Transcript Слайд 1 - Novosibirsk

8th International Conference on Open Magnetic Systems for Plasma Confinement
Study of microinstabilities in anisotropic plasmoid
of thermonuclear ions
Mariya Korzhavina
Budker Institute of Nuclear Physics, Novosibirsk, Russia
View of the Gas Dynamic Trap facility
General layout of gas dynamic trap
(GDT)
Length
Magnetic field: center
mirror
Mirror ratio
Bm/Bc
7m
0.3 Т
up to 12 Т
≈ 35
Target plasma:
1013-1014 cm-3, 150 eV
Fast ions (H+,D+):
~1013 cm-3, <E>≈10 keV
Experiment with compact mirror cell at
the Gas Dynamic Trap
Compact mirror at GDT
Experiment:
2ρfi << aw; nf / nw>>1;
β <<1;
E>>E||.
Compact
Compact
mirror
mirrorcell
cell
Compact mirror cell (CM):
L = 30 cm, D = 70 cm.
Magnetic field:
B0 = 2.4 T, Bm = 5.2 T
GDT central
cell
Background plasma:
hydrogen, nw ≈ 1013 cm-3,
Tw ≈ 150 eV, aw = 9 cm.
CM NBI system:
hydrogen, E0 = 20 keV, θ = 90º,
Pinj ≈ 1 MW, τinj= 4 ms,
af = 8-10 cm.
Strong high-frequency oscillations of
plasma potential during accumulation
of the fast ions in the compact mirror
Early studies of microinstabilities
M.S.Ioffe, B.B.Kadomcev, Uspekhi Fizicheskih Nauk, vol. 100,
№ 4, 1970
R.F.Post, Nuclear fusion, Vol.27, 1987
F.H.Coensgen, et al. Phys.Rev.Letters, Vol.35, 1975, [2XIIB]
T.A.Casper, G.R.Smith, Phys.Rev.Letters, Vol.45, 1982, [TMX]
M. Ichimura, et al. Phys.Rev.Letters, Vol.70, 1993, [Gamma-10]
Microinstabilities in anisotropic plasma
DCLC
The drift-cyclotron
losscone instability
k║ « k┴
k|| = 0
ω ≈ ωci
AIC
The Alfven ioncyclotron instability
k║ » k┴
k┴ = 0
ω < ωci
Estimation of developing DCLC and AIC
in the compact mirror of GDT
DCLC
Stabilization by addition
of small amount of
warm ions:
nw /nf > 0.06
GDT CM:
nw /nf ≈ 0.1
AIC
Instability grows if:
β┴A > const
GDT CM:
A ≡ <E┴>/<E║> ≈ 50,
β┴ ≈ 0.02
βA ≈ 1
R.F.Post, Nuclear fusion, Vol.27, 1987
M.J.Gerver, The Phys. of Fluids, Vol.19,1976
D.C.Watson, Phys.Fluids 23,1980
High-frequency oscillations in plasmoid have been
observed with special HF Langmuir and magnetic probes
10 mm
Set of special HF Langmuir
probes
Tree orthogonal loops of the
HF magnetic probe.
Layout of the HF Langmuir probes system in the
compact mirror of GDT
Modes:
k = m/rp
rp = 4.5 cm
m ≈ 1-6
HF magnetic probe
Cross amplitude spectrum
fosc
fci
Oscillation frequency:
fosc = 39.7 ± 0.2 MHz
Bmidplane = 27.6 ± 0.3 kGs
fci = 42 ± 0.5 MHz
f osc  f ci (1  E|| / E )
Voltage oscillations induced in loops of magnetic probe
Br  B
Bz  Br , B
Rotation of the wave magnetic field vector
Rotation in the direction of ion gyration
Mode structure analysis, azimuthal modes
Phase, rad...
0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
-0,1
19221
-0,3
19222
-0,5
19223
-0,7
19224
-0,9
19225
-1,1
19228
19231
-1,3
m=-1
-1,5
19226
-1,7
19235
-1,9
19236
-2,1
19239
-2,3
m=-2
-2,5
193xx
-2,7
19304
-2,9
19233
-3,1
Angle, rad
Azimuthal mode m = 1 , rarely 2.
Observation of AIC in the compact mirror of the GDT
RF Langmuir probes : frequency, azimuthal modes
Azimuthal vs radial induced loop voltages. The
field vector rotates in the direction of ion gyration.
Magnetic probes: polarization
Частотный
Cross amplitude
спектр колебаний
spectrum
f0f
0
fci
Фаза
колебаний,
radian
variation,радиан
Phase
0
-0,1
-0,3
-0,5
-0,7
-0,9
-1,1
-1,3
-1,5
-1,7
-1,9
-2,1
-2,3
-2,5
-2,7
-2,9
-3,1
0,4
fci
0,8
1,2
1,6
m=1
Azimuthal number m ~ 12
m=2
Main frequency f0 < fci
Азимутальный
между
зондами в radian
радианах
Azimuthalугол
probe
separation,
The magnetic field vector
of the wave rotates in the
direction of ion gyration.
AIC
Threshold of the oscillations
Diamagnetism of fast
ions in the compact
mirror
Amplitude of HF
oscillations induced
on magnetic probe
Anisotropy of the ion
plasmoid
n >3 х 1013 сm-3
A ≈ 40; β┴ = 0.02 => ┴A ~ 1.
сi/аp ≈ 0.23
Results:
• Microinstability developing in the compact mirror is Alfven ioncyclotron (AIC). This was proved by observing small azimuthal
modes numbers m = 1–2, oscillation frequency below the
diamagnetically depressed ion-cyclotron frequency and rotation of the
magnetic field of the wave in the direction of ion gyration.
• The threshold of the AIC fluctuation was determined relative to the
density of hot ions, ratio of ion pressure to magnetic field pressure β,
anisotropy A and the ion gyroradius to the plasmoid radius ratio ai/Rp.
AIC microinstability developed when the density of hot ions nf was
greater than 3x1013 cm-3, β ≈ 0.02, anisotropy A ≈ 50, for the ratio
ai/Rp of about 0.23.
• Experimentally was confirmed the criteria which defines the stability
region A < 1.
• Alfven ion cyclotron instability developing in the CM GDT does not
lead to the significant particle loss and plasma parameters limitation.
Thank you!
Dependence of fast ion density in the compact mirror
of GDT on the trapped power
Dots – experimental data, solid line – calculation (ITCS).
Регистрация AIC на TMX
Электрические зонды: частота и модовый состав
Магнитные зонды: поляризация
|m| ≈ 4
f0 < fci
Вращение магнитного поля
волны в направлении
ларморовского движения ионов
AIC
T.A.Casper, G.R.Smith, Phys.Rev.Letters , Vol.45, 1982
Анализ модового состава, продольные моды
DCLC: набег фазы между средним зондом в КП и зондом в расширителе,
силовая линия 15.5 cm – от выстрела к выстрелу случайный
DCLC нет
Оценки для DCLC мод в КП ГДЛ
Параметры ГДЛ:
c / Rpωci ≈ 18 ;
ω2ci / ω2pi ≈ 6.4•10-4
Стабилизация теплыми
ионами:
nw /nf > 0.06
ГДЛ: nw /nf ≈ 0.1
R.F.Post, Nuclear fusion, Vol.27, 1987
M.J.Gerver, The Phys. of Fluids, Vol.19,1976
Оценки для AIC мод в КП
Критерий развития неустойчивости:
Параметры
ГДЛ:
β║ < β┴ ~ 0.02
При β║ ~ β┴ « 1
β║ < const * β┴2
или
(β║ , β┴) → (A , β┴) :
β┴A > const
ГДЛ: A ≡ <W┴>/<W║> = 50,
β = 0.02
βA ≈ 1
T.A.Casper, G.R.Smith,
Phys.Rev.Letters , Vol.45, 1982
βA2 > 8
D.C.Watson, Phys.Fluids 23,1980
TMX
?
DCLC и AIC на установках 2X||B и TMX
Параметры
ai/Rp
β
A≡<W┴>/<W║>
βA
βA2
Ei (keV)
2X||B
0.37
0.33
5
1.65
8
13
TMX
0.13
0.07
14
0.98
14
8
ГДЛ
0.23
0.02
50
1
25
20
ƒci (MHz)
4.9
7.6
37
2XIIB : основная неустойчивость – DCLC,
TMX: основная неустойчивость – AIC,
Корреляционный анализ
Взаимная корреляционная функция:

R
(

)


(
t
)

(
t

)
dt
12
1
2



Сигналы с зондов φ1(t) , φ2(t) → БПФ →

(

)

A
(

)
exp[
i

(

)]

(

)

A
(

)
exp[
i

(

)]
1
1
2
2
Спектральная плотность взаимной
корреляционной функции:
P
(
)
|P
(
)|exp[
i
(
)],
12
12
12
|P
(
)|A

)A

)
12
1(
2(
12(
)

)

)
2(
1(
1
2

R
(

)


(
t
)

(
t

)
dt
12
1
2



Сделаем преобразование Фурье


1
i
P
(

)

e
d 1(t)2(t )dt
12

2 







1
i1t
i2(t)
i

d

e
dt
[
d

e

(

)]

[
d

e
2(2)]
1
1
1
2




2  




1
ii1ti2(t)

d

dt
d

d

e
1(1)2(2) 
1
2



2    










 d d1 d2(1 2)eii21(1)2(2) 
 d d2eii21(2)2(2) 2
)2()
1(