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 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.

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

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

MAIN DISCHARGE CHARACTERISTICS 3 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)

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

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, 134 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.

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).

PECULIARITIES OF PERIPHERAL ECE 9 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. - 140 GHz Trad, кэВ 1 - 2 3 - 4 1 – 2 ECH 1 Gyr. - 140 GHz 3 – 4 ECH 1 Gyr. - 129 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”.

DYNAMICS OF HIGH ENERGY ELECTRON SPECTRUM 10 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

PULSATORY ELECTRIC FIELD 11 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)

ELECTRON DISTRIBUTION FUNCTION AND PLASMA WAVES 12 COMMENTARY ELECTRON DISTRIBUTION FUNCTION AND PLASMA WAVES ωlow ωlow~ωpi 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 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 p. 1087 C D p. 1187

ELECTRON DISTRIBUTION FUNCTION PLASMA ELECTRIC CONDUCTIVITY 14 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 -5 5 v// ωpe/ωce= 0.9 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 Erun/ED

FORMING OF ECE SPECTRUM Ecr Erun Uloop/2πR №36057 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 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.