1. 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

2. 2
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.

3. EMISSION IN LOW FREQUENCY PARTS OF SPECTRA (P1-17)5
EMISSION IN LOW FREQUENCY PARTS OF SPECTRA (P1-17) 80
100
120
140
f, GHz 1 2
Trad, keV
Thermal ECE
Х-mode 4 10 2 6 8
№36057
100
300
500
700
900
t, ms
120
140
160
f, GHz 80
Trad, keV
ECH
f, GHz 40 50 70 60
Trad, keV 4 8 12
Thermal ECE
О-mode
Every discharges is accompanied by similar spectra. Necessary condition for observation – density on LFS must be smaller than critical value for low frequencies 6 40 50 60 70
f, GHz 12 18 24 30
100
300
500
700
900
t, ms
ECH

4. NATURE OF LOW FREQUENCY ECE (P1-17)6
NATURE OF LOW FREQUENCY ECE (P1-17)
ECE spectrum does not depend on antenna position and polarization filter.
LFS
HFS 00
Local resonance zones
ωmin
ωmax
600 00
1800
1200
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

5. MAIN DISCHARGE CHARACTERISTICS3
MAIN DISCHARGE CHARACTERISTICS
№36058
B = 24.8 KGs, I = 250 kA,
ne = 1.7·1013cm-3
On-axis
1 - 3 gyrotrons 140 GHz,
Off-axis
1 – 2 gyrotrons 129 GHz
№36057
The eigen frequencies of oscillations of m/n=1/1 mode in central plasma area - f11/1 ~ 6.3 kHz, f21/1 ~ 12.5 kHz, f21/1 ~ 23 kHz are discovered by disturbance velocity around torus. They coincide with eigen frequencies of plasma current oscillations in plasma periphery (by magnetic probes)

6. COMMON ANALISIS BY ECE IN 2nd X- AND 1st O-MODE (τ ~ 8-10)4
COMMON ANALISIS BY ECE IN 2nd X- AND 1st O-MODE (τ ~ 8-10)
1 GYROTRON
140 ГГц.
Phase shift
40 – 45 μs
1 – Х-mode
2 – О-mode
3 – plasma oscillations
Periodical pumping-over of energy from longitudinal to perpendicular degree of freedom 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 gyrotron
129 GHz
1 – 16 GHz
O-mode
X-mode

7. FORMING OF ECE SPECTRUM INITIAL STAGE OF DISCHARGE
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, GHz
X-ЕСЕ, 126 GHz
Dalfac
CIII
HXR
Gas
100
110
120
130 20 50
a.u.
0.5
Contbk
Dbetlm 7
№36058
Probe
HF, 1-16 GHz
t, ms
Rotation transformation
FORMING OF ECE SPECTRUM
INITIAL STAGE OF DISCHARGE 1 2
Trad, keV 3
2.5
100
200
400
600
800
t, мс
GHz 4 6 8
HF: 0.5 – 16 GHz
a.u. 20
100
110
120
t, ms
a.u.
f, GHz 10 4 5 2 1
0.5 6 8 12 14 16 18 22 24
10-3
t, s
10-4
10-5
1010
109
V//, cm/s
10-1
100
101
102
103
W//, keV
Quasineutrality
condition
j = en<v//>
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.

8. FEATURES OF PERIPHERAL ECE BACKGROUND OF O-ECE SPECTRUM.8
FEATURES OF PERIPHERAL ECE
BACKGROUND OF O-ECE SPECTRUM.
t, мс
f, ГГц
500
300 12 8 4
100
Trad, кэВ 46 38 50 42
Plasma
current, кА
No direct correlation with loop voltage, plasma current, electron density and temperature
250 1 5 2 3 4 12 11
ОН 1 – 5
110 – 200 ms
after 10 ms
ОН 1 – 12
200 –310 ms 38 42 46 50 54 58 62 66 70
f, GHz
Trad, кэВ 8 6
310 – 550 ms
after 60 ms
ECH 1 – 6
560 – 680 ms
after 20 ms
ECH 1 – 5
690 – 790 ms after 20 ms
ECH 1 – 4
800 – 880 ms after 20 ms
4-5
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).

9. PECULIARITIES OF PERIPHERAL ECE9
PECULIARITIES OF PERIPHERAL ECE
“Saw”
Spikes
№36055
RELAXATION PART OF FIRST O-ECE
№36057
Trad, keV 1 2 3 80 90
100
110
120
130
140
150
160
f, GHz
1 – 2 ОН
3 - 5
3 – 5
ECH
3 Gyr GHz
Trad, кэВ
1 - 2
3 - 4
1 – 2
ECH 1 Gyr GHz
3 – 4
ECH 1 Gyr GHz
BACKGROUND OF SECOND HARMONIC
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”.

10. DYNAMICS OF HIGH ENERGY ELECTRON SPECTRUM10
DYNAMICS OF HIGH ENERGY ELECTRON SPECTRUM
1st harmonic
№ 36057
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.
Start of saw after beginning of relaxation. m/n=1/1 oscillations before every disruption
t, ms
1.1
Trad, keV
0.95
Start of spike generation in plasma boundary only after hard disruptions
t, ms
1.1
Trad, keV
0.95
B, kGs
Width of spectrum is proportional to value of magnetic field
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.
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
Ценральный
ЭЦН
Нецентральный

11. PULSATORY ELECTRIC FIELD11
PULSATORY ELECTRIC FIELD
500
520
540
50 GHz ОН
461
462
463
t, мс
48 GHz
134 GHz 5 10 15 20 25
f11/1
f21/1
f41/1
ECE-ОН
f, kHz
Probe-ОН
№34429
a.u..
t, мс 5 10 15 20 25
f21/1
f41/1
f11/1
Probe-ECH
ECH
42 GHz
595
600
t, ms
580
620
640
f1mod
f2mod
f, kHz 2 4 6 8
ECE-ECH
134 GHz
a.u.
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 f1mod: 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.
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)

12. ELECTRON DISTRIBUTION FUNCTION AND PLASMA WAVES12
COMMENTARY
ELECTRON DISTRIBUTION FUNCTION AND PLASMA WAVES
ωlow
ωlow~ωpi
V.V. Parail, O.P. Pogutse. Problems of plasma theory, v. 11, p (Soviet plasma physics, 1976)
V.D. Shapiro, V.I. Shevchenko. JETP, v. 54, p. 1187, 1968
n ≤ 0
Resonance conditions
Propagation under – ωk < ωpe
Interaction of electrons and waves on abnormal Doppler resonance leads to particles diffusion in velocity space along lines
For Cherenkov interaction – along lines

13. 13
p. 1087 C D
p. 1187

14. ELECTRON DISTRIBUTION FUNCTION PLASMA ELECTRIC CONDUCTIVITY14
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, Nuclear Fusion 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 -5 5
v//
ωpe/ωce= 0.9
Conductivity depends on parameters
σ = σ(E, Ne, B, Te, Zeff)
А – “classical” conductivity under Erun/ED < Observation of high energy electrons is impossible.
В – “runaway” regime under Erun/ED > 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
Erun/ED

15. FORMING OF ECE SPECTRUM
Ecr
Erun
Uloop/2πR
№ ОН
r, cm 15
FORMING OF ECE SPECTRUM fе
vcr kC kD
vD ~ B/Е1/2
Trad, кэВ 1
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). 4 9
ОН 1 – 5
110 – 200 ms
after 10 ms 2 1 4 2 8 3 5
ОН 1 – 12
200 –310 ms
after 10 ms 6 2 4
On-axis ECH 1 11 12 2
f, ГГц 38 42 46 50 54 58 62 66 70
f, ГГц

16. 16
CONCLUSION
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.
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.
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.
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.