- Email: [email protected]
Density, potential and magnetic turbulence measurements by a heavy ion beam probe in tokamak plasmas
°
Fusion Engineering Fusion Engineering and Design 34-35
ELSEVIER
(1997)25-35
and
Design
Density, potential and magnetic turbulence measurements by a heavy ion beam probe in tokamak plasmas Y. Hamada National Institute for Fusion Science, Nagoya 464-01, Japan
Abstract
This paper reviews recent progress and unsolved fundamental problems in the turbulence study by the use of a heavy ion beam probe for the TEXT and JIPP TIIU tokamaks. The most serious problems are as follows. (1) The propagation velocity of the turbulence is faster than the fluid velocity. (2) Large fluctuation of the secondary beam energy up to several hundred electronvolts is observed. It is difficult to ascribe this to the plasma potential fluctuation. A probable mechanism is the resonant interaction of the beam with the tokamak turbulence. (3) The level of the magnetic fluctuation measured with a heavy ion beam probe is much greater than the level measured with the magnetic probe at the plasma boundary. © 1997 Elsevier Science S.A.
1. Introduction
A heavy ion beam probe (HIBP) has unique potential for local measurements of the density, potential and magnetic field in plasmas, although magnetic field measurement is not straightforward and computer simulations are required [1]. The intensity of the secondary beam is related to the local plasma density at the sample volume. In the density turbulence measurement for the T E X T tokamak, it was observed that the oscillations up to 500 kHz propagate in the electron diamagnetic drift direction. Their speed, which is determined using two-point measurement, was much faster than the fluid rotation velocity vp, the sum of the drift velocity Er/B t and the electron diamagnetic drift velocity [2-4]. This observation contradicts the drift wave prediction [3], and the beam emission spectroscopy (BES) [5] and far-IR scattering measurements [6].
In these experiments, the frequency spectrum is dominated by the Doppler effect of the k spectrum, i.e. kVp. To explain this discrepancy, the finite sample voluem effect and the path integral effect have been studied, and it has been found that these effects are small [3]. Therefore, this discrepancy has been considered to result from the failure of the two-point measurement, because it is not capable of distinguishing between two waves which propagate in opposite directions. Later, the JIPP T-IIU HIBP utilized multiple detectors for a precise k-profile measurement [7]. However, the results obtained by the coherence analysis of signals from five sample volumes supported the T E X T results, although the discrepancy was fairly small [7]. In addition, we discovered drastic changes in the correlation time, frequency of the oscillations and direction of the propagation near the edge of the JIPP T-IIU plasma [7,9].
0920-3796/97/$17.00 © 1997 Elsevier Science S.A. All rights reserved. PII S0920-3796(96)00674-6
26
Y. Hamada /Fusion Engineering and Design 34 35 (1997) 25 35
The energy change of the secondary beam is related to the local potential at the sample volume [1], or may result from the beam energy exchange with the turbulence. Large changes in the secondary beam energy with an amplitude of up to 100 V, with a frequency of about 20-40 kHz and mode number of m -- 0, have been observed in the TEXT and JIPP T-IIU HIBP experiments [8,10]. In the JIPP T-IIU tokamak, a few measurements have been performed to verify whether or not these changes originated from the plasma turbulence. Because these energy changes have little correlation with other measurements, such as multi-channel electron cyclotron emission (ECE) signals, reflectometry signals and magnetic probes, their origin is very mysterious. With regard to the micro-scale potential fluctuations, the (signal-to-noise ratio) (SNR) is insufficient in the core plasma, because a high voltage HIBP has a low sensitivity for small and fast potential turbulence. However, in the TEXT and JIPP T-IIU HIBP experiments, statistically stable data have been obtained for potential turbulence and the turbulence-driven particle flux near the plasma boundary, where the turbulence level is high [8,11]. The magnetic turublence may be measured through the horizontal displacement of the secondary beam at the analyzer. The detected horizontal displacement at the JIPP T-IIU HIBP gave us the estimated level of the magnetic fluctuation, which is two orders of magnitude higher than the level measured by the magnetic probe placed at the plasma boundary.
ple may be applicable for the local measurement of the magnetic stream function of rA~, by utilizing the canonical momentum conservation as a result of the axisymmetry of tokamak plasmas. The secondary beam, however, usually goes through an outer horizontal port to the analyzer, and crosses the region of 100% ripple of the toroidal magnetic field. As a result, the conservation law of the canonical momentum is violated and the local measurement of rA+ is not fully established experimentally. The 2 MeV HIBP in the TEXT tokamak covers a wide cross-section of the plasma, because it is equipped with two energy analyzers for the secondary beam detection and two (horizontal and lower) ports for the primary beam injection, since the divertor is placed in the region of smaller major radius. In this apparatus (for the TEXT and JIPP T-IIU HIBPs), accelerators are placed horizontally, because they are very large and heavy. The beam is bent into the tokamak by an
Total Beam Energy
o
~ o
Kinetic
Beam Energy
v
2. Experimental apparatus The principle of local plasma potential measurement with an HIBP is illustrated in Fig. 1, and an actual set-up of a 500 keV HIBP [12-14] in the JIPP T-IIU tokamak [15] is shown in Fig. 2(a) and 2(b); this set-up is similar to the former 500 keV HIPB [16] in the TEXT tokamak. Because of the energy conservation law, the amount of change in the secondary beam energy is equal to the plasma potential at the position where the secondary beam is generated. The similar princi-
D i s t a n c e along the B e a m Trajectory Fig. 1. Typical behavior of the total and kinetic energies of the primary and secondary beams, to illustrate the basic principle of the potential measurement in the plasma by a heavy ion beam probe. By the increase in the charge number from 1 to 2 in ionization, the total and potential energies of the secondary beam increase by eq~(r×), where rx is the place where the ionization takes place. Because of total energy conservation, the kinetic energy of the secondary beam outside the plasma deviates from the initial energy at injection by eq~(rx). This change in the energy is measured by an energy analyzer.
Y. Hamada ,/'Fusion Engineering and Design 34-35 (1997) 25-35
27
Cylindrical Deflector Beam Profile
1 500 keV Accelerator Upper Electrode (Optical Trap)
Setup of Heavy Ion Beam Probe (HIBP) in JIPPT-1IU
(a)
Upper Plate (
)
Mesh Hele J "
Beam Trajectory .._ Hole Mesh
~In-planeEntrance~ - - ~ ~ , Angle ,/ ~ Detector" Afl"ayof EntraceSlit Seco,n'dary ~ ~ \f'..Preamplifire , ~ U p p e r ~"x (b)
~
Plate
LoWerPl ate
Expanded View
Fig. 2. (a) The set-up of an HIBP for the JIPP T-IIU tokamak. The lower electrode in the analyzer is the vessel itself. (b) Schematic details of a parallel plate energy analyzer for an HIBP.
28
Y. Hamada / Fusion Engineering and Design 34-35 (1997) 25-35
electrostatic cylindrical deflector, instead of a magnetic deflector, because the electrostatic deflector is more effective than its magnetic counterpart for ions of large mass number. A thallium or cesium beam is mainly used. The beam can be focused to a diameter of 2-3 mm in the tokamak, by a system of a cylindrical deflector and two or three electrostatic quadrupole lenses (double or triplet). The energy analyzer is a parallel plate analyzer [17]. It often has a shaped high voltage plate to enlarge the region of the uniform electric field betv~een the plates [18]. This parallel plate analyzer is intrinsically suitable for multiple sets of entrance slits and detectors (many sample volumes), because the electric field is uniform, as shown in Fig. 2(b). We introduced arrays of 13 input slits and detectors to obtain more information on the propagation of the turbulence [14]. The lower electrode has a large opening for the entrance of the beam to the detector. Usually, the hole is covered by a wide mesh with many wires which are parallel to the beam trajectory. The large irregularity in the electric field near the wires deflects the beam towards the direction perpendicular to the trajectory and may affect the magnetic field measurement (mesh effect) [191. The secondary beam current is detected by seveal pairs of stainless steel plates, which are set up and down, or side by side, as shown in Fig. 2(b). Each plate is directly connected to a low noise preamplifier. The vertical motion of the secondary beam at the detector plates is caused by the change in the secondary beam energy (the change in the local plasma potential). Therefore, the potential is measured from the differences between the upper and lower plate currents (iau, ida) normalized by their sum as [13] ND = (idu- id~)/(idu q- ida) The local density fluctuation is considered to be proportional to the fluctuations of the intensity of the secondary current in the detector (sum of the upper and lower detector currents), although the fact that the density fluctuation on the beam path may be contaminated into the local information (path integral effect [20]) should be taken into account. A toroidal shift of the secondary beam is caused by the change in the poloidal magnetic field
and is detected by the normalized difference between the left-hand and right-hand detector currents. Compared with the local turbulence measurement, the potential profile measurement is much more troublesome. This is because, during the scan of the plasma cross-section, the secondary beam that passes through the entrance slit changes in two directions. A large error in the potential measurement with a high voltage HIBP is caused by these changes in the entrance angles. The change in the entrance angle in the plane of symmetry (a vertical plane if the parallel plate is horizontal), i.e. an in-plane entrance angle (as shown in Fig. 2(b)), may not be crucial, because a parallel plate electrostatic analyzer with an entrance angle of 30 ° is usually employed, which has a second-order focus to the change in the in-plane entrance angle [17]. The residual error caused by the change in the out-of-plane entrance angle ~b is still large for a high voltage HIBP, because the error fieb in the measurement of the beam energy (Eb) that the results from the change in the out-ofplane entrance angle ~b in a parallel plate analyzer is ~Eb = Eb{1 -- COS2(q~)} To suppress this error, the fast sweep method is employed in the JIPP T-IIU tokamak at the expense of time resolution. During the fast toroidal sweep of the primary beam, the out-of-plane entrance angle can be zero at a certain time and, at this time, ND exhibits a local maximum, as a result of the dependence of cos2(~b). This local maximum of ND represents the true local potential [13]. In the HIBP for the helical device of a compact helical system (CHS), where the magnetic field is determined by the external coils, Fujisawa et al. keep these entrance angles constant during a radial scan, by sweeping the secondary and primary beams two dimensionally [21]. This new method may be partially applicable to the tokamak and may contribute significantly to the turbulence study, by simultaneously providing data for both turbulence and potential profiles. For the measurement of the plasma turbulence, the stability of the various power supplies in the
Y. Hamada ,/Fusion Engineering and Design 34-35 (1997) 25-35
ionization of a primary beam with the neutral gas, which is puffed into a plasma device [12,22,23]. When we detect the fluctuation in the density or potential measurement, it is necessary to check carefully whether the fluctuation is caused by the HIBP itself or other effects, i.e. the mesh effect or ripples in the various power supplies of the HIBP. Because the intensity of the secondary beam in gas ionization with a high voltage HIBP can be as strong as in the plasma, in situ calibration of the HIBP can be carried out up to the higher frequency, and the verification of the fluctuation is feasible. Nowadays, the stability of the voltages of the accelerator and the analyzer is greatly improved. The ripple of the electrostatic accelerating voltage of the JIPP T-IIU HIBP is about 2 Vp _ p (peak to peak value) out of 500 kV. We have also reduced the high frequency ripple of the voltage of the upper electrode of the energy analyzer to about 0.02 V out of 100 kV, using an LC filter in the SF6 gas.
1.0 0.0
E~
1.0 0.0
~o g - 1.0 V~O.O 1.0 0.0 20
40
60
Time (ms) Fig. 3. Raw data of four sums of detector currents when the sample volumes are swept in steps as shown in Fig. 4: (a) for sample volume 1; (b) sample volume 2; (c) sample volume 3; (d) sample volume 5.
accelerator, beam transport and energy analyzer is very important. The calibration of an HIBP is significantly improved by the use of the collisional
electron diamag,
450k e V
250
<
~'~
.~ ~
29
(a) (1,6) ~
ion diamag. I >
?
(c)
(b)
T
(d)
(1,4)
20O
150
~'10O
te=36.8000+ \
-I0
10
0
0
o
5(~---r t elayTime(/1 \D s)
(I)
g4[~
N 0.0
-50
<
-100 900
T
0
(g)
i0
i
"~2 '~o 1
1000
Major Radius (mm)
1100
~
-
I -10
~ 0
i0
ts-52.900© 'm=55.7000
ts=59.2000 te=62.0000
0
0
Delay Time ( # s)
i0
Fig. 4. Positions of seven sample volumes at steps (a)-(g) in the plasma cross-section, and five correlation coefficient functions of the intensity (sum) of the secondary current from five sample volumes (1, 2, 3, 4, 6), p~j(t),j = 1, 2, 3, 4, 6. The thallium beam energy is 450 keV and the toroidal field is 3 T. The sample volume is swept step-wisely from (a)-(g) by the poloidal sweeper, which is placed at the entrance to the tokamak. The number of slits in the energy analyzer is seven (seven sample volumes) and 1 - 6 sample volumes are measured. The sixth slit is closed to check the noise that results from the U V radiation from the tokamak plasma. Therefore, plj(t), j = 1, 2, 3, 4, 6, are presented, p l j ( t ) is shifted upwards b y j to avoid confusion.
30
Y. Hamada /Fusion Engineering and Design 3 4 - 3 5 (1997) 2 5 - 3 5
electron diamag, ion diamag. 300 keV
-
250
' -
.~ 4
(e)
i
. . . . .
" ~ i~. . . .
~oo -
t6
I `00
'\a~,V
l \ t ~
(°>\
-~ol 900
IL)
~
~ - ' q ~ ~
'"" "~I/ \ I I ) ~ A I
JY._JY~--i
.....
.~ i (c) \ ~ 50 PlasmaAxis " ~
_~ool
~'~ =r~3 U ~ , ~
. .
:
I
/
I
/
(g)~-1000
Del:ty Time (g s) 4 (f) ~
/
1100 \ (h)
Major Radius (ram)
~e,I
(g)
(h)
"q~-"~l
__ II
II
1F~--Z~I
g ~ ~ . 1 I ~
~ 3 I"
'~
~.-/
II
"-dl/~
I/
II
0
20
0[ m l o a ~ i m l ~ i ~ ~
-20 0 20 0 Delay Time (/1 s)
0
Fig. 5. Position of eight sample volumes in the plasma cross-section at steps (a) (i), and five correlation coefficient functions from these sample volumes. The beam energy is 300 keV. 3. E x p e r i m e n t a l results
3.1. Density turbulence The JIPP T-IIU tokamak is operated at 3 T. Its major radius is 93 cm. The experiment is usually performed at an average density of about 2 x 1013 cm-3 to avoid beam attenuation by the plasma. The plasma current is about 200 kA (qa = 4.5). A study of the density fluctuation with the HIBP is performed by analyzing the intensity of the secondary beam at the detector. Fig. 3 shows the intensity of the secondary beam current Is (sum of the upper and lower plate currents) of four sample volumes as the position of the sample volume is swept in steps, as shown in Fig. 4. Is/Is is proportioanl to ~e/ne at the sample volume and is greater than the plasma boundary, decreasing as the sample volume is swept into the plasma center. A comparison of the intensity between the inside and the outside of the plasma shows that the measurement of the density turbulence has a high SNR and that the main noise results from
the amplifier noise in the detector circuits. In addition, Fig. 3 shows that the density turbulence at the plasma boundary is dominated by the low frequency fluctuations. Fig. 4 shows the behavior of five correlation coefficient functions of the intensities of the secondary currents of five sample volumes when the sample volumes are swept in eight steps (a-g) for a 450 keV thallium primary beam. The correlation coefficient function pij(t) of the signal si(t) at the ith sample volume and sj(t) at the kth sample volume is described by cu(~)
pij(~) = [ci,~(0)]~/2[Q. /0)11/2 where C~j(r) is the cross-correlation function given by
C~j(v) = [~ ~(t)gj(t + "C) dt d - oQ
where g,.(t) = si(t) - s D ) , and the integration time in this case is 2.8 ms. The sample volume moves from the boundary to the inner region of the
Y. Hamada /Fusion Engineering and Design 34-35 0907) 25-35
3"0 h/ aI',~,,,A~
h
2i
~
-0.5
z.065[~
,
,
22
,
,
23
,~
0.0 i: .
.
.
.
.
.
.
'
23 .
,
, 22.1
,
22.2
22.3
4 ..... .
22
2.5 22.0
24
....... 21
.
.
31
, ]-0.6
24
/
-0.31
22.0 ,.
22.1 ,
,
50
100
50
100
,t'° 4 ~2
22.2 ,
0
,
22.3 ,
/
.~ ~-o.4
0
0
. . . . . . . .
.--.21~
~1
-0.8
-0.55 22.0
Time (ms)
22.1
22.2
Time (ms)
22.3
0
0
~.x .~
~._....,__~ 50
.
100
Frequency (kHz)
Fig. 6. T y p i c a l t i m e b e h a v i o r s , e x p a n d e d views, a n d F o u r i e r spectra of the sum o f the s e c o n d a r y current, N D ( n o r m a l i z e d difference between the u p p e r a n d l o w e r d e t e c t o r currents) a n d t o r o i d a l shift ( n o r m a l i z e d difference between left- a n d r i g h t - h a n d d e t e c t o r currents (idl , id), defined b y the relation ( i d l - ia)/(ia~ + iar).
plasma, by changing the poloidal sweep voltage. The characteristics of the correlation curves change rapidly near the plasma boundary. The dominant frequency of the drift-wave turbulence near the core plasma is about 100-200 kHz, and the turbulence has a fairly short correlation time, while the turbulence at the plasma boundary is characterized by a long correlation time of the order of 10 ps and low frequency oscillations. The short correlation length inside the plasma (as shown in Fig. 4) means that the role of the path integral effect on the density turbulence is not dominant [201. The cross-correlation coefficient functions in the inner region show that the main turbulence propagates in the electron diamagnetic drift direction in the core region of the OH plasma. Because the direction of the arrays of the sample volumes near the plasma center ((e) of Fig. 4) is rather poloidal, we are able to obtain a poloidal propagation velocity of about 6 km s - 1 by a shift of peaks of the correlation curves. This velocity is a factor of about 2 faster than the fluid velocity, i.e. the total of the diamagnetic drift and E/B drift velocity. The total velocity is smaller than the velocity obtained by the HIBP experiments in the
TEXT tokamak [2-4]. The change in the characteristics of the turbulence along the minor radius was also found recently in TFTR, using BES [5]. The TFTR results showed that the turbulence propagating into the ion diamagnetic direction (ITG mode) dominates in the inner region of the hot core. Fig. 5 shows the correlation coefficient functions and positions of sample volumes when the beam energy is 300 keV [9]. In this case, the sample volume moves from the boundary to the inner part, and again to the boundary. Because the sample volume at the lower plasma boundary is small, a more local measurement of the turbulence is possible. The correlation time becomes longer towards both upper and lower plasma boundaries. The direction of the propagation of the turbulence changes from the ion diamagnetic drift to the electron diamagnetic drift as the sample volumes are swept from (b) to (c). The change in the correlation time in the turbulence at the plasma edge was recently observed by reciprocating electric probes [24,25]. We have verified this by the non-perturbative diagnostic method of the HIBP, and have shown that only a small monotonic change occurs towards the cen-
Y. Hamada / Fusion Engineering and Design 34-35 (1997) 25-35
32
electron diamag., ion diamag. i f
_.
300 keV
250
3[~---~J ~
'
~ 2 t ~ ~
200
¢~ 1r / . - ~
I50
0
-20
0
~
~
~
J
~
,~"~l~'~'~J
~
~
J
~'-~[~ ^ ~ ] , ] ~ " ~ / A ' ~ - ~ ' ~ - ~ ( 1 , 3 )
(1,4)
]~A~]-~A'----d~--~A'-~$~---'A'~tI~-d/~)----ly~----~-'-~-t(1,2) 20
0
0
0
0
0
0
0
20
(b) ~ 1
g
~0
3
(1,4)
(c) \ < S0 PlasmaAxis
\
1 /" J
,
i
~
(1,2)
eD
o.o
X
,
9DO
-20
0
20
0
0
0
0
0
0
0
20
<~
-20
0
20
0
0
0
0
0
0
0
20
(;-,
-50 -100
A
(g) \ I000
Major Radius (ram)
1100
1)
V Delay Time (,u s)
Fig. 7. Positions of sample volumes and correlation coefficient functions of the S U M , N D and ( ( S U M ( l ) + SUM(2))(ND(1) -N D ( 2 ) ) ) , which is p r o p o r t i o n a l to the correlation of the density and local electric field, at 300 keV.
ter of the plasma column. The noise is mainly from the current amplifier of the metal plate detectors. The sharp peak in the autocorrelation coefficient function of the ith step in Fig. 5 results from the circuit noise. The amplifier frequency range extends over 300 kHz and shows a sharp peak. The correlation curves in Figs. 4 and 5 are statistically stable, because of the high SNR. Similar correlation curves are obtained if we reduce the integration time to 0.4 ms.
3.2. Potential turbulence The measurement of the potential turbulence does not have a high SNR in small-scale, high frequency potential turbulence, because N D (difference between secondary currents normalized by their sum) has a poorer sensitivity (3 kV/ND for 450 keV beam and slit height of 3 mm in the JIPP-TIIU HIBP) in a higher voltage HIBP. The anticipated level of the potential fluctuations in the core may be about 10 V when Te = 1000 keV and fie/n~ = 0.01, if Boltzman's law is assumed. Therefore, for the SNR -- 1 measurement of the potential fluctuation in the core, we need to measure a small (0.003) and fast fluctuation of ND. The correlation analysis helps to improve the SNR. Therefore, the small-scale potential fluctuation measurement with
a high SNR is usually possible in the outer area, where the level of the turbulence is high. However, we have observed that the tokamak plasmas often have a large-scale potential fluctuations around 30 kHz [8,10]. Fig. 6 shows typical time behaviors, expanded views, and Fourier spectra of the intensity of the secondary current, the N D and the toroidal shift (normalized difference of the left- and right-hand detector current) (id,, idr), defined by the r e l a t i o n (idl - - idr)/(idl Jr /dr). The sample volume is at the step (d) of Fig. 7. Because the ratio of N D to the potential or beam energy is about 2 kV/ND in this case, the potential fluctuation or beam energy fluctuation in Fig. 6 is about 300 Vp_ p. F r o m the Fourier spectrum of ND, we can observe that the oscillations with frequency less than 40 kHz are dominant in ND. To verify that these oscillations are not induced by the several power supplies of the HIBP system, we have checked the ripple of all the power supplies and have found that these ripples are too small to explain the observed fluctuation. In addition, these oscillations are not observed when the plasma is replaced by the gas. We were able to perform this gas ionization experiment with the same level of SNR as that in the plasma experiment, because the detector currents were adjusted to almost the same level in both cases.
Y. Hamada / Fusion Engineering and Design 34-35 (1997) 25-35
33
250 keV 250
electron diamag, ion diamag. < I > (a) Co) (c) (d)
(e)
(f)
(g)
(h) (1,6)
150
\ (b
N
50
Plasma
]
(1,1) -20
(o)'~
Axis
0
20
2
(d)\[ ,,
0.0
0
0
i I
&
-50
20
.,
•
~' '
IiO0
1(300 Major
Radius
(nun)
0
0
20
0
,
11 . i
....
0
-2o o 2o o Delay Time (/~ s)
II
O
'F
• ~----,
,
~
0
J
z<~ .. lo. u / v
0
~ ,
<
-I00
900
eg \
0
0
,
,
0
0
I -
(i,3)
--
0
0
J.
r~
.
.
.
" ~1 ~T
,
T
T ,
o
o
o
o
o
Fig. 8. Positions of sample volumes a n d correlation coefficient functions of the S U M , N D a n d ( ( S U M ( I ) + ND(2))>, which is proportional to the correlation of the density and local electric field, at 250 keV.
The observed oscillation in N D in Fig. 6 correlates with the horizontal motion of the secondary beam at the detector. This implies that the poloidal magnetic field changes at a high frequency, because the horizontal deflection is induced only by the poloidal magnetic field. As mentioned, a parallel plate analyzer records the energy of the kinetic motion only in the analyzer plane (vertical and symmetry plane), i.e. eVo out of the total energy (eVt). The relation eVo = eVt cos2(~b) holds, where (b is the out-of-plane entrance angle of the secondary beam to the analyzer• We performed the potential measurement by rotating the energy analyzer horizontally around the vertical axis, with a fixed point of the middle of the entrance slit of the analyzer, only changing the out-of-plane entrance angle. Because the phases of the toroidal motions and the energy in the coherence analysis do not change in this series of the experiments, we can conclude that the N D oscillation does not result from the horizontal deflection (change of the outof-plane entrance angle)• Figs. 7 and 8 show the correlation coefficient functions of the sum of the upper and lower plate currents (SUM), ND, and ((SUM(I) + S U M ( 2 ) ) ( N D ( 1 ) - ND(2)>, which is proportional to the correlation of the density and local electric
20
i (1,1)
20
it ,
/
o
20
SUM(2))(ND(1)-
field for 300 keV and 250 keV thallium beams [8]. The estimated mode number of the dominant oscillation in N D in Fig. 7 is m = 0, because the phase shift of the correlation analysis of N D for five sample volumes is very small• The peak values of the correlation coefficient functions are almost 1. Therefore, we can conclude that these large potential fluctuations are large scale and quasi-coherent. However, we cannot observe the quasi-coherent mode in the case of the 250 keV beam, as shown in Fig. 8. This implies that, at the boundary layer, these fluctuations are not observed. The large fluctuations in N D may be ascribed to the local potential change at the sample volume. However, these energy changes have little correlation with other measurements of the core plasma, such as multi-channel ECE signals and reflectometry signals. These oscillations are expected to be a global mode, because the mode number is m = 0 and a high correlation with at least one channel of the eight-channel ECE signals or radial scanned reflectometry signals should be observed. At present, we ascribe these energy changes to the interaction with the turbulence in the tokamak plasmas. This is because the radial phase velocity of the turbulence is so fast that there is the possibility of resonant interaction of the beam with the turbulence, and the occurrence of a large energy exchange between the turbulence and the beam.
34
Y. Hamada / Fusion Engineering and Design 34 35 (1997) 25-35
The cross-correlation between the sum and difference of ND, which may be proportional to the particle flux electrostatically driven by the plasma turbulence, is found to be statistically reliable, as is shown in Figs. 7 and 8. The calculated particle confinement time based on this correlation (in the case of the step (d) of Fig. 8) is 1.5 ms, while the energy confinement time is about 10 ms. Magnetic turbulence measurement was attempted intensively in the TEXT tokamak [26] and later in the JIPP T-IIU. It tends to give a much larger fluctuation level at the plasma boundary than that in magnetic probe measurement. It is suspected that the density fluctuation contaminates the normalized difference of the right- and lefthand detector currents through the toroidal wave number [261.
4. Future improvements in HIBPs
Although the experiment with the present set-up is still fruitful for the study of tokamak turbulence, the technical issues for the future HIBP are as follows. 4. I. Detector development
The turbulence measurement in the core plasma is limited in the low density case in the present experiment. A low noise detector would expand the applicability of the HIBP. The micro-channel plate (MCP) detector saturates at the high intensity secondary beam used for turbulence measurement in HIBPs. It is necessary to develop an efficient low noise detector (quantum detector) to replace the simple stainless steel plate with a low noise electronic amplifier.
5. Conclusions
By the intensive efforts mainly of the group of Prof. R. Hickok, study of turbulence in tokamak plasmas with an HIBP has greatly improved. However, there are a number of basic problems to be solved, as are described in this paper. (1) The average poloidal wave number determined by the HIBP is very small and the propagation velocity is much faster than the poloidal rotation velocity. This is in contradiction with the drift wave theory, while other diagnostics, such as FIR scattering and BES, generally agree with the theory. (2) The large energy exchange in the secondary beam energy observed in the TEXT and JIPP T-IIU tokamaks may be explained by the acceleration of the beam by the turbulence. Because the basic principle of the measurement of the space potential in the plasma with an HIBP may be only applicable to the static potential, the measurement of the turbulent electric field must be carefully analyzed, although the transit time of the beam across the plasma is order of 0.1 gs, which is smaller than the observed characteristic time of the fluctuations. (3) The measurement of the magnetic turbulent field in the plasma with an HIBP still contains large errors. The main reason for this problem may be that the applicability of the probe's principles is limited to the static field. Although an HIBP has unique potential for local density, electric and magnetic turbulence measurements, it is still far from the established tool for the study of turbulence. Intensive research is necessary to analyze its applicability. The study of turbulence with an HIBP always requires careful checking of the applicability of the probe's basic principles.
4.2. M u l t i - b e a m H I B P
This will enable us to perform two-dimensional study of the turbulence. The present analyzer and detector system can easily detect the multi-secondary beams, if the beam is separated in the toroidal direction. The generation of the multibeam by an accelerator may be possible, because a television with three electron beams is available.
References
[1] F.C. Jobes and R.L. Hickok, A direct measurement of plasma space potential, Nucl. Fusion 10 (1970) 195. [2] T.P. Crowleyet al., Heavy ion beam probe wavenumber measurement from the TEXT tokamak edge, Nucl. Fusion 32 (1992) 1295. [3] D.W. Ross et al., Dispersion relation of density fluctuaa-
Y. Hamada / Fusion Engineering and Design 34-35 (1997) 25-35
[4]
[5] [6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
tions observed by the heavy ion beam probe in TEXT, Nucl. Fusion 31 (1991) 1355. J.W. Heard et al., Broadband density fluctuation measurements using ion beam probe in the Texas experimental tokamak, Phys. Plasmas 2 (1995) 3360. R.J. Fronck et al., Long-wavelength density turbulence in the TFTR tokamak, Phys. Rev. Lett. 70 (1993) 3736. D.L. Brower, S.K. Peebles and N.C. Luhman, Jr., The spectrum, spatial distribution and scaling of microturbulence in the TEXT tokamak, Nucl. Fusion 27 (1987) 2055. Y. Hamada et al., Proc. 15th Int. Conf. on Plasma Physics and Controlled Nuclear Fusion Research, Seville, 1994, vol. 1, IAEA, Vienna, 1995, p. 301. Y. Hamada et al., Potential fluctuations and large coherent modes observed by a heavy ion beam probe in the JIPP T-IIU tokamak, in press. Y. Hamada et al., Transition of fluctuation characteristics near the plasma boundary observed by a heavy ion beam probe in the JIPP T-IIU tokamak, in press. H.Y.W. Tsui et al., Observation of a quasi-coherent mode in the Texas experimental tokamak, Phys. Fluids B 5 (1993) 1274. J.C. Forster et al., Study of density and potential fluctuations in the TEXT tokamak with a heavy ion probe, Trans. Plasma Sci. 22 (1994) 359. Y. Hamada et al., Proposal of a single sweep measurement of a potential profile in tokamak plasmas by high voltage heavy ion beam probe, J. Plasma Phys. Fusion Res. 69 (1993) 1050. Y. Hamada et al., Measurement of profiles of the space potential in JIPP T-IIU tokamak plasmas by slow poloidal and fast poloidal sweeps of a heavy ion beam, Plasma Phys. Controlled Fusion 36 (1994) 1743. Y. Hamada et al., Improvement of a 500 keV heavy-ionbeam probe for JIPP T-IIU tokamak, Rev. Sci. Instrum. 66 (1995) 321.
35
[15] K. Toi et al., Proc. 14th Int. Conf. on Plasma Physics and Controlled Nuclear Fusion Research, Wurzburg, 1992, vol. 1, IAEA, Vienna, 1993, p. 301. [16] P.M. Schoch et al., TEXT heavy ion beam probe, Rev. Sci. Instrum. 57 (t986) 1825. [17] T.S. Green and G.A. Proca, A parallel plate electrostatic spectrograph, Rev. Sci. Instrum. 41 (1970) 1409. [18] Y. Hamada et al., Shaped electrode system for high voltage parallel plate analyzer, Rev. Sci. Instrum. 63 (1992) 4446. [19] Y. Hamada et a1., Mesh effect in a parallel-plate analyzer, Rev. Sci. Instrum. 65 (1994) 1606. [20] J.W. Heard et al., A path integral effects in heavy ion beam probe density measurements, Rev. Sci. Instrum. 64 (1993) 1001. [21] A. Fujisawa et al., Active control of beam trajectories for heavy ion beam probe on helical magnetic configurations, Rev. Sci. Instrum. 63 (1992) 3694 (and also in this conference). [22] J.J. Zielinski, S.C. Aceto et al.0 In situ analyzer calibration methods for heavy ion beam probes installed in stellarator-like devices, Rev. Sci. Instrum. 63 (1992) 4574. [23] Y. Hamada et at., Calibration of a heavy ion beam probe in JIPP T-IIU tokamak by gas puffing, in press. [24] M. Endler et al., Experimental and theoretical investigation of density and potential fluctuations in the scrape-off layer of ASDEX, Proc. 20th Euro. Conf. on Controlled Fusion and Plasma Physics, Lisboa, 1993, Vol. 1, p. 301. [25] A.V. Filippas et al., Conditional analysis of floating potential fluctuations at the edge of the TEXT experimental tokamak upgrade (TEXT-U), Phys. Plasmas 2 (1995) 839. [26] B.Z. Zhang et al., Investigation of the HIBP toroidal beam motion as a method for measuring broadband magnetic fluctuation, Proc. US Japan Workshop on Technical Issues in the Application of a Heavy Ion Beam Probes, Troy, NY, 1993.
Fusion Engineering Fusion Engineering and Design 34-35
ELSEVIER
(1997)25-35
and
Design
Density, potential and magnetic turbulence measurements by a heavy ion beam probe in tokamak plasmas Y. Hamada National Institute for Fusion Science, Nagoya 464-01, Japan
Abstract
This paper reviews recent progress and unsolved fundamental problems in the turbulence study by the use of a heavy ion beam probe for the TEXT and JIPP TIIU tokamaks. The most serious problems are as follows. (1) The propagation velocity of the turbulence is faster than the fluid velocity. (2) Large fluctuation of the secondary beam energy up to several hundred electronvolts is observed. It is difficult to ascribe this to the plasma potential fluctuation. A probable mechanism is the resonant interaction of the beam with the tokamak turbulence. (3) The level of the magnetic fluctuation measured with a heavy ion beam probe is much greater than the level measured with the magnetic probe at the plasma boundary. © 1997 Elsevier Science S.A.
1. Introduction
A heavy ion beam probe (HIBP) has unique potential for local measurements of the density, potential and magnetic field in plasmas, although magnetic field measurement is not straightforward and computer simulations are required [1]. The intensity of the secondary beam is related to the local plasma density at the sample volume. In the density turbulence measurement for the T E X T tokamak, it was observed that the oscillations up to 500 kHz propagate in the electron diamagnetic drift direction. Their speed, which is determined using two-point measurement, was much faster than the fluid rotation velocity vp, the sum of the drift velocity Er/B t and the electron diamagnetic drift velocity [2-4]. This observation contradicts the drift wave prediction [3], and the beam emission spectroscopy (BES) [5] and far-IR scattering measurements [6].
In these experiments, the frequency spectrum is dominated by the Doppler effect of the k spectrum, i.e. kVp. To explain this discrepancy, the finite sample voluem effect and the path integral effect have been studied, and it has been found that these effects are small [3]. Therefore, this discrepancy has been considered to result from the failure of the two-point measurement, because it is not capable of distinguishing between two waves which propagate in opposite directions. Later, the JIPP T-IIU HIBP utilized multiple detectors for a precise k-profile measurement [7]. However, the results obtained by the coherence analysis of signals from five sample volumes supported the T E X T results, although the discrepancy was fairly small [7]. In addition, we discovered drastic changes in the correlation time, frequency of the oscillations and direction of the propagation near the edge of the JIPP T-IIU plasma [7,9].
0920-3796/97/$17.00 © 1997 Elsevier Science S.A. All rights reserved. PII S0920-3796(96)00674-6
26
Y. Hamada /Fusion Engineering and Design 34 35 (1997) 25 35
The energy change of the secondary beam is related to the local potential at the sample volume [1], or may result from the beam energy exchange with the turbulence. Large changes in the secondary beam energy with an amplitude of up to 100 V, with a frequency of about 20-40 kHz and mode number of m -- 0, have been observed in the TEXT and JIPP T-IIU HIBP experiments [8,10]. In the JIPP T-IIU tokamak, a few measurements have been performed to verify whether or not these changes originated from the plasma turbulence. Because these energy changes have little correlation with other measurements, such as multi-channel electron cyclotron emission (ECE) signals, reflectometry signals and magnetic probes, their origin is very mysterious. With regard to the micro-scale potential fluctuations, the (signal-to-noise ratio) (SNR) is insufficient in the core plasma, because a high voltage HIBP has a low sensitivity for small and fast potential turbulence. However, in the TEXT and JIPP T-IIU HIBP experiments, statistically stable data have been obtained for potential turbulence and the turbulence-driven particle flux near the plasma boundary, where the turbulence level is high [8,11]. The magnetic turublence may be measured through the horizontal displacement of the secondary beam at the analyzer. The detected horizontal displacement at the JIPP T-IIU HIBP gave us the estimated level of the magnetic fluctuation, which is two orders of magnitude higher than the level measured by the magnetic probe placed at the plasma boundary.
ple may be applicable for the local measurement of the magnetic stream function of rA~, by utilizing the canonical momentum conservation as a result of the axisymmetry of tokamak plasmas. The secondary beam, however, usually goes through an outer horizontal port to the analyzer, and crosses the region of 100% ripple of the toroidal magnetic field. As a result, the conservation law of the canonical momentum is violated and the local measurement of rA+ is not fully established experimentally. The 2 MeV HIBP in the TEXT tokamak covers a wide cross-section of the plasma, because it is equipped with two energy analyzers for the secondary beam detection and two (horizontal and lower) ports for the primary beam injection, since the divertor is placed in the region of smaller major radius. In this apparatus (for the TEXT and JIPP T-IIU HIBPs), accelerators are placed horizontally, because they are very large and heavy. The beam is bent into the tokamak by an
Total Beam Energy
o
~ o
Kinetic
Beam Energy
v
2. Experimental apparatus The principle of local plasma potential measurement with an HIBP is illustrated in Fig. 1, and an actual set-up of a 500 keV HIBP [12-14] in the JIPP T-IIU tokamak [15] is shown in Fig. 2(a) and 2(b); this set-up is similar to the former 500 keV HIPB [16] in the TEXT tokamak. Because of the energy conservation law, the amount of change in the secondary beam energy is equal to the plasma potential at the position where the secondary beam is generated. The similar princi-
D i s t a n c e along the B e a m Trajectory Fig. 1. Typical behavior of the total and kinetic energies of the primary and secondary beams, to illustrate the basic principle of the potential measurement in the plasma by a heavy ion beam probe. By the increase in the charge number from 1 to 2 in ionization, the total and potential energies of the secondary beam increase by eq~(r×), where rx is the place where the ionization takes place. Because of total energy conservation, the kinetic energy of the secondary beam outside the plasma deviates from the initial energy at injection by eq~(rx). This change in the energy is measured by an energy analyzer.
Y. Hamada ,/'Fusion Engineering and Design 34-35 (1997) 25-35
27
Cylindrical Deflector Beam Profile
1 500 keV Accelerator Upper Electrode (Optical Trap)
Setup of Heavy Ion Beam Probe (HIBP) in JIPPT-1IU
(a)
Upper Plate (
)
Mesh Hele J "
Beam Trajectory .._ Hole Mesh
~In-planeEntrance~ - - ~ ~ , Angle ,/ ~ Detector" Afl"ayof EntraceSlit Seco,n'dary ~ ~ \f'..Preamplifire , ~ U p p e r ~"x (b)
~
Plate
LoWerPl ate
Expanded View
Fig. 2. (a) The set-up of an HIBP for the JIPP T-IIU tokamak. The lower electrode in the analyzer is the vessel itself. (b) Schematic details of a parallel plate energy analyzer for an HIBP.
28
Y. Hamada / Fusion Engineering and Design 34-35 (1997) 25-35
electrostatic cylindrical deflector, instead of a magnetic deflector, because the electrostatic deflector is more effective than its magnetic counterpart for ions of large mass number. A thallium or cesium beam is mainly used. The beam can be focused to a diameter of 2-3 mm in the tokamak, by a system of a cylindrical deflector and two or three electrostatic quadrupole lenses (double or triplet). The energy analyzer is a parallel plate analyzer [17]. It often has a shaped high voltage plate to enlarge the region of the uniform electric field betv~een the plates [18]. This parallel plate analyzer is intrinsically suitable for multiple sets of entrance slits and detectors (many sample volumes), because the electric field is uniform, as shown in Fig. 2(b). We introduced arrays of 13 input slits and detectors to obtain more information on the propagation of the turbulence [14]. The lower electrode has a large opening for the entrance of the beam to the detector. Usually, the hole is covered by a wide mesh with many wires which are parallel to the beam trajectory. The large irregularity in the electric field near the wires deflects the beam towards the direction perpendicular to the trajectory and may affect the magnetic field measurement (mesh effect) [191. The secondary beam current is detected by seveal pairs of stainless steel plates, which are set up and down, or side by side, as shown in Fig. 2(b). Each plate is directly connected to a low noise preamplifier. The vertical motion of the secondary beam at the detector plates is caused by the change in the secondary beam energy (the change in the local plasma potential). Therefore, the potential is measured from the differences between the upper and lower plate currents (iau, ida) normalized by their sum as [13] ND = (idu- id~)/(idu q- ida) The local density fluctuation is considered to be proportional to the fluctuations of the intensity of the secondary current in the detector (sum of the upper and lower detector currents), although the fact that the density fluctuation on the beam path may be contaminated into the local information (path integral effect [20]) should be taken into account. A toroidal shift of the secondary beam is caused by the change in the poloidal magnetic field
and is detected by the normalized difference between the left-hand and right-hand detector currents. Compared with the local turbulence measurement, the potential profile measurement is much more troublesome. This is because, during the scan of the plasma cross-section, the secondary beam that passes through the entrance slit changes in two directions. A large error in the potential measurement with a high voltage HIBP is caused by these changes in the entrance angles. The change in the entrance angle in the plane of symmetry (a vertical plane if the parallel plate is horizontal), i.e. an in-plane entrance angle (as shown in Fig. 2(b)), may not be crucial, because a parallel plate electrostatic analyzer with an entrance angle of 30 ° is usually employed, which has a second-order focus to the change in the in-plane entrance angle [17]. The residual error caused by the change in the out-of-plane entrance angle ~b is still large for a high voltage HIBP, because the error fieb in the measurement of the beam energy (Eb) that the results from the change in the out-ofplane entrance angle ~b in a parallel plate analyzer is ~Eb = Eb{1 -- COS2(q~)} To suppress this error, the fast sweep method is employed in the JIPP T-IIU tokamak at the expense of time resolution. During the fast toroidal sweep of the primary beam, the out-of-plane entrance angle can be zero at a certain time and, at this time, ND exhibits a local maximum, as a result of the dependence of cos2(~b). This local maximum of ND represents the true local potential [13]. In the HIBP for the helical device of a compact helical system (CHS), where the magnetic field is determined by the external coils, Fujisawa et al. keep these entrance angles constant during a radial scan, by sweeping the secondary and primary beams two dimensionally [21]. This new method may be partially applicable to the tokamak and may contribute significantly to the turbulence study, by simultaneously providing data for both turbulence and potential profiles. For the measurement of the plasma turbulence, the stability of the various power supplies in the
Y. Hamada ,/Fusion Engineering and Design 34-35 (1997) 25-35
ionization of a primary beam with the neutral gas, which is puffed into a plasma device [12,22,23]. When we detect the fluctuation in the density or potential measurement, it is necessary to check carefully whether the fluctuation is caused by the HIBP itself or other effects, i.e. the mesh effect or ripples in the various power supplies of the HIBP. Because the intensity of the secondary beam in gas ionization with a high voltage HIBP can be as strong as in the plasma, in situ calibration of the HIBP can be carried out up to the higher frequency, and the verification of the fluctuation is feasible. Nowadays, the stability of the voltages of the accelerator and the analyzer is greatly improved. The ripple of the electrostatic accelerating voltage of the JIPP T-IIU HIBP is about 2 Vp _ p (peak to peak value) out of 500 kV. We have also reduced the high frequency ripple of the voltage of the upper electrode of the energy analyzer to about 0.02 V out of 100 kV, using an LC filter in the SF6 gas.
1.0 0.0
E~
1.0 0.0
~o g - 1.0 V~O.O 1.0 0.0 20
40
60
Time (ms) Fig. 3. Raw data of four sums of detector currents when the sample volumes are swept in steps as shown in Fig. 4: (a) for sample volume 1; (b) sample volume 2; (c) sample volume 3; (d) sample volume 5.
accelerator, beam transport and energy analyzer is very important. The calibration of an HIBP is significantly improved by the use of the collisional
electron diamag,
450k e V
250
<
~'~
.~ ~
29
(a) (1,6) ~
ion diamag. I >
?
(c)
(b)
T
(d)
(1,4)
20O
150
~'10O
te=36.8000+ \
-I0
10
0
0
o
5(~---r t elayTime(/1 \D s)
(I)
g4[~
N 0.0
-50
<
-100 900
T
0
(g)
i0
i
"~2 '~o 1
1000
Major Radius (mm)
1100
~
-
I -10
~ 0
i0
ts-52.900© 'm=55.7000
ts=59.2000 te=62.0000
0
0
Delay Time ( # s)
i0
Fig. 4. Positions of seven sample volumes at steps (a)-(g) in the plasma cross-section, and five correlation coefficient functions of the intensity (sum) of the secondary current from five sample volumes (1, 2, 3, 4, 6), p~j(t),j = 1, 2, 3, 4, 6. The thallium beam energy is 450 keV and the toroidal field is 3 T. The sample volume is swept step-wisely from (a)-(g) by the poloidal sweeper, which is placed at the entrance to the tokamak. The number of slits in the energy analyzer is seven (seven sample volumes) and 1 - 6 sample volumes are measured. The sixth slit is closed to check the noise that results from the U V radiation from the tokamak plasma. Therefore, plj(t), j = 1, 2, 3, 4, 6, are presented, p l j ( t ) is shifted upwards b y j to avoid confusion.
30
Y. Hamada /Fusion Engineering and Design 3 4 - 3 5 (1997) 2 5 - 3 5
electron diamag, ion diamag. 300 keV
-
250
' -
.~ 4
(e)
i
. . . . .
" ~ i~. . . .
~oo -
t6
I `00
'\a~,V
l \ t ~
(°>\
-~ol 900
IL)
~
~ - ' q ~ ~
'"" "~I/ \ I I ) ~ A I
JY._JY~--i
.....
.~ i (c) \ ~ 50 PlasmaAxis " ~
_~ool
~'~ =r~3 U ~ , ~
. .
:
I
/
I
/
(g)~-1000
Del:ty Time (g s) 4 (f) ~
/
1100 \ (h)
Major Radius (ram)
~e,I
(g)
(h)
"q~-"~l
__ II
II
1F~--Z~I
g ~ ~ . 1 I ~
~ 3 I"
'~
~.-/
II
"-dl/~
I/
II
0
20
0[ m l o a ~ i m l ~ i ~ ~
-20 0 20 0 Delay Time (/1 s)
0
Fig. 5. Position of eight sample volumes in the plasma cross-section at steps (a) (i), and five correlation coefficient functions from these sample volumes. The beam energy is 300 keV. 3. E x p e r i m e n t a l results
3.1. Density turbulence The JIPP T-IIU tokamak is operated at 3 T. Its major radius is 93 cm. The experiment is usually performed at an average density of about 2 x 1013 cm-3 to avoid beam attenuation by the plasma. The plasma current is about 200 kA (qa = 4.5). A study of the density fluctuation with the HIBP is performed by analyzing the intensity of the secondary beam at the detector. Fig. 3 shows the intensity of the secondary beam current Is (sum of the upper and lower plate currents) of four sample volumes as the position of the sample volume is swept in steps, as shown in Fig. 4. Is/Is is proportioanl to ~e/ne at the sample volume and is greater than the plasma boundary, decreasing as the sample volume is swept into the plasma center. A comparison of the intensity between the inside and the outside of the plasma shows that the measurement of the density turbulence has a high SNR and that the main noise results from
the amplifier noise in the detector circuits. In addition, Fig. 3 shows that the density turbulence at the plasma boundary is dominated by the low frequency fluctuations. Fig. 4 shows the behavior of five correlation coefficient functions of the intensities of the secondary currents of five sample volumes when the sample volumes are swept in eight steps (a-g) for a 450 keV thallium primary beam. The correlation coefficient function pij(t) of the signal si(t) at the ith sample volume and sj(t) at the kth sample volume is described by cu(~)
pij(~) = [ci,~(0)]~/2[Q. /0)11/2 where C~j(r) is the cross-correlation function given by
C~j(v) = [~ ~(t)gj(t + "C) dt d - oQ
where g,.(t) = si(t) - s D ) , and the integration time in this case is 2.8 ms. The sample volume moves from the boundary to the inner region of the
Y. Hamada /Fusion Engineering and Design 34-35 0907) 25-35
3"0 h/ aI',~,,,A~
h
2i
~
-0.5
z.065[~
,
,
22
,
,
23
,~
0.0 i: .
.
.
.
.
.
.
'
23 .
,
, 22.1
,
22.2
22.3
4 ..... .
22
2.5 22.0
24
....... 21
.
.
31
, ]-0.6
24
/
-0.31
22.0 ,.
22.1 ,
,
50
100
50
100
,t'° 4 ~2
22.2 ,
0
,
22.3 ,
/
.~ ~-o.4
0
0
. . . . . . . .
.--.21~
~1
-0.8
-0.55 22.0
Time (ms)
22.1
22.2
Time (ms)
22.3
0
0
~.x .~
~._....,__~ 50
.
100
Frequency (kHz)
Fig. 6. T y p i c a l t i m e b e h a v i o r s , e x p a n d e d views, a n d F o u r i e r spectra of the sum o f the s e c o n d a r y current, N D ( n o r m a l i z e d difference between the u p p e r a n d l o w e r d e t e c t o r currents) a n d t o r o i d a l shift ( n o r m a l i z e d difference between left- a n d r i g h t - h a n d d e t e c t o r currents (idl , id), defined b y the relation ( i d l - ia)/(ia~ + iar).
plasma, by changing the poloidal sweep voltage. The characteristics of the correlation curves change rapidly near the plasma boundary. The dominant frequency of the drift-wave turbulence near the core plasma is about 100-200 kHz, and the turbulence has a fairly short correlation time, while the turbulence at the plasma boundary is characterized by a long correlation time of the order of 10 ps and low frequency oscillations. The short correlation length inside the plasma (as shown in Fig. 4) means that the role of the path integral effect on the density turbulence is not dominant [201. The cross-correlation coefficient functions in the inner region show that the main turbulence propagates in the electron diamagnetic drift direction in the core region of the OH plasma. Because the direction of the arrays of the sample volumes near the plasma center ((e) of Fig. 4) is rather poloidal, we are able to obtain a poloidal propagation velocity of about 6 km s - 1 by a shift of peaks of the correlation curves. This velocity is a factor of about 2 faster than the fluid velocity, i.e. the total of the diamagnetic drift and E/B drift velocity. The total velocity is smaller than the velocity obtained by the HIBP experiments in the
TEXT tokamak [2-4]. The change in the characteristics of the turbulence along the minor radius was also found recently in TFTR, using BES [5]. The TFTR results showed that the turbulence propagating into the ion diamagnetic direction (ITG mode) dominates in the inner region of the hot core. Fig. 5 shows the correlation coefficient functions and positions of sample volumes when the beam energy is 300 keV [9]. In this case, the sample volume moves from the boundary to the inner part, and again to the boundary. Because the sample volume at the lower plasma boundary is small, a more local measurement of the turbulence is possible. The correlation time becomes longer towards both upper and lower plasma boundaries. The direction of the propagation of the turbulence changes from the ion diamagnetic drift to the electron diamagnetic drift as the sample volumes are swept from (b) to (c). The change in the correlation time in the turbulence at the plasma edge was recently observed by reciprocating electric probes [24,25]. We have verified this by the non-perturbative diagnostic method of the HIBP, and have shown that only a small monotonic change occurs towards the cen-
Y. Hamada / Fusion Engineering and Design 34-35 (1997) 25-35
32
electron diamag., ion diamag. i f
_.
300 keV
250
3[~---~J ~
'
~ 2 t ~ ~
200
¢~ 1r / . - ~
I50
0
-20
0
~
~
~
J
~
,~"~l~'~'~J
~
~
J
~'-~[~ ^ ~ ] , ] ~ " ~ / A ' ~ - ~ ' ~ - ~ ( 1 , 3 )
(1,4)
]~A~]-~A'----d~--~A'-~$~---'A'~tI~-d/~)----ly~----~-'-~-t(1,2) 20
0
0
0
0
0
0
0
20
(b) ~ 1
g
~0
3
(1,4)
(c) \ < S0 PlasmaAxis
\
1 /" J
,
i
~
(1,2)
eD
o.o
X
,
9DO
-20
0
20
0
0
0
0
0
0
0
20
<~
-20
0
20
0
0
0
0
0
0
0
20
(;-,
-50 -100
A
(g) \ I000
Major Radius (ram)
1100
1)
V Delay Time (,u s)
Fig. 7. Positions of sample volumes and correlation coefficient functions of the S U M , N D and ( ( S U M ( l ) + SUM(2))(ND(1) -N D ( 2 ) ) ) , which is p r o p o r t i o n a l to the correlation of the density and local electric field, at 300 keV.
ter of the plasma column. The noise is mainly from the current amplifier of the metal plate detectors. The sharp peak in the autocorrelation coefficient function of the ith step in Fig. 5 results from the circuit noise. The amplifier frequency range extends over 300 kHz and shows a sharp peak. The correlation curves in Figs. 4 and 5 are statistically stable, because of the high SNR. Similar correlation curves are obtained if we reduce the integration time to 0.4 ms.
3.2. Potential turbulence The measurement of the potential turbulence does not have a high SNR in small-scale, high frequency potential turbulence, because N D (difference between secondary currents normalized by their sum) has a poorer sensitivity (3 kV/ND for 450 keV beam and slit height of 3 mm in the JIPP-TIIU HIBP) in a higher voltage HIBP. The anticipated level of the potential fluctuations in the core may be about 10 V when Te = 1000 keV and fie/n~ = 0.01, if Boltzman's law is assumed. Therefore, for the SNR -- 1 measurement of the potential fluctuation in the core, we need to measure a small (0.003) and fast fluctuation of ND. The correlation analysis helps to improve the SNR. Therefore, the small-scale potential fluctuation measurement with
a high SNR is usually possible in the outer area, where the level of the turbulence is high. However, we have observed that the tokamak plasmas often have a large-scale potential fluctuations around 30 kHz [8,10]. Fig. 6 shows typical time behaviors, expanded views, and Fourier spectra of the intensity of the secondary current, the N D and the toroidal shift (normalized difference of the left- and right-hand detector current) (id,, idr), defined by the r e l a t i o n (idl - - idr)/(idl Jr /dr). The sample volume is at the step (d) of Fig. 7. Because the ratio of N D to the potential or beam energy is about 2 kV/ND in this case, the potential fluctuation or beam energy fluctuation in Fig. 6 is about 300 Vp_ p. F r o m the Fourier spectrum of ND, we can observe that the oscillations with frequency less than 40 kHz are dominant in ND. To verify that these oscillations are not induced by the several power supplies of the HIBP system, we have checked the ripple of all the power supplies and have found that these ripples are too small to explain the observed fluctuation. In addition, these oscillations are not observed when the plasma is replaced by the gas. We were able to perform this gas ionization experiment with the same level of SNR as that in the plasma experiment, because the detector currents were adjusted to almost the same level in both cases.
Y. Hamada / Fusion Engineering and Design 34-35 (1997) 25-35
33
250 keV 250
electron diamag, ion diamag. < I > (a) Co) (c) (d)
(e)
(f)
(g)
(h) (1,6)
150
\ (b
N
50
Plasma
]
(1,1) -20
(o)'~
Axis
0
20
2
(d)\[ ,,
0.0
0
0
i I
&
-50
20
.,
•
~' '
IiO0
1(300 Major
Radius
(nun)
0
0
20
0
,
11 . i
....
0
-2o o 2o o Delay Time (/~ s)
II
O
'F
• ~----,
,
~
0
J
z<~ .. lo. u / v
0
~ ,
<
-I00
900
eg \
0
0
,
,
0
0
I -
(i,3)
--
0
0
J.
r~
.
.
.
" ~1 ~T
,
T
T ,
o
o
o
o
o
Fig. 8. Positions of sample volumes a n d correlation coefficient functions of the S U M , N D a n d ( ( S U M ( I ) + ND(2))>, which is proportional to the correlation of the density and local electric field, at 250 keV.
The observed oscillation in N D in Fig. 6 correlates with the horizontal motion of the secondary beam at the detector. This implies that the poloidal magnetic field changes at a high frequency, because the horizontal deflection is induced only by the poloidal magnetic field. As mentioned, a parallel plate analyzer records the energy of the kinetic motion only in the analyzer plane (vertical and symmetry plane), i.e. eVo out of the total energy (eVt). The relation eVo = eVt cos2(~b) holds, where (b is the out-of-plane entrance angle of the secondary beam to the analyzer• We performed the potential measurement by rotating the energy analyzer horizontally around the vertical axis, with a fixed point of the middle of the entrance slit of the analyzer, only changing the out-of-plane entrance angle. Because the phases of the toroidal motions and the energy in the coherence analysis do not change in this series of the experiments, we can conclude that the N D oscillation does not result from the horizontal deflection (change of the outof-plane entrance angle)• Figs. 7 and 8 show the correlation coefficient functions of the sum of the upper and lower plate currents (SUM), ND, and ((SUM(I) + S U M ( 2 ) ) ( N D ( 1 ) - ND(2)>, which is proportional to the correlation of the density and local electric
20
i (1,1)
20
it ,
/
o
20
SUM(2))(ND(1)-
field for 300 keV and 250 keV thallium beams [8]. The estimated mode number of the dominant oscillation in N D in Fig. 7 is m = 0, because the phase shift of the correlation analysis of N D for five sample volumes is very small• The peak values of the correlation coefficient functions are almost 1. Therefore, we can conclude that these large potential fluctuations are large scale and quasi-coherent. However, we cannot observe the quasi-coherent mode in the case of the 250 keV beam, as shown in Fig. 8. This implies that, at the boundary layer, these fluctuations are not observed. The large fluctuations in N D may be ascribed to the local potential change at the sample volume. However, these energy changes have little correlation with other measurements of the core plasma, such as multi-channel ECE signals and reflectometry signals. These oscillations are expected to be a global mode, because the mode number is m = 0 and a high correlation with at least one channel of the eight-channel ECE signals or radial scanned reflectometry signals should be observed. At present, we ascribe these energy changes to the interaction with the turbulence in the tokamak plasmas. This is because the radial phase velocity of the turbulence is so fast that there is the possibility of resonant interaction of the beam with the turbulence, and the occurrence of a large energy exchange between the turbulence and the beam.
34
Y. Hamada / Fusion Engineering and Design 34 35 (1997) 25-35
The cross-correlation between the sum and difference of ND, which may be proportional to the particle flux electrostatically driven by the plasma turbulence, is found to be statistically reliable, as is shown in Figs. 7 and 8. The calculated particle confinement time based on this correlation (in the case of the step (d) of Fig. 8) is 1.5 ms, while the energy confinement time is about 10 ms. Magnetic turbulence measurement was attempted intensively in the TEXT tokamak [26] and later in the JIPP T-IIU. It tends to give a much larger fluctuation level at the plasma boundary than that in magnetic probe measurement. It is suspected that the density fluctuation contaminates the normalized difference of the right- and lefthand detector currents through the toroidal wave number [261.
4. Future improvements in HIBPs
Although the experiment with the present set-up is still fruitful for the study of tokamak turbulence, the technical issues for the future HIBP are as follows. 4. I. Detector development
The turbulence measurement in the core plasma is limited in the low density case in the present experiment. A low noise detector would expand the applicability of the HIBP. The micro-channel plate (MCP) detector saturates at the high intensity secondary beam used for turbulence measurement in HIBPs. It is necessary to develop an efficient low noise detector (quantum detector) to replace the simple stainless steel plate with a low noise electronic amplifier.
5. Conclusions
By the intensive efforts mainly of the group of Prof. R. Hickok, study of turbulence in tokamak plasmas with an HIBP has greatly improved. However, there are a number of basic problems to be solved, as are described in this paper. (1) The average poloidal wave number determined by the HIBP is very small and the propagation velocity is much faster than the poloidal rotation velocity. This is in contradiction with the drift wave theory, while other diagnostics, such as FIR scattering and BES, generally agree with the theory. (2) The large energy exchange in the secondary beam energy observed in the TEXT and JIPP T-IIU tokamaks may be explained by the acceleration of the beam by the turbulence. Because the basic principle of the measurement of the space potential in the plasma with an HIBP may be only applicable to the static potential, the measurement of the turbulent electric field must be carefully analyzed, although the transit time of the beam across the plasma is order of 0.1 gs, which is smaller than the observed characteristic time of the fluctuations. (3) The measurement of the magnetic turbulent field in the plasma with an HIBP still contains large errors. The main reason for this problem may be that the applicability of the probe's principles is limited to the static field. Although an HIBP has unique potential for local density, electric and magnetic turbulence measurements, it is still far from the established tool for the study of turbulence. Intensive research is necessary to analyze its applicability. The study of turbulence with an HIBP always requires careful checking of the applicability of the probe's basic principles.
4.2. M u l t i - b e a m H I B P
This will enable us to perform two-dimensional study of the turbulence. The present analyzer and detector system can easily detect the multi-secondary beams, if the beam is separated in the toroidal direction. The generation of the multibeam by an accelerator may be possible, because a television with three electron beams is available.
References
[1] F.C. Jobes and R.L. Hickok, A direct measurement of plasma space potential, Nucl. Fusion 10 (1970) 195. [2] T.P. Crowleyet al., Heavy ion beam probe wavenumber measurement from the TEXT tokamak edge, Nucl. Fusion 32 (1992) 1295. [3] D.W. Ross et al., Dispersion relation of density fluctuaa-
Y. Hamada / Fusion Engineering and Design 34-35 (1997) 25-35
[4]
[5] [6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
tions observed by the heavy ion beam probe in TEXT, Nucl. Fusion 31 (1991) 1355. J.W. Heard et al., Broadband density fluctuation measurements using ion beam probe in the Texas experimental tokamak, Phys. Plasmas 2 (1995) 3360. R.J. Fronck et al., Long-wavelength density turbulence in the TFTR tokamak, Phys. Rev. Lett. 70 (1993) 3736. D.L. Brower, S.K. Peebles and N.C. Luhman, Jr., The spectrum, spatial distribution and scaling of microturbulence in the TEXT tokamak, Nucl. Fusion 27 (1987) 2055. Y. Hamada et al., Proc. 15th Int. Conf. on Plasma Physics and Controlled Nuclear Fusion Research, Seville, 1994, vol. 1, IAEA, Vienna, 1995, p. 301. Y. Hamada et al., Potential fluctuations and large coherent modes observed by a heavy ion beam probe in the JIPP T-IIU tokamak, in press. Y. Hamada et al., Transition of fluctuation characteristics near the plasma boundary observed by a heavy ion beam probe in the JIPP T-IIU tokamak, in press. H.Y.W. Tsui et al., Observation of a quasi-coherent mode in the Texas experimental tokamak, Phys. Fluids B 5 (1993) 1274. J.C. Forster et al., Study of density and potential fluctuations in the TEXT tokamak with a heavy ion probe, Trans. Plasma Sci. 22 (1994) 359. Y. Hamada et al., Proposal of a single sweep measurement of a potential profile in tokamak plasmas by high voltage heavy ion beam probe, J. Plasma Phys. Fusion Res. 69 (1993) 1050. Y. Hamada et al., Measurement of profiles of the space potential in JIPP T-IIU tokamak plasmas by slow poloidal and fast poloidal sweeps of a heavy ion beam, Plasma Phys. Controlled Fusion 36 (1994) 1743. Y. Hamada et al., Improvement of a 500 keV heavy-ionbeam probe for JIPP T-IIU tokamak, Rev. Sci. Instrum. 66 (1995) 321.
35
[15] K. Toi et al., Proc. 14th Int. Conf. on Plasma Physics and Controlled Nuclear Fusion Research, Wurzburg, 1992, vol. 1, IAEA, Vienna, 1993, p. 301. [16] P.M. Schoch et al., TEXT heavy ion beam probe, Rev. Sci. Instrum. 57 (t986) 1825. [17] T.S. Green and G.A. Proca, A parallel plate electrostatic spectrograph, Rev. Sci. Instrum. 41 (1970) 1409. [18] Y. Hamada et al., Shaped electrode system for high voltage parallel plate analyzer, Rev. Sci. Instrum. 63 (1992) 4446. [19] Y. Hamada et a1., Mesh effect in a parallel-plate analyzer, Rev. Sci. Instrum. 65 (1994) 1606. [20] J.W. Heard et al., A path integral effects in heavy ion beam probe density measurements, Rev. Sci. Instrum. 64 (1993) 1001. [21] A. Fujisawa et al., Active control of beam trajectories for heavy ion beam probe on helical magnetic configurations, Rev. Sci. Instrum. 63 (1992) 3694 (and also in this conference). [22] J.J. Zielinski, S.C. Aceto et al.0 In situ analyzer calibration methods for heavy ion beam probes installed in stellarator-like devices, Rev. Sci. Instrum. 63 (1992) 4574. [23] Y. Hamada et at., Calibration of a heavy ion beam probe in JIPP T-IIU tokamak by gas puffing, in press. [24] M. Endler et al., Experimental and theoretical investigation of density and potential fluctuations in the scrape-off layer of ASDEX, Proc. 20th Euro. Conf. on Controlled Fusion and Plasma Physics, Lisboa, 1993, Vol. 1, p. 301. [25] A.V. Filippas et al., Conditional analysis of floating potential fluctuations at the edge of the TEXT experimental tokamak upgrade (TEXT-U), Phys. Plasmas 2 (1995) 839. [26] B.Z. Zhang et al., Investigation of the HIBP toroidal beam motion as a method for measuring broadband magnetic fluctuation, Proc. US Japan Workshop on Technical Issues in the Application of a Heavy Ion Beam Probes, Troy, NY, 1993.