ECE and ECH application for investigation of plasma self-organization at T-10 tokamak
EPJ Web of Conferences
ECE AND ECH APPLICATION FOR INVESTIGATION OF PLASMA SELF-ORGANIZATION AT T-10 TOKAMAK
0 V.I. Poznyak , T.V. Gridina, V.V. Pitersky, G.N. Ploskirev, E.G. Ploskirev , O. Valencia RRC “Kurchatov Institute” , IFT, 123182, Kurchtov Sq. 1, Moscow , Russia
A behaviour of the high energy electrons appointed by their ECE simultaneously on two first harmonics are used for the electron distribution function analysis. Experiments were fulfilled in Ohmic regime and with on-axis ECH. The explored spectrum of emission from the extreme column periphery comes into existence after a relaxation of the primary flow of electrons with energy more than 1 MeV on the plasma waves. Maximum energy of the generated electrons does not vary during all discharge time also as the spectrum shape of i ts emission. The form of spectrum does not depend on electron temperature and density but its character width is directly proportional to the value of magnetic field. The appointed connection of the dynamical features between the peripheral high energy ele ctrons and the periodical kinetic instability in the central plasma area (mode m/n=1/1) confirms an existence of the wave transport from the center to the plasma edge. The set of experimental data corresponds to the theory of the stationary electron distribution function formation by the potential plasma waves which apparently are the main mechanism of plasma self -organization in tokamak.
The plasma self-organization is put into effect only by the accidentally emergent wave
processes which possess by a fast far-ranging transport. The best mechanism of the plasma
selforganization is the 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 an y
plasma, in any conditions. Their velocities are maximal among all kind of the potential waves.
The wave transport of the electron momentum leads to an alteration of the holding magnetic
field structure. The connection between micro and macro plasma param eters appears. A
spontaneous wave generation is more active under an influence of the internal and external
forces. This process into frames of the probability theory is described by the electron
distribution function change.
The goal of this work 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 means of the analysis in this work is electron cyclotron emission of the
high energy electrons. Fig. 1 shows the full spectra into the ranges of 1 st and 2nd ECE
harmonics. Similar spectra of emission comprising the slow changing background component
and series of the short-time (10 – 30 μs) spikes of a high amplitude emission are obser ved in all
discharge types (magnetic field Bt = 23–26 kGs) under the condition that plasma density in its
external boundary (LFS) does not exceed the critical value for the ordinary waves with
frequencies 39–59 GHz. The high frequency parts of both spectra (60–77 and 119–175 GHz) are
the thermal plasma emission on 1st and 2nd resonance correspondingly. It was determine that the
low frequency parts of both spectra are ECE of the high energy electrons . The measuring
emission arises from the narrow in vertical direction (~5 cm) and along radius (~2 cm) plasma
area on LFS. The first harmonic emission was identified as ECE in ordinary polarization. Such
waves propagate only between the plasma cut-off line and chamber wall practically without
absorption. This is confirmed by that that ECE spectrum does not depend on positions of
antenna (LFS or HFS) and polarizer in antenna output.
2 Main discharge characteristics
We use on-axis ECH (140 GHz, power up to 1 MW) for a striking demonstration of the plasma
self-organization phenomena. Off-axis ECH (129 GHz, up to 0.8 MW) is applied in addition.
The discharge parameters are: magnetic field Bt(0)=25 kGs, average density ne=(1.5–2)1013cm-3,
plasma current Ip = 250 kA. In such conditions the emission zone is situated in the vicinity of
the magnetic surface q=3. ECH leads to essential amplification of the global plasma oscillations
in mode m/n=1/1 up to 50% of a slow changeable level (fig. 2 a) .
The amplitude disturbances of the signals in second ECE harmonic move along magnetic
force lines unevenly. The measuring velocities of the disturbance passage from LFS to HFS
determine the frequencies of circulation around the torus. The transit time 90 μs on fig. 2b is
equal here to the period of frequency ~11 kHz. Those frequencies are in good correspondence
with the frequencies of current oscillations which are measured by magnetic probes . Notably
they are the characteristics of the eigen plasma oscillations. Their values f11/1 ~6.2–6.5 kHz, f21/1
~10-12 kHz и f41/1 ~22-24 kHz are practically permanent during all discharge. Upper index
stands a number of harmonic, lower – mode structure.
The space structure of oscillations under their strong build -up is being more complicate
during on-axis ECH. New rational surface q*=1 springs up on radius r=4.5 cm that is equal to
half of the main surface q = 1 radius r = 8.7 cm . A motion of disturbances inside surface q*
=1 quickens defining the doubled frequency relative to frequency determined by driving surface
q=1 in the regime of the weak oscillation. A motion of the disturbances out the surface q*=1 on
part of their trajectory from HFS to LFS occurs twice slowly than in case of weak oscillations.
This effect determines frequency of oscillating process repetition f1mod ~3.6 kHz.
It was discovered by simultaneous ECE measurements in two polarizations from plasma
with high optical depth that energy in main part of distribution pum ps over from longitudinal
degree of freedom to transverse degree: fast in every period of global oscillations and relatively
slow in every period of sawtooth process. It means that the periodical kinetic instability takes
place . Strong oscillations both relaxation and background parts of O-ECE signals are
observed under high ECH power (fig. 3). Variations of the longitudinal velocity can be
comparable with its average value pending period of “saw”. An equality of O-ECE and X-ECE
signals just after every internal disruption shows to the establishment of the almost equilibrium
distribution function. Maximal deformation of distribution function happens in the first phase of
ECH. The diagram of the plasma noise signal (HF) in this time is similar to that of O-ECE that
corresponds to the driving role of the electron plasma waves in a creation of certain shape of
electron distribution function.
3 ECE spectra of peripheral high energy electrons
Fig. 4а shows the diagnostics data in the initial state of discharge: loop voltage, plasma
current, density, electron temperature, spectral lines, O -ECE signals, HF monitor and other. Any
signs of the discharge breakdown are absent during first 4 ms after the swi tching-on of the
vortex field (100 ms). Only some increase of the molecular (Cont) and atomic (Dalfa) lines
testifies a weak exposure of electric field to the main plasma. Electrons in the high electric field
(~30 mV/cm) reach to energy ~1 MeV per 1 ms passing fast the energy region ~100 eV when
they are able to ionized effectively the deuterium atoms. Their velocities approach to the speed
of light and creating them current is saturated. In the sequel energy of field expends only to the
increase of mass. However the considerable level of HF signal (here is limited by comparator) is
more two orders of value higher than that in quasi-stationary stage. This indicates the strong
plasma wave excitation. Really the spectral components 2 –8 GHz (fig 4b) can represent the
plasma wave dynamics. In the same time it is obvious that frequencies 10 –24 GHz are higher
than electron plasma frequency during first 4 ms. It means that those frequencies can be only
ECE of electrons with energy considerably more than 1 MeV. Any emission in this range
disappears when the powerful relaxation process stops. As result secondary flow of electrons
with energy no more than 200 keV is generated as the O -ECE signals show. Distribution
function of this electrons remains all discharge time and executes only short-time oscillations
relative certain position. The dynamics of the second flow O -ECE corresponds clear to the
plasma density growth. In this time the avalanche ionization happens and the rotation
transformation forms in the chamber center.
Рис. 4. #36058. Initial stage of discharge. (а) – Main plasma parameters. (b) – Spectral components of
Fig. 5 illustrates a dynamic of the background part of the first resonance O -mode
spectrum. In the first stage after breakdown, ECE intensity increases without any changes of a
spectrum form (fig. 5a). Amount of the high energy electrons grows with the conservation of
their distribution function. The beginning of spectrum relaxation precedes an appearance of
sawtooth oscillations in the central plasma zones (5b). The emission power decreases, the
spectral maximum shifts to the low frequencies that is energy of electrons diminishes. Such
scenario lasts ~100 ms. Then the spectrum goes back to the primary form. Without ECH, the
spectrum maintains its shape up to the end of discharge. The switching -on of the on-axis ECH
distorts spectrum to the low frequencies (fig. 5c, curve 1) during the electron temperature grows
phase. It means that a fall of Coulomb friction intensifies the accelerative process. Then the
spectrum is reinstated anew (curves 2–6). The central ECH is accompanied by new peculiarity
55–57 GHz. Its maximum accomplishes the strong pulsations with a frequency of the sawtooth
repetition. In this pulse the weak peculiarity arises in Ohmic stage. Fig. 5e shows spectrum after
one of three central gyrotron switching off. Fig. 5f – only one off-axis gyrotron operates.
Fig. 6 shows the changes of the second ECE harmonic spectrum in different discharge phases.
The level of ECE emission in the low frequency part of spectrum in Ohmic phase is many times
lower than in thermal frequency range. Only small ascending grade is observed near the low
frequency boundary. Under the powerful central ECH switching-on, ECE intensity in this range is
being comparable with the maximal level of emission in the thermal range. Similar effect
corresponds to the growth of the perpendicular electron energy near the energy spectrum boundary
owing to the turn of electron velocity under interactions with waves on the abnormal Doppler
resonance. The peculiarity on frequencies 110–115 GHz, which are multiple to the frequencies on
first resonance, appears in addition. This phenomenon was discovered also on others installations,
particularly ASDEX . A reduction of on-axis ECH power decreases the amplitude of this
maximum up to its disappearance as in this pulse (fig 6b, curves 1–2). Off-axis ECH does not create
Fig. 6. #36057. Second harmonic ECE spectrum. (а) - 1 and 2 – Ohmic stage; 3–5 – three on-axis gyrotrons and
one off-axis. (b) - 1 and 2 – two on-axis and one off-axis gyrotrons; 3 and 4 – only off-axis gyrotron.
A generation of spikes happens also by certain lows. The first spikes appear in the phase of a
spectrum restoration (fig. 5c) only after internal disruptions. The current frequencies decrease (fig.
7a) that corresponds to the growth of energy in a relaxation range. ECE amplitudes increase
considerably with the ECH start. They can fill almost all period of “saw”. On the second ECE
harmonic, splashes of the high amplitude happen only just after ECH start.
Fig. 7b represents a full dynamics of O-ECE spectrum background during discharge. In the
first phase, spectrum preserves its form, than the frequency of maximum reduces during ~50 ms and
returns to the initial position after ~100 ms. A reduction of Coulomb friction after ECH switch-on
leads to the short-time intensification of the accelerating process (a decrease of spectrum
frequencies). Similar effect is observed in this time in main part of distribution in the central plasma
area (fig. 3a). The spectral peculiarity 55–56 GHz does not change also. It was discovered earlier
that rational magnetic surfaces possess the property to accumulate electrons with the high
longitudinal energy . The position of the zone emitting main maximum of O-mode ECE is in good
correlation with the position of surface q=3 (28 cm). We assume that emission with frequencies 55–
56 GHz is provided by electrons which are on the surface q=2. A great number of factors show to
that that the peripheral electron population is a consequence of the wave transport from the central
area. Those are the different correlations with sawtooth process, equality of frequencies both
splashes appearance and global oscillations in mode m/n=1/1 and others. O-ECE signals contain also
the modulating component with a frequency of sawtooth repetition. Oscillations into the ranges 50–
52 and 53–55 GHz have the opposite phase that shows to a swing of electron energy spectrum. The
longitudinal energy oscillations in central area have just that character (fig. 3b). Taking into account
integration with time constant 25–30 ms (life-time of the high energy electrons) several times more
than saw period, we will observe simultaneously two smoothed spectral maxima. Consequently this
spectral dynamics is similar to the splitting of spectral line that the dotted arrow illustrates on fig 7b.
It is important to emphasize that the spectrum form does not depend on electron temperature and
density. The width of spectrum (from the cyclotron frequency on the plasma boundary to the
frequency of maximum) is in direct proportion to the value of magnetic field.
In plasma with electric field, the stationary electron distribution function is established by the
action of electron plasma waves as it was shown in a whole number of theoretical works, for
example [7, 8]. A plateau with boundary conditions vc < v// < vD (look at fig. 8) and small
longitudinal velocity (v//) derivative is formed if ωpe / ωce < 1 (ωpe and ωce correspondingly electron
plasma and cyclotron frequencies). Oscillations exciting on Cherenkov resonance and spreading in
small angles relative to magnetic field direction play the constitutive role here. vc is the critical
velocity when the electric force is equal to the Coulomb friction force. In the area v// > vD, waves
exciting on the abnormal Doppler resonance are driving force. Upper boundary of plateau vD does
not depend on electron temperature and density but has the functional dependence on magnetic and
longitudinal electric field vD ~ B / E Fig. 8 illustrates a change of distribution function by a
growth both temperature and density (the current ramp up phase) in the constant operating
electric field. It can confront the change of maximum position in O -ECE spectrum that is
proportional to magnetic field with the introduced dependence for vD taking into account that
ECE power connects linearly with the longitudinal energy. We think that the current pinch velocity
increases in the last stage of the current penetration to the central plasma area enhancing the electric
field and shortening the electron distribution tail (reduction of vD value) that ECE measurements
show as relaxation.
Fig. 8. Schematic illustration of distribution function
change with temperature and density grows after
breakdown for constant operating electric field Е.
Fig. 9. Dependence of plasma electric
conductivity on electric field for different
relations ωpe / ωce: 1 – 0.5, 2 – 0.7, 3 – 0.9.
If we know a shape of distribution function we can obtain the dependence of plasma
electric conductivity on electric field (fig. 9) . It can separate out three character areas in this
dependence. In area A with E<Erun, the conductivity corresponds to the Spitzer formula. The
flow of high energy electrons is negligible and their life -time is enough small. Therefore their
emission cannot be measured by ECE diagnostics. Area B corresponds to so-called runway
regime. The superthermal emission is registered the easier than value ωpe/ωce lower. In area С
with E>Ecr ~0.1ED, current and electric field are connected by the positive feedback that is the reason
of the observing kinetic instability in central plasma region when the fast irreversible compression of
electron distribution and correspondingly current decay happen. It should to understand that
realization of instability is possible only in uniform plasma which we have in experiment.
Fig. 10. – #36057. Creation of high
energy periphery electron population.
Fig. 11. #36058. Plasma waves spectral dynamics. 1 – OH
stage. Later – with on-axis ECH. 2 – in stable stage of
sawtooth; 3 – before, 4 – just in and 5 – after disruption.
Fig. 8 shows an interval of the electric field values (with taking into account of the real
temperature and density distributions) when considerable amount of electrons can be accelerated to
high energies. The rectangle on the graph captures the range of the necessary fields (in vertical
direction) in the space area (in horizontal direction). It is obvious that the direct acceleration of
electrons at the plasma edge by electric field cannot provide sufficient level of ECE. But such
process is possible into central plasma zone under the condition that real electric field is 2–6 time
higher than value Uloop/2πR (as the curved arrow shows). Thus an appearance of the high energy
electrons at the edge of plasma column is a result of wave transport from the plasma center (dotted
arrow). The formation of the second maximum in ECE spectra is apparently conditioned be similar
processes into zone inside the surface q*=1 which appears under a strong build-up of the global
oscillations in m/n=1/1 mode.
Extraction of distribution function of the high energy electrons in the plasma periphery 
shows that they are strongly trapped (and ripple trapped). Their perpendicular energy is ten times
more at the average than the longitudinal one. This is in compliance with measured spectrum of
plasma oscillations (fig. 11). Plasma oscillation spectrum has the bell like form which is provided
mainly by q=2 wave excitation. Such spectrum collapses fully under disruption according to q=2
surface. The alteration of plasma state during sawtooth process is accompanied by a change of
plasma oscillation spectrum only in the narrow frequency band less than 7–8 GHz (curves 3 and 4,
above bell like spectrum by q=2). Upper boundary of 1st high frequency oscillation mode (by q=1) is
~42 GHz (according density on radius q=1, see ). Only waves with low frequencies can reach the
plasma edge. They propagation angles can be evaluated according to expression ω ~ ωpecosΘ, where
Θ is angle between magnetic field direction and wave vector k. As far as for potential waves k||v,
only almost transverse waves provided by interactions of trapped electrons inside q=1 surface can
reproduce them at the plasma edge. Oblique waves cannot reach peripheral area by plasma cut-off
and absorb along plasma radius against density profile. A growth of energy storage inside of q=2
surface after internal disruption leads to the strengthening of wave excitation by q=2 surface
(boundary frequency ~ 18 GHz). This secondary process can determine the growth of high frequency
part of the measured spectrum (higher 8 GHz) and can provide more weak trapped electrons.
Hereby experiments on T-10 show that spectrum of the peripheral electrons preserves its
shape during all discharge. Only short-time deviations of frequency: upwards (reduction of electron
energy) with completion of current profile establishment and downwards (growth of electrons
energy) with the fast growth of electron temperature after start of on-axis ECH - happen. The
spectrum form does not depend on electron temperature and density but its width is in direct
proportion to magnetic field. Great number of dynamic characteristics of spectra shows to that the
appearance of the high energy electrons on the plasma periphery becomes formed by the wave
transport from the central plasma area. The consistency of the measured spectrum and its
dependence on magnetic field shows that the reason of the stationary shape of spectrum is the
potential plasma waves exciting on abnormal Doppler resonance. The observing during all discharge
kinetic instability (mode m/n=1/1 including internal disruptions) as we assume is the consequence of
the periodical nonlinear current pinch creating the critical value of electric field.
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