Transcript f, GHz - DIFFER

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.
5
EMISSION IN LOW FREQUENCY PARTS OF SPECTRA
Trad, keV
№36057
Trad, keV
10
(P1-17)
8
2
6
f, GHz
4
160
2
1
140
0
100
120
300
500
700
0
900
80
80
t, ms
30
Thermal ECE
Х-mode
100
Trad, keV
12
Trad, keV
f, GHz
70
12
8
60
6
0
50
100
300
500
700
900
t, ms
120
140
f, GHz
Every discharges is accompanied by
similar spectra. Necessary condition
for observation – density on LFS
must be smaller than critical value
for low frequencies
24
18
100
Thermal ECE
О-mode
4
40
0
40
50
60
70 f, GHz
6
NATURE OF LOW FREQUENCY ECE (P1-17)
ECE spectrum does not depend on antenna position and polarization filter.
1200
   pe
600
  ce 2
2
   ce   pe
   pe (LFS )
2
  ce / 2  (ce / 2) 2   pe
1800
00
00
Local
resonance
zones
HFS
ωmax
LFS
ωmin
Regime with increasing density
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.
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)
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
X-mode
O-mode
Te
Te
Te
2 gyrotrons
140 GHz,
1 gyrotron
129 GHz
1 – 16 GHz
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
7
20
0
50
0
0.5
0
FORMING OF ECE SPECTRUM
Rotation transformation
3a.u. T , keV
rad
I, kA
f, GHz
20
X-ЕСЕ, 134
GHz
O-ЕСЕ, 43 GHz
O-ЕСЕ, 45 GHz
a.u.
O-ЕСЕ, 50 GHz
Contbk
Dalfac
0
CIII
Dbetlm
1
00
23
Gas
0
10
1
0
1
HXR
a.u.
GHz
1
2
3
4
Probe
120
6
10-5
6
8
0
130 t, ms 0 100
100
Ti Te
 r
2
4πne (Ti  Te )
D
8
1010
V//,
cm/s
12
14
j = en<v//>
109
W//, keV
10-1
100
101
102
103
Primary electron flows (> 1 MeV)
relaxes
by
plasma
waves.
Consequence of relaxation is
18
secondary flow (<W> ~ 200 keV).
Amount
of
slow
electrons
increases fast. Avalanche-like
20
ionization
happens.
Rotation
transformation
arises
in the
22
plasma center.
Secondary beam ECE spectrum
24
persists its form up to end of
HF: 0.5 – 16 GHz
t, ms discharge.
16
00
0.5
2.5
HF, 1-16 GHz
10-4
10
0
03
10
0
20
O-ЕСЕ, 52 GHz
110
0
50
03
5
t, Quasineutrality
s
condition
4
0
41
X-ЕСЕ, 126 GHz
10-3
2
02
10
ne, 1013cm-3
100
INITIAL STAGE OF DISCHARGE
№36058
Uloop, V
110
200
120
400
600
800
t, мс
8
FEATURES OF PERIPHERAL ECE
Trad, кэВ
BACKGROUND OF O-ECE SPECTRUM.
No direct correlation with loop voltage, plasma current,
electron density and temperature
12
250
8
0
f, ГГц
4
50
0
46
42
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).
38
Trad, кэВ
Trad, кэВ
4
5
ОН 1 – 5
110 – 200 ms
after 10 ms
2
0
8
6
4
2
46
50
54
0
2
58
62
1
ОН 1 – 5
310 – 550 ms
after 60 ms
3
1
ECH 1 – 6
560 – 680 ms
after 20 ms
2
4
2
0
11
12
42
2
6
1
2
0
38
2
ОН 1 – 12
200 –310 ms
after 10 ms
2
3
4-5
0
4
1
4
5
3
1
2
66
0
70 f, GHz 38
ECH 1 – 5
690 – 790 ms after 20 ms
1
5
ECH 1 – 4
800 – 880 ms after 20 ms
1
4
42
46
50
54
58
5
6
62
66
70 f, GHz
9
PECULIARITIES OF PERIPHERAL ECE
BACKGROUND OF SECOND HARMONIC
№3605
73 – 5
ECH
3 Gyr. - 140 GHz
Trad, keV
3
2
№36055
3-5
“Saw”
1
1 – 2 ОН
0
80
90
Trad, кэВ
100
110
120
1–2
ECH 1 Gyr. - 140 GHz
1
3–4
ECH 1 Gyr. - 129 GHz
0
80
90
100
110
130
140
150
160 f, GHz
1-2
2
RELAXATION PART OF FIRST O-ECE
3-4
120 130
140
150
160 f, GHz
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 onetwo period of saw after ECH start. All subsequent
spikes have essentially lower amplitude as during
so called “fan instability”.
Spikes
10
DYNAMICS OF HIGH ENERGY ELECTRON SPECTRUM
harmonic № 36057
Distribution function accomplishes strong periodical
Start of saw
1.1
longitudinal
oscillations
near certain equilibrium
after beginning
position:
compression in the time of current pinch and
of relaxation.
broadening with fast temperature rise by ECH.
m/n=1/1
oscillations
Total spectrum can be sum of local that emitting by
before
every
several
layers (here
0.95 q=3 and 2).
disruption
t, ms
All dynamical changes in peripheral spectra fully
Start
of spike to 1.1
correspond
changes in central plasma with mode
generation
in sawtooth oscillations.
m/n=1/1 and
plasma
No dependence of spectrum on electron
boundary only
temperature
and density.
after hard
Trad, keV
Trad, keV
1st
disruptions
0.95
t, ms
ω

ω
*
Strong
0,30 lim
longitudinal
It should to take into consideration the
0,27 ofω lim persistence of “screen” (life time of high energy
deformation
Ценральный
ЭЦН
Нецентральный
ЭЦН
electrons on q=3 is several periods of saw)
main part
0,24
electron
distribution in
0,21
X-mode
plasma center.
Period
of saw is
0,18
two times
shorter.
0,15
24
25
26B, kGs
Powerful spikes 23
during
every
Width
of spectrum is proportional to value of
tooth of saw.
magnetic field
11
PULSATORY ELECTRIC FIELD
a.u.. №34429
ECEОН
134 GHz
ОН
a.u..
48 GHz
50 GHz
f11/1
f11/1
ProbeОН
f21/1
f41/1
f21/1
500
540 t,
мс
520
a.u.
461
ECH
462
463 t, мс
ECEECH
134 GHz
a.u.
42 GHz
5 1015 20 25f, kHz 5 10 15 20 25
600
620
42 GHz
640 t, ms 595
ProbeECH
f2mod
f1mod
580
f21/1
t, ms 600
f11/1
f41/1
2 4 6 8 10 f, kHz 5 10 15 20 25
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
COMMENTARY
ELECTRON DISTRIBUTION FUNCTION AND PLASMA WAVES
V.D. Shapiro, V.I. Shevchenko. JETP, v. 54, p. 1187, 1968
V.V. Parail, O.P. Pogutse. Problems of plasma theory, v. 11,
p. 5. 1982. (Soviet plasma physics, 1976)
low~ωpi
ωωlow
Resonance conditions
ω k  nωce 1  β 2  k // v //
n≤0
Propagation under – ωk < ωpe
Interaction of electrons and waves on abnormal Doppler resonance leads to particles diffusion in
ω 2
(v

)  v 2  const
//
velocity space along lines
k //
For Cherenkov interaction – along lines v   const
13
p. 1087
f   2 f(v  )v  dv 
C
C  vcr  v te E D E
ω pe 
4πn e e
me
2
D
ωce
D  v D  v cr
ωpe
eB
ωce 
v te 
mec
2Te
me
p. 1187
n
E D  4πe3 Λ e
Te
B
D  vD ~
E
B2
E~ 2
vD
14
lnf
0
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
ωpe/ωce= 0.9
1
-5
-5
0
5
v//
E/ED
0.20
ГE ~ exp (- ED / 4E) ~ nr
0.15
γw~ nГ
0.10
Гw ~ - exp γw ~
0.05
~ exp (exp(- ED / 4E))
Erun/ED
PLASMA ELECTRIC CONDUCTIVITY
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.
ωpe/ωce: 1 – 0.5, 2 – 0.7, 3 – 0.9
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.
15
100
FORMING OF ECE SPECTRUM
kD
№36057 ОН
Erun
fе
vcr
E,mV/cm
kC
Ecr
10
Uloop/2πR
1
vD ~ B/Е1/2
Trad, кэВ
4
ОН 1 – 5
110 – 200 ms
after 10 ms
9
2
0
8
1
4
5
3
1
2
ОН 1 – 12
200 –310 ms
after 10 ms
6
2
0
10
15
20
25
30 r, cm
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 W /W//  1 creates
trapped electrons in plasma periphery. This
assumption was checked by calculations (P2-15).
4
On-axis ECH
1
11
12
2
0
38
5
42
46
50
54
58
62
66
70
f, ГГц
f, ГГц
16
CONCLUSION
1. Quasi-stationary spectrum of high energy electrons arises in first step of selforganization 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.