Study of Sawtooth Oscillations on Aditya Tokamak by Electron
Cyclotron Emission Measurements
Hitesh Kumar B. Pandya, K. K. Jain and Aditya Team
Institute for Plasma Research, Bhat, Gandhinagar-382 428 India
Abstract. Experimental investigation of sawtooth oscillations in ohmic plasma of medium sized Aditya
tokamak has been performed by electron cyclotron emission measurement diagnostics. A multi-channel
Ka-Band radiometer, which measures second harmonic frequencies (30 – 40 GHz) and other multi-channel
E-Band radiometer, which measures third harmonic frequencies (63 – 84 GHz) have been used for these
measurements. The sawtooth oscillation features are presented. The sawtooth period and amplitude
dependency on measurable plasma parameters is determined by using appropriate scaling laws.
Measurements at many radial location of the sawtooth oscillation have been found to be advantageous for
heat pulse propagation study. A correlation study and temporal and spatial propagation of the heat pulse has
been discussed.
Email of Hitesh Pandya : hitesh@ipr.res.in
1. INTRODUCTION
A regular periodic behavior of the tokamak core plasma parameters like electron
temperature, density and other radiations manifest a slow increases in the amplitude
followed by a rapid drop. This behavior is known as sawtooth oscillation. There is also
opposite development that is called inverse sawtooth at outside core plasma (inversion
radiation). In 1974, von Goeler et al [1] to first time measured the sawtooth oscillation.
This periodic oscillation degrades the total energy as well as particle confinement at
plasma core. This makes important to have detailed understanding of sawtooth
phenomena.
Kadomtsev[2] gave the first model to explain this phenomenon. According to his
model the generated internal kink mode instability due to the safety factor on axis q0
below one, become stable when q0  1. This model gives good physical explanation of
sawtooth oscillation. However, this model cannot convincingly explain the experimental
observations. The sawtooth crash time scales observed in JET[3] are inconsistent with
this model. Further, it was discovered in experiments on TEXTOR[4] and TEXT[5] that
there is sawtooth oscillation below unity q0 also. Porcelli and coworker[6] gave the
explanation for sawtooth oscillations with q0 below unity. Review paper on this topic was
published by Kuvshinov and Savrukhin[7]. Incomplete reconnection in sawtooth crashes
was studied on ASDEX-U[8]. The numerical simulation of the sawtooth oscillation had
also been done[8,9]. The tailoring of sawtooth oscillation had been done by using RF
heating like electron cyclotron resonance heating (ECRH)[10]. The oscillation was
suppressed, when ECRH absorbed at particular position in the plasma[11].
The simultaneous measurement of sawtooth oscillation at several radial locations
is useful to study the heat pulse propagation and estimate the heat diffusion
coefficient[12,13]. These measurements give the physics of transport of heat and particles
in tokamak plasma. This study of heat pulse propagation is interest of this paper. This
paper reports the sawtooth oscillation measurement at several radial locations during the
Aditya plasma (Ro=75 cm, a=25 cm)[14] discharge. A Ka-Band (27- 39 GHz) radiometer
of eight channels and other multi-channel E-Band radiometer[15], which measures third
harmonic frequencies (63 – 84 GHz) are used for this measurement. The estimation of
heat diffusion coefficient is presented. The dependence of the sawtooth period on the
measurable plasma parameters[7,16,17] is determined by using the appropriate scaling
law and presented in the paper. The scaling laws derived from second harmonic and third
harmonic ECE measurements are compared and discussed.
A brief description about the radiometer and experimental setup is given in section
2. In section 3, Experimental observations of sawtooth oscillation, heat pulse
propagation, scaling law for sawtooth period and related discussion are presented. The
conclusions of the study are described in section 4.
2. THE EXPERIMENTAL DEVICE AND DIAGNOSTIC
This experiment is conducted on Aditya tokamak[14]. Aditya is a medium-sized
tokamak of major radius 0.75 m and limiter radius 0.25 m with circular plasma. The
tokamak has carbon limiter. The experiment is carried at the toroidal magnetic field of
0.75 Tesla and electron density of 1.8 – 3 1019 m-3.
The eight channels Ka-Band and multi-channels E-Band (63 – 84 GHz)
radiometers are used as diagnostic tools for sawtooth oscillation measurements. At a
toroidal field of 0.75 Tesla, we measure extraordinary mode (X-mode) optically thick
second harmonic cyclotron radiation between 33 to 40 GHz and optically thin third
harmonic radiation between 63 – 84 GHz. The radiation of this frequency range (33 – 40
GHz) is acquired in first five channels of the Ka-Band radiometer. Remaining three
channels are out of plasma cross-section. These three channels do not acquire the second
harmonic cyclotron radiation. This can be perceived from figure 1. ECE radiation at this
frequency range depends critically on the
electron density. There is cut off and
resonance effects at the typical Aditya
plasma density. These effects reduce the
detected ECE signals in all the channels. It is
not possible to provide absolute electron
temperature
information
from
this
measurement. However, the measurement
appears useful to study sawtooth oscillation.
70
60
2Fce
Frequency (GHz)
50
Fuc
40
Fuh
32.1
38.9
Fce
37.2
35.5
30
33.8
30.4
28.7
27
20
Flc
10
0
-25
-20
-15
-10
-5
0
5
10
15
20
25
r (cm)
FIGURE 1 Characteristics frequencies
The detailed design of the E-Band radiometer is described elsewhere[15]. The
Ka-Band radiometer design is distinct from traditional radiometer. The design consists of
band pass filter of pass band frequency 26 – 40 GHz, two low noise high gain amplifiers
of frequency 26 – 40 GHz and eight channel power divider (Figure 2). The cavity filters
of different central frequency but same bandwidth of 400 MHz are connected to each
channel out put of the power divider. The center frequency of the cavity filters is varying
from 27.0 GHz to 38.9 GHz in step of 1.7 GHz. A Schottky barrier diode detector is
connected to the output of each cavity filter. The block diagram of the radiometer is
shown in figure 2. The integration of the band pass filter, two high gain amplifiers and
eight channel filter bank construct the radiometer without a mixer and a local oscillator.
The cyclotron radiation is collected from the Aditya plasma through vacuum view
port by a Ka-Band (or E-Band) horn antenna kept at low field side and mid plane of the
tokamak. The collected radiation is transmitted through oversized S-Band wave-guide.
There are two taper transitions of Ka-band (E-Band) to S-Band at the ends of the over
sized wave-guide. The transmission wave-guide is connected to the radiometer system
through wave-guide to co-axial converter. The total transmission power loss is 12 dB.
The total power gain of the two amplifiers is 62 dB and sensitivity of the diode detector is
1000 V/W. The measurement power sensitivity of the radiometer is 108 V/W. The noise
temperature of the radiometer is approximately 3 eV
The temporal resolution depends on time response of the diode detector and video
amplifier bandwidth. The time response of the detector is 1 sec. The video amplifier
bandwidth is 20 KHz. This limits the temporal resolution to 50 sec, because of video
amplifier. The output of the amplifiers are fed into the opto-isolators and then acquired
by INCAA 5548 module with sampling frequency of 125 kHz.
The electron temperature Te determined by the cyclotron radiation power
measured in each channel of the radiometer is averaged over a finite plasma volume. This
plasma volume determines the spatial resolution of the radiometer. The cavity filter
bandwidth (400 MHz) gives the radial resolution of 0.8 – 1.3 cm. The vertical resolution
is determined by the beam width of the
antenna. It is rather poor (~ 10 – 3 cm) due
TAPER Ka-S BAND
TRANSITION FROM
to low directive gain of the antenna.
W/G TO COAXIAL
HORN
BAND PASS
FILTER
26 - 40 GHz
3 METRE LONG OVERSIZE W/G
TWO STAGE AMPLIFIERS
GAIN = 62 dB
CAVITY FILTER
DETECTOR
8-WAY POWER
DIVIDER
FIGURE 2 Block diagram of Ka-Band radiometer
The
relation
between
the
radiometer received signal and plasma
emissivity can be found by calibrating the
radiometer. Employing a hot and a cold
black body source, we calibrated the KaBand radiometer and determined the
calibration coefficient (eV/V) for each
channel. The electron temperature can be
evaluated by multiplying the calibration
coefficient with the out put signal of the
radiometer channel.
3. ANALYSIS OF SAWTOOTH OSCILLATION
The experimental parameters of the Aditya plasma discharge are as follows. The
plasma current is in the range of 60 – 70 kA. The electron temperature is around 300
eV[18]. We present experimental results and related discussion in this section.
3.1 General Feature of Sawtooth
The temporal behavior of the
signal levels in first five channels of
Ka-Band radiometer within 50 – 60 ms
is depicted in figure 3. The nice
inverse sawtooth oscillations are
illustrated. All the measurement radial
locations (out board) are after
inversion radius. The multi channels
E-Band radiometer can measure
simultaneously sawtooth and inverse
sawtooth. It is exhibited in figure 4.
The transition from sawtooth to
inverse sawtooth can be perceived
from this figure and it is at 68.7 cm,
major radius for E-Band radiometer
measurements. Typical time period of
sawtooth oscillation is 0.71 to 0.94 ms.
Ffi
FIGURE 3 Sawtooth oscillation in Ka-band radiometer
3.2 Heat Pulse Propagation
The transport physics should be understood to get success in the thermonuclear
fusion[19]. It is useful to understand the basic interaction in the fusion plasma. The main
aim of the transport study is to evaluate the transport coefficient. There are two types of
methods to evaluate the transport coefficient, viz: (1) Static transport analysis and (2)
Perturbative experiments. In static transport analysis, there is considerable amount of
error introduced from both systematic as well as random. Thus, it is difficult task to
evaluate the transport coefficient by static method. In perturbative method, a small
perturbation either externally or internally is given to a stationary plasma state. Then a
dynamic evaluation of the transport coefficient can be derived from the evaluation of
plasma parameters like electron temperature, density or current density. The sawtooth is
the good example of internal perturbation of the plasma. In this the sawtooth oscillation
induced heat pulse propagation is analyzed and that gives an evaluation of the
incremental electron thermal diffusivity. In 1977, Callen and Jahns established this
method[12]. After that many experiments were used this method to derive the diffusivity.
Same method will be used to analyze our measurements.
The linearized form of simple diffusion equation is given by[12]
 t  32 T    
e
ep
 

Te
r
r  r
r
(1)
Where Te is the observed electron temperature fluctuation. ep is the generalized
electron-heat-conduction coefficient that governs the pulse evolution.
The approximate solution of equation (1) for a single isolated pulse subjected to the
condition Te  0 for r   in spatial region of interest (aD << r<< a) can be
expressed as
8
 t p 
 t

Te   a D Q
 exp   p t  (2)
2 
t
n
r
3
e




Fi
Where Q is the electron energy density in each
heat pulse, aD is the disruption radius, ne is the
electron density and tp is a time when the peak of
Te occurs. The expression for tp is given by
3 2
(3)
tp  r
8  ep
The above equation (3) is compared with
experimental data and ep is evaluated.
The propagation of inverse sawtooth pulse is
depicted in figure 5. We illustrate a functional
relation between the peak arrival time tp and square
of radial locations of the ECE measurement channel
in figure 6a (i.e. for E-Band radiometer) and
FIGURE 4 Sawtooth oscillation in E-Band
figure 6b(i.e. for Ka-Band radiometer). The inverse of the slop of these graphs give the
value of thermal diffusivity eHP . These are 93 m2/sec for E-band radiometer with
correlation coefficient 0. 92 and 62 for Ka-Band radiometer with correlation coefficient
0.98. These values indicate that the heat propagation is a ballistic type[20].
FIGURE 5 Heat pulse propagation (a) E-Band radiometer (b) Ka-Band radiometer
3.3 Scaling of the Sawtooth Period and Amplitude
It is required to investigate, the dependence of the sawtooth period on the plasma
parameters for tailoring the tokamak hot plasma condition to achieve ignition. Besides,
there are great variations in the sawtooth period in experiments on different tokamaks and
FIGURE 6 Data comparison with diffusive model for (a) E-Band radiometer (b) Ka-Band radiometer
in different operating regimes. List of the some experimental and theoretical scaling laws
for the sawtooth period are given in ref. [21,7]. Here we present the scaling law for the
Aditya tokamak plasma. These are shown in figure 7 for the period and figure 8 for the
amplitude.
FIGURE 7 scaling law (a) for sawtooth period (a) sawtooth amplitude
4 CONCLUSIONS
Experimental observations of the sawtooth oscillations on Adiya ohmic plasma have been
presented. Two radiometers E-Band (60 – 90 GHz) and Ka-Band (27 - 39 GHz) have
been utilized for third harmonic and second harmonic cyclotron radiation measurements
respectively. The measurements could not give electron temperature information.
However, the measurements appear to be useful to study physical phenomena like
sawtooth oscillations. The features of sawtooth oscillation have been presented. Multi
location ECE measurements facilitate study of sawtooth heat pulse propagation. The
thermal diffusivity is evaluated. This indicates that the heat pulse is in ballistic nature.
The scaling laws for the sawtooth period and amplitude are furnished.
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