

4

0

8

4

2

6

2

1

2

9

vD ~ B/Е1/2

FORMING OF ECE SPECTRUM

Long-range action of transport depends on angle of wave propagation. Only plasma waves which directions are almost perpendicular to magnetic field can reach plasma edge. Such wave exciting by interaction of electron with creates trapped electrons in plasma periphery. This assumption was checked by calculations (P2-15).

1/WW //

f, ГГц

On-axis ECH

CONCLUSION 1.Quasi-stationary spectrum of high energy electrons arises in first step of self-organization as result of relaxation of primary electron beam with energy much more than 1 MeV on plasma waves.

2.Spectrum preserves its shape during all discharge with short time deviations that demonstrates consistency of periphery electron distribution function. Spectrum does not depend on electron temperature and density but its width is proportional to magnetic field value. Such properties fully correspond to conception on stationary distribution function creating by potential plasma waves on abnormal Doppler resonance.

3.Many phenomena: pamping-over of energy from longitudinal degree of freedom to perpendicular that in central plasma area, relaxation of high energy part of distribution with ECE spike generation at periphery, motion of global disturbances around torus with velocities of current disturbances almost all discharge time and other - show to existence of periodical kinetic instability (m/n=1/1 mode) in central zone.

4.Discovered by ECE from plasma edge high energy electrons can not be consequence of acceleration in electric field at periphery but can be result of potential wave transport from central zone. In this case quasi-stationary electric field in plasma center exceed several times value Uloop/2πR. Probably the shape of distribution function tends to certain attractor which is determined by critical value of electric field Еcr ~ 0.1 ED in central zone.

16