- Email: [email protected]
Probe measurements of ICRF surface waves in the TORTUS tokamak
Fusion Engineering and Design 12 (1990) 197-201 North-Holland
PROBE MEASUREMENTS
M.J. BALLICO Plasma
Physics
197
OF ICRF SURFACE WAVES IN THE TORTUS
TOKAMAK
and R.C. CROSS
Department,
University
01 Sydney,
Sydney,
NS W 2006, Ausrralia
Experimental results are presented on the behaviour of Alfven surface waves at frequencies of interest for ICW heating. These waves were observed, using a poloidal array of magnetic probes, to propagate as a guided beam along steady magnetic field lines in the plasma edge.
1. Introduction In ICRF heating experiments, it is commonly observed that a significant fraction of the input power is dissipated in the plasma edge. This effect is still not well understood, partly because there is very little data available concerning the wave fields in the plasma edge. In this paper, measurements are presented of the edge wave magnetic fields generated by fast wave antennas in the TORTUS tokamak. All measurements were made in single ion species plasmas and at frequencies in the range 1 < o/wci < 4, where oci is the ion cyclotron frequency. In this frequency range, a large number of high Q fast wave cavity modes was expected on the basisof cold plasma calculations. However, cavity modes were observed only for the m = + 1 mode, where m is the azimuthal mode number. High m modes were also observed, not as cavity modes, but in the form of a narrow beam which propagated along steady magnetic field lines in the plasma edge. These results are consistent with the expected behaviour of Alfven surface waves in an inhomogeneous plasma. 2. Properties of ICRF surface waves
Theoretical results for Alfven surface waves at finite frequency have been presented previously, both for slab and cylindrical plasma geometries [l-4]. In essence, Alfven surface waves are fast Alfven waves which propagate in the plasma edge region and which are evanescent in the radial direction over the whole plasma cross-section,In a WKB sense,fast wave propagation in a cylindrical, single ion speciesplasma immersed in a z directed B field can be described by the approximate dispersion relation o2 = (k$ +kl)vi where VA is the
0920-3796/90/$03.50
Alfven speed, k: = kz + kg and ke = m/r. Hence, kz = o’/I$ - kz - m2/r2. In an inhomogeneous plasma, all kf > 0, m2 > 0 fast wave modes are radially evanescent near the plasma edge, since k: < 0 when IJ~+ co. In the body of the plasma, kf may be positive (body wave behaviour) or negative (surface wave behaviour). When w > Wci,surface waves exist only when m > 0. All first radial m > 0 modes propagate as surface waves at low (average) densities, but evolve into body waves at high densities. However, high m > 0 modes evolve into body waves only at densities much higher than those usually encountered in tokamak devices. Alfven surface waves have the property, when kz > 0, that the wave fields of all modes, other than m = + 1, peak near the plasma edge and become more highly localised at the edge as m increases (the fields vary approximately as r”‘). The m = + 1 mode is exceptional since the radial (b,) and poloidal (be) magnetic field components peak at r =O. The dominant wave magnetic field component for m > 1 surface modes is the b, component, which increases in relation to the other components, as m increases. The dominant wave electric field component is the radial (E,) component. Consequently, the Poynting and group velocity vectors for high m surface modes are directed closely parallel to the steady magnetic field, B. For TORTUS conditions, it is only the m = +l mode which has a significant radial component of the Poynting vector. Any poloidally localised source will generate a broad spectrum of modes. The implication of the above results is that the m = +l mode will form cavity modes, but high m modes will interfere constructively, propagating away from the source as a magnetically guided beam. Fast wave dispersion relations, for typical TORTUS parameters, are shown in fig. 1. For clarity, only a small sample of modes is shown in fig. 1. There is in fact a
0 1990 - Elsevier Science Publishers B.V. (North-Holland)
M.J. Ballico, R C. Cross / ICRF Surface Waves in the TORTUS tokamak
198
f?
'0
1
3
2
4
5
0
Fig. 1. Cold plasma, fast wave dispersion relations for deuterium with no = 2 X 1Ol9 m-‘, B, = 0.8 T, wall radius a = 0.14 m for m = 0, f 1, and + 5, where D = o/wci. The kz -z 0 branches are shown only for m = 0, + 1 and + 5 modes.
very broad spectrum of surface modes which propagate in the ICRF range, even in small devices[l]. The results in fig. 1 were computed for a cylindrical, current-free plasma with a density profile of the form n,(O < r < rO) =tl 0, n,(a) = O.Oln,, using a cubic fit in the region r,, < r < D to obtain a smooth transition with dnJdr = 0 at r= r,, and r= u, where u is the conducting wall radius (a = 14 cm) and r,, = 7 cm. Finite electron mass was included in these calculations in order to determine the mode behaviour at frequencies below the cutoff frequency where kz < 0. The kz < 0 branch of each mode has the remarkable and previously unnoticed property of being Alfven resonant at the surface locally satisfying the relation 02= k$i(l - W’/W~i). At the resonance layer, which moves towards the plasma edge as kt -f 0, a toroidally evanescent fast wave mode-converts to a high k, toroidahy evanescent ion cyclotron wave which propagates on the low n, side of the resonance layer. The wave fields at the plasma edge are strongly oscillatory in the radial direction, and the dominant edge wave magnetic field component is the be component.
3. Experimental
tally shielded antenna inserted in a top port and oriented with all conducting elements perpendicular to the steady toroidal field, B+, as shown in fig. 2. The poloidal extent of the centre conductor is 70 O.This antenna was designed to couple primarily to low m fast waves modes. Nevertheless, this type of antenna also couples to high m modes due to the poloidal discontinuity introduced by the radial feeds. A smaller antenna was also used to deliberately excite high M modes. This antenna consisted of a rectangular wire loop inserted in a 6 mm OD quartz tube formed in the shape of a rectangle of dimensions 10 cm X 3 cm. It was also inserted in a top port. It was located at the same minor radius as the large antenna (r = 11 cm) and could be rotated through 360 o to align the coil axis parallel or perpendicular to B (or at any other angle). Both the small and larger antennas were driven, via matching networks, at frequencies in the range lo-18 MHz. The antenna current was held constant at 20 A. The toroidal field, Be - 0.8 T, was chosen so that the excitation frequency could be varied in the range 1 -Zo/oci < 4 by operating either in pure hydrogen or in pure deuterium. The wave magnetic fields at the plasma edge were measured with poloidal and toroidal arrays of magnetic probes. The poloidal array was mounted inside an 8 mm OD quartz tube, surrounding the plasma poloidally at minor radius r = 11 cm as shown in fig. 2. The probe array consisted of 8 identical 20-turn coils wound on a flexible tube, spaced at intervals separated poloidally by loo and connected externally to coaxial cable via twisted leads within the flexible tube. The array was oriented to detect the poloidal (be) wave magnetic field component. A complete profile of be versus 19could be obtained in 5 or 6 discharges by moving the array between successivedischarges. The poloidal probe array
arrangement
The TORTUS tokamak is a small research device with major radius R = 44 cm and with a rectangular cross section, 25 cm x 33 cm, as shown in fig. 2. Two different antennas were used in the experiments described below. The first was an all-metal, electrostati-
Fig. 2. Experimental arrangement, showing the 70° sector antenna, the small rotatable antenna and the 8 coil poloidal probe array. The beam path from the small antenna to the probe array is also shown.
M.J.
Ballico,
R.C.
Cross / ICRF
Sur/oce
was located toroidally +67.5O away from the small antenna and - 112.5’ from the large antenna. The toroidal probe array consisted of 5 separate, identical coils inserted in 11 mm OD quartz tubes spaced at irregular intervals toroidally and mounted vertically through the top surface of the vacuum vessel. All 13 coils were fed to hybrid combiners [5] to eliminate electrostatic pickup and then to a multichannel mixer to extract both the amplitude of the wave magnetic field and its phase (with respect to the antenna current). Most of the data was recorded for nominally identical discharge parameters. The electron density. was ramped early in the discharge by puff filling to an on-axis peak of 2 X 1019 rnm3, both in hydrogen and in deuterium plasmas. The edge safety factor q(u) = 5.5 at peak plasma current (20 kA). The plasma remained well-centred both vertically and horizontally and the peak electron temperature was about 100 eV. The edge temperature, estimated from Langmuir probe measurements, was approximately 10 eV. The edge density, also measured with a Langmuir probe, was approximately 10% of the central density at the limiter radius (10.5 cm), dropping to zero at the vacuum vesselwall.
Waves
in the TORTUS
199
tokamak
b, antenna 2okA ‘II
J
10’Qnl-3
J--
1
K2
1
2o” 4o”
60” 70”
60” 90” loo0 llo” 120” 140” 20 10 tb-4 Fig. 3. Data obtained from the poloidal probe array using the small antemla aligned to generate a be near field.
0
4. Experimental results Typical probe signals, observed with the poloidal array, are shown in figs. 3, 4 and 5. These results were all obtained in deuterium, at f= 18 MHZ(o/w,i = 3 at R = 44 cm). The results shown in fig. 3 were obtained with the small antenna aligned with its axis perpendicular to the toroidal field in order to generate a strong be near field. A similar set of results, with the antenna rotated through 90” to generate a strong 4 near field, is shown in fig. 4. The results in fig. 5 were obtained with the large antenna. The poloidal angle, 0, defined in fig. 2, is taken to be zero on the high field side of the plasma, + 90 o at the top of the plasma, and -90” at the bottom of the plasma. Inspection of the raw data in figs. 3, 4 and 5 reveals the following features: (1) Distinct peaks in the b0 waveforms are observed simultaneously at all poloidal (and toroidal) locations, at several different times during the discharge. These peaks correspond to moderatively high Q cavity eigenmodes. Despite the fact that the small antenna excites a broad spectrum of modes, and despite the fact that at w = 3wCithe frequency is well above the cutoff frequency for a wide range of m > 0 modes (see fig. l), the eigenmode peaks are all due to the m = +l mode. Peaks occurring at different times during the density rise (up to t = 12 ms) correspond to different toroidal
mode numbers. The same modes appear, in reverse order, as the density falls (t > 12 ms). (2) At times during the discharge where there are no cavity modes, the magnitude of be is relatively small at most poloidal locations. However, be remains relatively large on B field lines passing through and near the antenna. In fig. 3, a large be signal is observed at poloidal locations 70 o < B < 90 O. The fluctuation level in the be waveforms is also large at these locations. A similar effect can be seen in fig.4 except that the magnitude of the guided signal is not as large. There is no evidence of a guided signal propagating from the antenna to the probe array via the longer toroidal path round the torus, nor does the short path beam travel more than once around the torus. We have determined that the beam is strongly localised in the radial direction but it is strongly attenuated in the toroidal direction, with an attenuation length about 30 cm. The mechanisms responsible for wave attenuation have not yet been identified, but are likely to include contributions from toroidally evanescent modes as well as phase mixing of propagating modes.
M.J.
200
Ballico,
R.C.
Cross
/ ICRF
Surface
There is also some evidence of a guided signal from the large antenna (fig. 5), since the be waveforms are relatively large and noisy at poloidal locations 90’ < 0 -c 130”. Since the large and small antennas are on opposite sides of the poloidal array, waves are guided to +80” from the small antenna and to +110° from the centre of the large antenna. The q signals in fig. 5 are also relatively large on the low field side (near 0 = f 180 o ), suggesting that the plasma may have moved to a large major radius. However, the in-out position signals were .identical for all results presented in this paper. Consequently, we believe that the large be signals on the low field side are associated with low M modes and the fact that the vessel walls are much nearer the plasma at 8= f180’ than at 8= f90’. Several tests were conducted to ensure that the observed wave signals were magnetic in origin and not associated with electrostatic pickup. We were also concerned that the small antenna might couple capacitively to the plasma through the surrounding quartz tube to draw a Langmuir current along steady magnetic field lines passing through the antenna. This effect is clearly
Waves in the TORTUS
tokamak 70”
heoting
ontenno
0” 3o” 60” 60” 9o” loo0
110° 120” 140°
180° -150° -120” -90” -60’ -30° 5
b, antenna
15
10
20
+4
Fig. 5. Data obtained from the poloidal probe array using the 70’ sector antenna. 1 O’“m-s
20”
4o” 60” 70” 60” 90”
100” 110” 120” 140° 10
0
20
tb>
Fig. 4. Data obtained from the poloidal probe array using the small antenna aligned to generate a 4 near field.
negligible since rotation of the antenna has a strong effect on the amplitude of the wave fields. Results qualitatively similar to those in figs. 3-5 were also obtained at f= 18 MHz in hydrogen, (O/Q = 1.5), and for a range of other frequencies and toroidal fields in deuterium. In all cases, cavity modes were observed only for the m = +l mode. A guided beam was also observed under ail conditions although its amplitude was found to decreaseat low n,, as indicated in figs. 3-5. The beam amplitude was also strongly dependent on the in-out position of the plasma, increasing as the plasma moved out. The above results are similar to previous observations made in TORTUS of magnetically guided shear Alfven and ion-ion hybrid waves [5]. They are also similar to observations made by Van Nieuwenhove et al. in TEXTOR and ASDEX, using probes at a fixed poloidal location [6,7]. These authors also observed a radially localised field structure, but excluded surface waves as a possible explanation since the structure was found to be independent of the plasma density, current and toroidal field. We disagree with these authors and
M.J.
Ballico,
R. C. Cross
/ ZCRF
find that a localised beam is entirely consistent with the behaviour of surface waves. The behaviour of any individual mode clearly depends on a variety of plasma parameters, but a beam contains a broad spectrum of modes. Since all fist radial high m modes propagate only in the plasma edge region, and since the Poynting vector for each mode is parallel to B, these modes combine to form a localised beam regardless of variations in the plasma parameters. The only variation we observe is a rapid fluctuation in the beam amplitude, directly correlated with MHD activity in the plasma edge. The most likely explanation for the guided beam observed in these experiments is that it represents a broad spectrum of surface waves. Several other possibilities can be rejected as being inconsistent with observations. A potential candidate is the ion Bernstein wave since it is launched most efficiently by current elements parallel to B and since the group velocity vector is closely parallel to B in the plasma edge. However, this wave is excited most efficiently when the w = 20,~ layer pass through the antenna [8]. In our experiments, we find that the guided beam is excited with roughly equal efficiency, regardless of the location of the o = 2~ layer. The existence of a radially localised, DC or RF current along the steady magnetic field lines, as described in ref. [6], is not excluded by our observations. Further experiments are planned to determine in detail the radial structure of the guided beam, and the precise location of the beam with respect to the vessel wall, the antenna radius and the plasma “edge”.
Surface
Waoes in the TORTUS
tokamak
201
References
PI M.J. Ballico and R.C. Cross, Fast Alfven eigenmodes in a cylindrical inhomogeneous plasma, Plasma Phys. Contr. Fus. 31 (1989) 1141-55. PI A.M. Messiaen, R. Koch, V.P. Bhatnagar, P.E. Vandenplas and R.R. Weynants, Analysis of the plasma edge radiation by ICRF antenna, Proc. 4th Joint VarennaGrenoble Int. Symp. on Heating in Toroidal Plasmas, Rome, 1984, Vol 1, p. 315. [31 M.J. Ballico and R.C. Cross, ICRF spectrum of fast Alfven eigenrnodes in a cylindrical current-carrying plasma, Physics of Fluids B, in press. [41 R. Van Nieuwenhove et al., Theoretical and experimental investigation of the impact of surface waves and bulk absorption on ICRF fields measured at the edge in tokamaks, 14th Eur. Conf. on Controlled Fusion and Plasma Physics (Madrid, Spain, 1987). Europhysics Conf. Abstracts, Vol llD, Part III, pp. 928-931. 151G.G. Borg and R.C. Cross, Guided propagation of Alfven and ion-ion hybrid waves in a plasma with two ion species, Plasma Phys. Contr. Fus. 29 (1987) 681-696. Fl R. Van Nieuwenhove et al., Observation of a localised rf electric field structure in the scrape-off layer during ICRF on TEXTOR and ASDEK, 16th Eur. Conf. on Controlled Fusion and Plasma Physics (Venice, Italy, 1989). Europhysics Conf. Abstracts, Vol13B, Part III, pp. 10651068. 171 R. Van Nieuweuhove et al., Observations of harmonics and parametric decay instabilities during ICRF heating on TEXTOR, 15th Eur. Conf. on Controlled Fusion and Plasma Heating (Dubrovnik, Yuguslavia, 1988), Europhysics Conf. Abstracts, Vol 12B, Part II, pp. 778-782. 181M. Brambilla, Theory of Bernstein wave coupling with loop antennas, Nucl. Fus. 28 (1988) 549-563.
PROBE MEASUREMENTS
M.J. BALLICO Plasma
Physics
197
OF ICRF SURFACE WAVES IN THE TORTUS
TOKAMAK
and R.C. CROSS
Department,
University
01 Sydney,
Sydney,
NS W 2006, Ausrralia
Experimental results are presented on the behaviour of Alfven surface waves at frequencies of interest for ICW heating. These waves were observed, using a poloidal array of magnetic probes, to propagate as a guided beam along steady magnetic field lines in the plasma edge.
1. Introduction In ICRF heating experiments, it is commonly observed that a significant fraction of the input power is dissipated in the plasma edge. This effect is still not well understood, partly because there is very little data available concerning the wave fields in the plasma edge. In this paper, measurements are presented of the edge wave magnetic fields generated by fast wave antennas in the TORTUS tokamak. All measurements were made in single ion species plasmas and at frequencies in the range 1 < o/wci < 4, where oci is the ion cyclotron frequency. In this frequency range, a large number of high Q fast wave cavity modes was expected on the basisof cold plasma calculations. However, cavity modes were observed only for the m = + 1 mode, where m is the azimuthal mode number. High m modes were also observed, not as cavity modes, but in the form of a narrow beam which propagated along steady magnetic field lines in the plasma edge. These results are consistent with the expected behaviour of Alfven surface waves in an inhomogeneous plasma. 2. Properties of ICRF surface waves
Theoretical results for Alfven surface waves at finite frequency have been presented previously, both for slab and cylindrical plasma geometries [l-4]. In essence, Alfven surface waves are fast Alfven waves which propagate in the plasma edge region and which are evanescent in the radial direction over the whole plasma cross-section,In a WKB sense,fast wave propagation in a cylindrical, single ion speciesplasma immersed in a z directed B field can be described by the approximate dispersion relation o2 = (k$ +kl)vi where VA is the
0920-3796/90/$03.50
Alfven speed, k: = kz + kg and ke = m/r. Hence, kz = o’/I$ - kz - m2/r2. In an inhomogeneous plasma, all kf > 0, m2 > 0 fast wave modes are radially evanescent near the plasma edge, since k: < 0 when IJ~+ co. In the body of the plasma, kf may be positive (body wave behaviour) or negative (surface wave behaviour). When w > Wci,surface waves exist only when m > 0. All first radial m > 0 modes propagate as surface waves at low (average) densities, but evolve into body waves at high densities. However, high m > 0 modes evolve into body waves only at densities much higher than those usually encountered in tokamak devices. Alfven surface waves have the property, when kz > 0, that the wave fields of all modes, other than m = + 1, peak near the plasma edge and become more highly localised at the edge as m increases (the fields vary approximately as r”‘). The m = + 1 mode is exceptional since the radial (b,) and poloidal (be) magnetic field components peak at r =O. The dominant wave magnetic field component for m > 1 surface modes is the b, component, which increases in relation to the other components, as m increases. The dominant wave electric field component is the radial (E,) component. Consequently, the Poynting and group velocity vectors for high m surface modes are directed closely parallel to the steady magnetic field, B. For TORTUS conditions, it is only the m = +l mode which has a significant radial component of the Poynting vector. Any poloidally localised source will generate a broad spectrum of modes. The implication of the above results is that the m = +l mode will form cavity modes, but high m modes will interfere constructively, propagating away from the source as a magnetically guided beam. Fast wave dispersion relations, for typical TORTUS parameters, are shown in fig. 1. For clarity, only a small sample of modes is shown in fig. 1. There is in fact a
0 1990 - Elsevier Science Publishers B.V. (North-Holland)
M.J. Ballico, R C. Cross / ICRF Surface Waves in the TORTUS tokamak
198
f?
'0
1
3
2
4
5
0
Fig. 1. Cold plasma, fast wave dispersion relations for deuterium with no = 2 X 1Ol9 m-‘, B, = 0.8 T, wall radius a = 0.14 m for m = 0, f 1, and + 5, where D = o/wci. The kz -z 0 branches are shown only for m = 0, + 1 and + 5 modes.
very broad spectrum of surface modes which propagate in the ICRF range, even in small devices[l]. The results in fig. 1 were computed for a cylindrical, current-free plasma with a density profile of the form n,(O < r < rO) =tl 0, n,(a) = O.Oln,, using a cubic fit in the region r,, < r < D to obtain a smooth transition with dnJdr = 0 at r= r,, and r= u, where u is the conducting wall radius (a = 14 cm) and r,, = 7 cm. Finite electron mass was included in these calculations in order to determine the mode behaviour at frequencies below the cutoff frequency where kz < 0. The kz < 0 branch of each mode has the remarkable and previously unnoticed property of being Alfven resonant at the surface locally satisfying the relation 02= k$i(l - W’/W~i). At the resonance layer, which moves towards the plasma edge as kt -f 0, a toroidally evanescent fast wave mode-converts to a high k, toroidahy evanescent ion cyclotron wave which propagates on the low n, side of the resonance layer. The wave fields at the plasma edge are strongly oscillatory in the radial direction, and the dominant edge wave magnetic field component is the be component.
3. Experimental
tally shielded antenna inserted in a top port and oriented with all conducting elements perpendicular to the steady toroidal field, B+, as shown in fig. 2. The poloidal extent of the centre conductor is 70 O.This antenna was designed to couple primarily to low m fast waves modes. Nevertheless, this type of antenna also couples to high m modes due to the poloidal discontinuity introduced by the radial feeds. A smaller antenna was also used to deliberately excite high M modes. This antenna consisted of a rectangular wire loop inserted in a 6 mm OD quartz tube formed in the shape of a rectangle of dimensions 10 cm X 3 cm. It was also inserted in a top port. It was located at the same minor radius as the large antenna (r = 11 cm) and could be rotated through 360 o to align the coil axis parallel or perpendicular to B (or at any other angle). Both the small and larger antennas were driven, via matching networks, at frequencies in the range lo-18 MHz. The antenna current was held constant at 20 A. The toroidal field, Be - 0.8 T, was chosen so that the excitation frequency could be varied in the range 1 -Zo/oci < 4 by operating either in pure hydrogen or in pure deuterium. The wave magnetic fields at the plasma edge were measured with poloidal and toroidal arrays of magnetic probes. The poloidal array was mounted inside an 8 mm OD quartz tube, surrounding the plasma poloidally at minor radius r = 11 cm as shown in fig. 2. The probe array consisted of 8 identical 20-turn coils wound on a flexible tube, spaced at intervals separated poloidally by loo and connected externally to coaxial cable via twisted leads within the flexible tube. The array was oriented to detect the poloidal (be) wave magnetic field component. A complete profile of be versus 19could be obtained in 5 or 6 discharges by moving the array between successivedischarges. The poloidal probe array
arrangement
The TORTUS tokamak is a small research device with major radius R = 44 cm and with a rectangular cross section, 25 cm x 33 cm, as shown in fig. 2. Two different antennas were used in the experiments described below. The first was an all-metal, electrostati-
Fig. 2. Experimental arrangement, showing the 70° sector antenna, the small rotatable antenna and the 8 coil poloidal probe array. The beam path from the small antenna to the probe array is also shown.
M.J.
Ballico,
R.C.
Cross / ICRF
Sur/oce
was located toroidally +67.5O away from the small antenna and - 112.5’ from the large antenna. The toroidal probe array consisted of 5 separate, identical coils inserted in 11 mm OD quartz tubes spaced at irregular intervals toroidally and mounted vertically through the top surface of the vacuum vessel. All 13 coils were fed to hybrid combiners [5] to eliminate electrostatic pickup and then to a multichannel mixer to extract both the amplitude of the wave magnetic field and its phase (with respect to the antenna current). Most of the data was recorded for nominally identical discharge parameters. The electron density. was ramped early in the discharge by puff filling to an on-axis peak of 2 X 1019 rnm3, both in hydrogen and in deuterium plasmas. The edge safety factor q(u) = 5.5 at peak plasma current (20 kA). The plasma remained well-centred both vertically and horizontally and the peak electron temperature was about 100 eV. The edge temperature, estimated from Langmuir probe measurements, was approximately 10 eV. The edge density, also measured with a Langmuir probe, was approximately 10% of the central density at the limiter radius (10.5 cm), dropping to zero at the vacuum vesselwall.
Waves
in the TORTUS
199
tokamak
b, antenna 2okA ‘II
J
10’Qnl-3
J--
1
K2
1
2o” 4o”
60” 70”
60” 90” loo0 llo” 120” 140” 20 10 tb-4 Fig. 3. Data obtained from the poloidal probe array using the small antemla aligned to generate a be near field.
0
4. Experimental results Typical probe signals, observed with the poloidal array, are shown in figs. 3, 4 and 5. These results were all obtained in deuterium, at f= 18 MHZ(o/w,i = 3 at R = 44 cm). The results shown in fig. 3 were obtained with the small antenna aligned with its axis perpendicular to the toroidal field in order to generate a strong be near field. A similar set of results, with the antenna rotated through 90” to generate a strong 4 near field, is shown in fig. 4. The results in fig. 5 were obtained with the large antenna. The poloidal angle, 0, defined in fig. 2, is taken to be zero on the high field side of the plasma, + 90 o at the top of the plasma, and -90” at the bottom of the plasma. Inspection of the raw data in figs. 3, 4 and 5 reveals the following features: (1) Distinct peaks in the b0 waveforms are observed simultaneously at all poloidal (and toroidal) locations, at several different times during the discharge. These peaks correspond to moderatively high Q cavity eigenmodes. Despite the fact that the small antenna excites a broad spectrum of modes, and despite the fact that at w = 3wCithe frequency is well above the cutoff frequency for a wide range of m > 0 modes (see fig. l), the eigenmode peaks are all due to the m = +l mode. Peaks occurring at different times during the density rise (up to t = 12 ms) correspond to different toroidal
mode numbers. The same modes appear, in reverse order, as the density falls (t > 12 ms). (2) At times during the discharge where there are no cavity modes, the magnitude of be is relatively small at most poloidal locations. However, be remains relatively large on B field lines passing through and near the antenna. In fig. 3, a large be signal is observed at poloidal locations 70 o < B < 90 O. The fluctuation level in the be waveforms is also large at these locations. A similar effect can be seen in fig.4 except that the magnitude of the guided signal is not as large. There is no evidence of a guided signal propagating from the antenna to the probe array via the longer toroidal path round the torus, nor does the short path beam travel more than once around the torus. We have determined that the beam is strongly localised in the radial direction but it is strongly attenuated in the toroidal direction, with an attenuation length about 30 cm. The mechanisms responsible for wave attenuation have not yet been identified, but are likely to include contributions from toroidally evanescent modes as well as phase mixing of propagating modes.
M.J.
200
Ballico,
R.C.
Cross
/ ICRF
Surface
There is also some evidence of a guided signal from the large antenna (fig. 5), since the be waveforms are relatively large and noisy at poloidal locations 90’ < 0 -c 130”. Since the large and small antennas are on opposite sides of the poloidal array, waves are guided to +80” from the small antenna and to +110° from the centre of the large antenna. The q signals in fig. 5 are also relatively large on the low field side (near 0 = f 180 o ), suggesting that the plasma may have moved to a large major radius. However, the in-out position signals were .identical for all results presented in this paper. Consequently, we believe that the large be signals on the low field side are associated with low M modes and the fact that the vessel walls are much nearer the plasma at 8= f180’ than at 8= f90’. Several tests were conducted to ensure that the observed wave signals were magnetic in origin and not associated with electrostatic pickup. We were also concerned that the small antenna might couple capacitively to the plasma through the surrounding quartz tube to draw a Langmuir current along steady magnetic field lines passing through the antenna. This effect is clearly
Waves in the TORTUS
tokamak 70”
heoting
ontenno
0” 3o” 60” 60” 9o” loo0
110° 120” 140°
180° -150° -120” -90” -60’ -30° 5
b, antenna
15
10
20
+4
Fig. 5. Data obtained from the poloidal probe array using the 70’ sector antenna. 1 O’“m-s
20”
4o” 60” 70” 60” 90”
100” 110” 120” 140° 10
0
20
tb>
Fig. 4. Data obtained from the poloidal probe array using the small antenna aligned to generate a 4 near field.
negligible since rotation of the antenna has a strong effect on the amplitude of the wave fields. Results qualitatively similar to those in figs. 3-5 were also obtained at f= 18 MHz in hydrogen, (O/Q = 1.5), and for a range of other frequencies and toroidal fields in deuterium. In all cases, cavity modes were observed only for the m = +l mode. A guided beam was also observed under ail conditions although its amplitude was found to decreaseat low n,, as indicated in figs. 3-5. The beam amplitude was also strongly dependent on the in-out position of the plasma, increasing as the plasma moved out. The above results are similar to previous observations made in TORTUS of magnetically guided shear Alfven and ion-ion hybrid waves [5]. They are also similar to observations made by Van Nieuwenhove et al. in TEXTOR and ASDEX, using probes at a fixed poloidal location [6,7]. These authors also observed a radially localised field structure, but excluded surface waves as a possible explanation since the structure was found to be independent of the plasma density, current and toroidal field. We disagree with these authors and
M.J.
Ballico,
R. C. Cross
/ ZCRF
find that a localised beam is entirely consistent with the behaviour of surface waves. The behaviour of any individual mode clearly depends on a variety of plasma parameters, but a beam contains a broad spectrum of modes. Since all fist radial high m modes propagate only in the plasma edge region, and since the Poynting vector for each mode is parallel to B, these modes combine to form a localised beam regardless of variations in the plasma parameters. The only variation we observe is a rapid fluctuation in the beam amplitude, directly correlated with MHD activity in the plasma edge. The most likely explanation for the guided beam observed in these experiments is that it represents a broad spectrum of surface waves. Several other possibilities can be rejected as being inconsistent with observations. A potential candidate is the ion Bernstein wave since it is launched most efficiently by current elements parallel to B and since the group velocity vector is closely parallel to B in the plasma edge. However, this wave is excited most efficiently when the w = 20,~ layer pass through the antenna [8]. In our experiments, we find that the guided beam is excited with roughly equal efficiency, regardless of the location of the o = 2~ layer. The existence of a radially localised, DC or RF current along the steady magnetic field lines, as described in ref. [6], is not excluded by our observations. Further experiments are planned to determine in detail the radial structure of the guided beam, and the precise location of the beam with respect to the vessel wall, the antenna radius and the plasma “edge”.
Surface
Waoes in the TORTUS
tokamak
201
References
PI M.J. Ballico and R.C. Cross, Fast Alfven eigenmodes in a cylindrical inhomogeneous plasma, Plasma Phys. Contr. Fus. 31 (1989) 1141-55. PI A.M. Messiaen, R. Koch, V.P. Bhatnagar, P.E. Vandenplas and R.R. Weynants, Analysis of the plasma edge radiation by ICRF antenna, Proc. 4th Joint VarennaGrenoble Int. Symp. on Heating in Toroidal Plasmas, Rome, 1984, Vol 1, p. 315. [31 M.J. Ballico and R.C. Cross, ICRF spectrum of fast Alfven eigenrnodes in a cylindrical current-carrying plasma, Physics of Fluids B, in press. [41 R. Van Nieuwenhove et al., Theoretical and experimental investigation of the impact of surface waves and bulk absorption on ICRF fields measured at the edge in tokamaks, 14th Eur. Conf. on Controlled Fusion and Plasma Physics (Madrid, Spain, 1987). Europhysics Conf. Abstracts, Vol llD, Part III, pp. 928-931. 151G.G. Borg and R.C. Cross, Guided propagation of Alfven and ion-ion hybrid waves in a plasma with two ion species, Plasma Phys. Contr. Fus. 29 (1987) 681-696. Fl R. Van Nieuwenhove et al., Observation of a localised rf electric field structure in the scrape-off layer during ICRF on TEXTOR and ASDEK, 16th Eur. Conf. on Controlled Fusion and Plasma Physics (Venice, Italy, 1989). Europhysics Conf. Abstracts, Vol13B, Part III, pp. 10651068. 171 R. Van Nieuweuhove et al., Observations of harmonics and parametric decay instabilities during ICRF heating on TEXTOR, 15th Eur. Conf. on Controlled Fusion and Plasma Heating (Dubrovnik, Yuguslavia, 1988), Europhysics Conf. Abstracts, Vol 12B, Part II, pp. 778-782. 181M. Brambilla, Theory of Bernstein wave coupling with loop antennas, Nucl. Fus. 28 (1988) 549-563.