- Email: [email protected]
Fast wave transmisssion measurements on the Alcator C-Mod tokamak
3 January 2000
Physics Letters A 264 Ž2000. 407–411 www.elsevier.nlrlocaterphysleta
Fast wave transmisssion measurements on the Alcator C-Mod tokamak J. Reardon a
a,1
, P.T. Bonoli a , M. Porkolab a , Y. Takase b, S.J. Wukitch
a
Massachusetts Institute of Technology, Plasma Science and Fusion Center, Cambridge, MA 02139, USA b UniÕersity of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan Received 13 October 1999; accepted 19 November 1999 Communicated by V.M. Agranovich
Abstract During fundamental minority fast-wave heating in DŽH., the fraction T of power transmitted through the plasma core Žmeasured by loop probes on the inner wall. decreases with increasing minority concentration, in agreement with the predictions of a simple analytic theory and a full wave code. T also varies synchronously with the sawtooth instability in the plasma center. q 2000 Published by Elsevier Science B.V. All rights reserved. PACS: 52.70.Gw; 52.50.Gj; 52.55.Fa Keywords: ICRF heating; Tokamak; Loop probes; Plasma
1. Introduction On the Alcator C-Mod tokamak the standard heating scenario is minority fundamental heating in DŽH. at B0 s 5.4 T Žthe minority species is indicated parenthetically. w1x. Up to 90 % of the injected power can be absorbed by the plasma, as determined from the break-in-slope of the plasma stored energy at RF turn-off w2x. For such high absorptions, the toroidal extent of the fast wave is finite, and a one-dimensional Ž1-D. slab theory of wave propagation is appropriate.
1
Current Address: University of Wisconsin, Department of Physics, 1150 University Ave., Madison, WI 53706, USA; e-mail: [email protected]
This Letter reports measurements of the fast wave power which has traversed the plasma center, using loop probes installed directly across the plasma from the antenna. This measurement is independent of measurements of the absorbed power. It can be directly compared to a simple analytic theory, described below, and to the results of full-wave codes. The 1-D full wave code FELICE w3x ŽFinite Element Ion Cyclotron Emulator. has been chosen for comparison because of its superior modelling of the antenna geometry and near-fields. The plan of this Letter is as follows: data summarizing a 31-shot minority concentration scan are presented in Section 2. Theory pertaining to minority fast-wave heating in tokamaks is given in Section 3. A brief description of the full-wave code FELICE is given in Section 4. Data, theory, and code are compared in Section 5. In
0375-9601r00r$ - see front matter q 2000 Published by Elsevier Science B.V. All rights reserved. PII: S 0 3 7 5 - 9 6 0 1 Ž 9 9 . 0 0 8 2 5 - 7
408
J. Reardon et al.r Physics Letters A 264 (2000) 407–411
Section 6 more data is presented, showing the variation of fast wave transmission during a sawtooth cycle. This variation is interpreted in light of theory to be caused by the ejection of minority ions from the plasma core.
2. Experimental arrangement and data A toroidal cross-section of C-Mod, detailing the geometry of the antennas and the inner-wall probes is shown in Fig. 1. The array of inner-wall probes, which is located at the toroidal midplane, consists of four pairs of two single-turn loops with oppositely directed normals, located in four pockets carved into the back of eight molybdenum protection tiles. A diagram of a pair of loops is shown in Fig. 2. The fast wave fields leak through the slits between the tiles. During manned access following the run campaign, the field attentuation was measured to be B TS rBloop ; 20, where BTS is the rf magnetic field at the tile surface, and B loop is the rf magnetic field deduced from the loop signal. During plasma operations, B TS F 5 = 10y2 T. The tiles shield the loops from electrostatic fields. The electrostatic component of the loop signals was measured at the beginning of the run campaign, by comparing the sum and the difference of the signals from adjacent loops, and found to be negligible. The fast wave launchers on Alcator C-Mod during the 1997–1998 run campaign consisted of two twostrap antennas w4x installed on adjacent horizontal ports, phased Ž0,p ,0,p . to launch a symmetric
Fig. 1. Toroidal cross-section of C-Mod
Fig. 2. Cross-section of loop probes
toroidal spectrum peaked at nf s ckf rv ; 6.5. On two successive run days a 31-shot scan of Hydrogen ŽH. fraction was conducted, with other parameters fixed: B0 s 5.4 T, I P s 1 MA, n eŽ0. s 1.5 =10 20 my3 , Prf s 2.5 MW, and plasma-wall gaps: 0.8 cm Žinner., and 1.5 cm Žouter.. The heating scenario was fundamental minority heating in DŽH.. All shots entered a high-confinement mode ŽH-mode. soon after the rf turned on. Data from one probe is shown in Fig. 3. Each point corresponds to a plasma shot. The abscissa is the H fraction m measured by the Charge Exchange ŽCX. diagnostic, averaged over the rf pulse. The concentration scan moved from low concentrations to high concentrations, then back to low concentrations. The ordinate is the transmission factor, T s P looprPrf , averaged over the rf pulse. The error bars indicate the rms temporal variation of T Žmuch of this variation is not random, but shows the same timing as the sawtooth instability, and is discussed in Section 6..
Fig. 3. Data from hydrogen fraction scan
J. Reardon et al.r Physics Letters A 264 (2000) 407–411
409
3. Theory A recent guide to fast-wave absorption in tokamaks is given in w5x. The geometry of fast wave propagation in a two-species plasma is shown in Fig. 4. Fast wave is evanescent immediately in front of the antenna, in the narrow, low-density region outside the n 2I s R cut-off; propagates throughout the outer regions of the plasma, including the minority cyclotron resonance v s V Cm at the plasma center, where some fast-wave power is absorbed by the plasma; and is evanescent in another narrow region in the center, in between the n2I s L cut-off and the n 2I s S resonance. The coupling of rf power to the fast wave through the edge evanescence layer is not directly measured, but should have been similar for all shots since the magnetic geometry was kept fixed, and is not considered here. The transmission T1 through the minority cyclotron resonance layer is given by w5x: T1 s ey2 hA , 2hA s
p v p M n m Zm 2
c
n M ZM
R P,
Ž 1.
ž
Ps 1q
vc M
p v p2m 4
v
v p2M k I Õthm
/
ž
1y
v c2M v2
2
,
Ž 2.
/
while the transmission through the central evanescent layer is given by: T2 s ey p r2 k` x ,
k` s vrÕa s
Zm v p M ZM
c
,
Ž 3.
where x is the thickness of the evanescent layer, for DŽH. plasmas calculated from cold-plasma theory as: x s R0
8 m q 17m2 y 7m 3 2
3
32 Ž 1 q 5m q 8 m q 4 m .
,
ms
`
Ý Ž 1 y T2 . ny 1T12 ny1 .
Ž 5.
ns1
2
y1
minority concentrations m G 0.1, fast wave power is reflected multiple times between the evanescent layer and the n 2Is R layer on the low-field side, forming an internal resonator which enhances both absorption and transmission over the single-pass values: T IR s 1 y A IR s T2
where the polarization of the fast wave is:
v
Fig. 4. Diagram of fast-wave propagation in C-Mod
nm nM
.
Ž 4. At low minority concentrations m F 0.1 the absorption and evanescent layers overlap, so that the evanescent layer vanishes and the transmission through the plasma is given by Eq. Ž1.. At high
Eqs. Ž1. – Ž5. require as inputs the minority fraction m, the majority species density n M , the minority temperature Tm , the magnetic field at the absorption layer B0 , and the k I associated with the fast wave. Eq. Ž1. Žsingle-pass. is predicted to apply at low m, and Eq. Ž5. Žinternal resonator. at high m. This analysis ignores the process of mode conversion at the n 2Is S layer. For the DŽH. scanario mode conversion is negligible in the low-m case w5x. When m becomes large the evanescent layer is thick and little power crosses the evanescent layer. The power going into mode conversion in this case could be comparable to the transmitted power, which is nonetheless a small fraction of the incident fast wave power.
4.
FELICE
code
FELICE is a full-wave code in slab geometry. It independently evolves multiple toroidal and poloidal modes established as initial conditions by the current
410
J. Reardon et al.r Physics Letters A 264 (2000) 407–411
distribution in the antenna current straps. The code was run 31 times, corresponding to the 31 plasma shots, with input parameters taken from measurement: central electron density n eŽ0. ŽAbel-inverted interferometer measurement.; central electron temperature Te Ž0. Žgrating polychromator ŽGPC..; Hydrogen fraction m ŽCX.; central deuterium temperature T D Ž0. Žneutron detector, assuming m as estimated by the CX.; edge electron density n eŽ a. and temperature TeŽ a. Žestimated from typical scanning Langmuir probe data.; outer gap Žfrom the 2D Grad–Shafranov solver EFIT w6x.; electron density profile n eŽ r . Žparabolic model based on Abel-inverted interferometer measurement and Thomson scattering data.; and electron temperature profile TeŽ r . Žparabolic model based on polychromator and Thomson Scattering data.. The minority temperature is not diagnosed on C-Mod. Mode conversion at the n2I s S layer was turned off for these code runs, and outward radiative boundary conditions were established on the high-field side, in between the n 2I s S layer and the plasma boundary.
5. Comparison of data, theory, and code The FELICE code results were found to be insensitive to minority temperature, within the range 5 keV - TH - 100 keV. The measured transmission factor T was multiplied by 3.75 = 10 6 so that it agreed numerically with the FELICE results. The analytic theory was sensitive to minority temperature and required TH s 100 keV to be quantitatively similar to FELICE. Data, theory, and code are plotted together in Fig. 5. The abscissa is the ratio n H rŽ n H
Fig. 5. Comparison of data, code, and theory
Fig. 6. Sawtooth modulation on PL at low m and high m
q n D . measured by the CX. The ordinate is the transmission factor T Ž0 - T - 1.. Plotted are the measurement Žtriangles with error bars., the results of FELICE Ždiamonds., the analytic single-pass transmission, given by Eq. Ž1. Žsquares., and the transmission including the effect of the internal resonator, given by Eq. Ž5. Žcrosses.. FELICE correctly predicts the measurement at all ranges of m. The single-pass model does well at low m, while the internal resonator model does well at high m.
6. Sawtooth modulation of transmission The net injected rf power Ž Prf ., the signal from a loop probe Ž PL ., and the central Te measured by the GPC are shown in Fig. 6 for a low m shot Ž m s 0.025, left hand column. and a high m shot Ž m s 0.20, right hand column.. At low m, inverse sawtooth crashes appear on P L , while at high m normal sawtooth crashes appear. The magnitude of P L is much smaller at high m than low m, in accordance with Fig. 3. At intermediate values of m there can be substantial sinusoidal variation in P L , without an abrupt change at the sawtooth crash. At both high and low m, the abrupt change in PL is synchronous with the sawtooth crashes in the central Te measured by the GPC, and precede the inverse sawtooth crashes that appear on GPC measurements of Te outside the inversion radius. The instantaneous variation in transmission factor T at a sawtooth crash, averaged over a shot, is plotted for the 31 shots in the H fraction scan, in Fig. 7.
J. Reardon et al.r Physics Letters A 264 (2000) 407–411
Fig. 7. Variation of sawtooth sense with hydrogen fraction.
The sawtooth modulation of P L may be evidence of the redistribution of fast minority ions during a sawtooth cycle. It was found on JET that fast ions were expelled from the center at a sawtooth crash, leaving a hollow minority density profile w7x. At low m, the transmission through the absorption layer ŽEq. Ž1.. decreases with increasing m, due to the increasing thickness of the resonance layer. At high m, the transmission increases with increasing m, due to degradement of P. A 30 % decrease in m at the sawtooth crash is required to produce the decrease in P L shown in the left-hand side of Fig. 6 Žlow m case.. A 50 % decrease in m would be required to produce the increase in PL seen during high m.
411
during H-mode Ž n e s 3 = 10 20 my3, Te s 3 keV.. An independent measurement of the minority temperature is required to quantitatively verify the theory. Not only can the transmission factor T change significantly during a sawtooth cycle, as shown in Fig. 6, but also the antenna loading, which is inferred from measurements of the forward and reflected power, can change by as much as a factor of 2 in 0.1 ms at a sawtooth crash. Evidently the coupling of the fast wave to the plasma is affected by changes in the plasma core. The high-m data provides crucial support for the minority-ejection hypothesis. The low-m data could be explained either by variations in m Žthe minorityejection hypothesis., or by supposing that T H varied similarly to Te during a sawtooth cycle, which it is likely to do. This variation in T H would not produce the sawtooth variation in P L seen at high-m. Acknowledgements The authors acknowledge useful discussions with Dr. E. Lomon and Dr. E. Marmar. This work was supported by the US Department of Energy under Contracts No. DE-AC02-78ET51013 and DE-FC0299ER54512.
7. Discussion The dependence of the transmission factor on minority concentration is well-predicted by theory and code ŽFig. 5.. FELICE does a better job than the theory, which requires a surprisingly high minority temperature to predict even the qualitative dependence. The minority temperature is approximately w8x TH s Te q
P 3n H
ts .
Ž 6.
Here P is the power density flowing into the minority, and ts is the slowing-down time of minority ions. Assuming slowing down on electrons, the minority temperature in Alcator is estimated to be TH s Te q
3 keV m
Ž 7.
References w1x M. Porkolab et al., in: Plasma Physics and Controlled Nuclear Fusion ŽProc. 15th IAEA Conf. Seville 1994., Vol. 1 IAEA, Vienna, 1995, p. 123. w2x J. Reardon, Ph.D. thesis, June 1999, Massachusetts Institute of Technology, Cambridge, MA 02139. w3x M. Brambilla, Nucl. Fus. 28 Ž1988. 549. w4x Y. Takase et al., in: Fusion Engineering, Proc. 14th IEEErNPSS Symp. San Diego 1991, Vol. 1, IEEE, Piscataway, NJ, 1992, p. 118. w5x M. Porkolab, Plasma Heating by Fast Magnetosonic Waves in Tokamaks, in: Advances in Plasma Physics, T.H. Stix Symposium, AIP Conference Proceedings 314, N. Fisch ŽEd.., AIP, New York, 1994. w6x L.L. Lao, H.St. John, R.D. Stambaugh, A.G. Kellman, W. Pfeiffer, Nucl. Fus. 25 Ž1985. 1611. w7x L.-G. Eriksson, T. Hellsten, U. Willen, Nucl. Fus. 33 Ž1988. 1037. w8x T.H. Stix, Nucl. Fus. 15 Ž1975. 737.
Physics Letters A 264 Ž2000. 407–411 www.elsevier.nlrlocaterphysleta
Fast wave transmisssion measurements on the Alcator C-Mod tokamak J. Reardon a
a,1
, P.T. Bonoli a , M. Porkolab a , Y. Takase b, S.J. Wukitch
a
Massachusetts Institute of Technology, Plasma Science and Fusion Center, Cambridge, MA 02139, USA b UniÕersity of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan Received 13 October 1999; accepted 19 November 1999 Communicated by V.M. Agranovich
Abstract During fundamental minority fast-wave heating in DŽH., the fraction T of power transmitted through the plasma core Žmeasured by loop probes on the inner wall. decreases with increasing minority concentration, in agreement with the predictions of a simple analytic theory and a full wave code. T also varies synchronously with the sawtooth instability in the plasma center. q 2000 Published by Elsevier Science B.V. All rights reserved. PACS: 52.70.Gw; 52.50.Gj; 52.55.Fa Keywords: ICRF heating; Tokamak; Loop probes; Plasma
1. Introduction On the Alcator C-Mod tokamak the standard heating scenario is minority fundamental heating in DŽH. at B0 s 5.4 T Žthe minority species is indicated parenthetically. w1x. Up to 90 % of the injected power can be absorbed by the plasma, as determined from the break-in-slope of the plasma stored energy at RF turn-off w2x. For such high absorptions, the toroidal extent of the fast wave is finite, and a one-dimensional Ž1-D. slab theory of wave propagation is appropriate.
1
Current Address: University of Wisconsin, Department of Physics, 1150 University Ave., Madison, WI 53706, USA; e-mail: [email protected]
This Letter reports measurements of the fast wave power which has traversed the plasma center, using loop probes installed directly across the plasma from the antenna. This measurement is independent of measurements of the absorbed power. It can be directly compared to a simple analytic theory, described below, and to the results of full-wave codes. The 1-D full wave code FELICE w3x ŽFinite Element Ion Cyclotron Emulator. has been chosen for comparison because of its superior modelling of the antenna geometry and near-fields. The plan of this Letter is as follows: data summarizing a 31-shot minority concentration scan are presented in Section 2. Theory pertaining to minority fast-wave heating in tokamaks is given in Section 3. A brief description of the full-wave code FELICE is given in Section 4. Data, theory, and code are compared in Section 5. In
0375-9601r00r$ - see front matter q 2000 Published by Elsevier Science B.V. All rights reserved. PII: S 0 3 7 5 - 9 6 0 1 Ž 9 9 . 0 0 8 2 5 - 7
408
J. Reardon et al.r Physics Letters A 264 (2000) 407–411
Section 6 more data is presented, showing the variation of fast wave transmission during a sawtooth cycle. This variation is interpreted in light of theory to be caused by the ejection of minority ions from the plasma core.
2. Experimental arrangement and data A toroidal cross-section of C-Mod, detailing the geometry of the antennas and the inner-wall probes is shown in Fig. 1. The array of inner-wall probes, which is located at the toroidal midplane, consists of four pairs of two single-turn loops with oppositely directed normals, located in four pockets carved into the back of eight molybdenum protection tiles. A diagram of a pair of loops is shown in Fig. 2. The fast wave fields leak through the slits between the tiles. During manned access following the run campaign, the field attentuation was measured to be B TS rBloop ; 20, where BTS is the rf magnetic field at the tile surface, and B loop is the rf magnetic field deduced from the loop signal. During plasma operations, B TS F 5 = 10y2 T. The tiles shield the loops from electrostatic fields. The electrostatic component of the loop signals was measured at the beginning of the run campaign, by comparing the sum and the difference of the signals from adjacent loops, and found to be negligible. The fast wave launchers on Alcator C-Mod during the 1997–1998 run campaign consisted of two twostrap antennas w4x installed on adjacent horizontal ports, phased Ž0,p ,0,p . to launch a symmetric
Fig. 1. Toroidal cross-section of C-Mod
Fig. 2. Cross-section of loop probes
toroidal spectrum peaked at nf s ckf rv ; 6.5. On two successive run days a 31-shot scan of Hydrogen ŽH. fraction was conducted, with other parameters fixed: B0 s 5.4 T, I P s 1 MA, n eŽ0. s 1.5 =10 20 my3 , Prf s 2.5 MW, and plasma-wall gaps: 0.8 cm Žinner., and 1.5 cm Žouter.. The heating scenario was fundamental minority heating in DŽH.. All shots entered a high-confinement mode ŽH-mode. soon after the rf turned on. Data from one probe is shown in Fig. 3. Each point corresponds to a plasma shot. The abscissa is the H fraction m measured by the Charge Exchange ŽCX. diagnostic, averaged over the rf pulse. The concentration scan moved from low concentrations to high concentrations, then back to low concentrations. The ordinate is the transmission factor, T s P looprPrf , averaged over the rf pulse. The error bars indicate the rms temporal variation of T Žmuch of this variation is not random, but shows the same timing as the sawtooth instability, and is discussed in Section 6..
Fig. 3. Data from hydrogen fraction scan
J. Reardon et al.r Physics Letters A 264 (2000) 407–411
409
3. Theory A recent guide to fast-wave absorption in tokamaks is given in w5x. The geometry of fast wave propagation in a two-species plasma is shown in Fig. 4. Fast wave is evanescent immediately in front of the antenna, in the narrow, low-density region outside the n 2I s R cut-off; propagates throughout the outer regions of the plasma, including the minority cyclotron resonance v s V Cm at the plasma center, where some fast-wave power is absorbed by the plasma; and is evanescent in another narrow region in the center, in between the n2I s L cut-off and the n 2I s S resonance. The coupling of rf power to the fast wave through the edge evanescence layer is not directly measured, but should have been similar for all shots since the magnetic geometry was kept fixed, and is not considered here. The transmission T1 through the minority cyclotron resonance layer is given by w5x: T1 s ey2 hA , 2hA s
p v p M n m Zm 2
c
n M ZM
R P,
Ž 1.
ž
Ps 1q
vc M
p v p2m 4
v
v p2M k I Õthm
/
ž
1y
v c2M v2
2
,
Ž 2.
/
while the transmission through the central evanescent layer is given by: T2 s ey p r2 k` x ,
k` s vrÕa s
Zm v p M ZM
c
,
Ž 3.
where x is the thickness of the evanescent layer, for DŽH. plasmas calculated from cold-plasma theory as: x s R0
8 m q 17m2 y 7m 3 2
3
32 Ž 1 q 5m q 8 m q 4 m .
,
ms
`
Ý Ž 1 y T2 . ny 1T12 ny1 .
Ž 5.
ns1
2
y1
minority concentrations m G 0.1, fast wave power is reflected multiple times between the evanescent layer and the n 2Is R layer on the low-field side, forming an internal resonator which enhances both absorption and transmission over the single-pass values: T IR s 1 y A IR s T2
where the polarization of the fast wave is:
v
Fig. 4. Diagram of fast-wave propagation in C-Mod
nm nM
.
Ž 4. At low minority concentrations m F 0.1 the absorption and evanescent layers overlap, so that the evanescent layer vanishes and the transmission through the plasma is given by Eq. Ž1.. At high
Eqs. Ž1. – Ž5. require as inputs the minority fraction m, the majority species density n M , the minority temperature Tm , the magnetic field at the absorption layer B0 , and the k I associated with the fast wave. Eq. Ž1. Žsingle-pass. is predicted to apply at low m, and Eq. Ž5. Žinternal resonator. at high m. This analysis ignores the process of mode conversion at the n 2Is S layer. For the DŽH. scanario mode conversion is negligible in the low-m case w5x. When m becomes large the evanescent layer is thick and little power crosses the evanescent layer. The power going into mode conversion in this case could be comparable to the transmitted power, which is nonetheless a small fraction of the incident fast wave power.
4.
FELICE
code
FELICE is a full-wave code in slab geometry. It independently evolves multiple toroidal and poloidal modes established as initial conditions by the current
410
J. Reardon et al.r Physics Letters A 264 (2000) 407–411
distribution in the antenna current straps. The code was run 31 times, corresponding to the 31 plasma shots, with input parameters taken from measurement: central electron density n eŽ0. ŽAbel-inverted interferometer measurement.; central electron temperature Te Ž0. Žgrating polychromator ŽGPC..; Hydrogen fraction m ŽCX.; central deuterium temperature T D Ž0. Žneutron detector, assuming m as estimated by the CX.; edge electron density n eŽ a. and temperature TeŽ a. Žestimated from typical scanning Langmuir probe data.; outer gap Žfrom the 2D Grad–Shafranov solver EFIT w6x.; electron density profile n eŽ r . Žparabolic model based on Abel-inverted interferometer measurement and Thomson scattering data.; and electron temperature profile TeŽ r . Žparabolic model based on polychromator and Thomson Scattering data.. The minority temperature is not diagnosed on C-Mod. Mode conversion at the n2I s S layer was turned off for these code runs, and outward radiative boundary conditions were established on the high-field side, in between the n 2I s S layer and the plasma boundary.
5. Comparison of data, theory, and code The FELICE code results were found to be insensitive to minority temperature, within the range 5 keV - TH - 100 keV. The measured transmission factor T was multiplied by 3.75 = 10 6 so that it agreed numerically with the FELICE results. The analytic theory was sensitive to minority temperature and required TH s 100 keV to be quantitatively similar to FELICE. Data, theory, and code are plotted together in Fig. 5. The abscissa is the ratio n H rŽ n H
Fig. 5. Comparison of data, code, and theory
Fig. 6. Sawtooth modulation on PL at low m and high m
q n D . measured by the CX. The ordinate is the transmission factor T Ž0 - T - 1.. Plotted are the measurement Žtriangles with error bars., the results of FELICE Ždiamonds., the analytic single-pass transmission, given by Eq. Ž1. Žsquares., and the transmission including the effect of the internal resonator, given by Eq. Ž5. Žcrosses.. FELICE correctly predicts the measurement at all ranges of m. The single-pass model does well at low m, while the internal resonator model does well at high m.
6. Sawtooth modulation of transmission The net injected rf power Ž Prf ., the signal from a loop probe Ž PL ., and the central Te measured by the GPC are shown in Fig. 6 for a low m shot Ž m s 0.025, left hand column. and a high m shot Ž m s 0.20, right hand column.. At low m, inverse sawtooth crashes appear on P L , while at high m normal sawtooth crashes appear. The magnitude of P L is much smaller at high m than low m, in accordance with Fig. 3. At intermediate values of m there can be substantial sinusoidal variation in P L , without an abrupt change at the sawtooth crash. At both high and low m, the abrupt change in PL is synchronous with the sawtooth crashes in the central Te measured by the GPC, and precede the inverse sawtooth crashes that appear on GPC measurements of Te outside the inversion radius. The instantaneous variation in transmission factor T at a sawtooth crash, averaged over a shot, is plotted for the 31 shots in the H fraction scan, in Fig. 7.
J. Reardon et al.r Physics Letters A 264 (2000) 407–411
Fig. 7. Variation of sawtooth sense with hydrogen fraction.
The sawtooth modulation of P L may be evidence of the redistribution of fast minority ions during a sawtooth cycle. It was found on JET that fast ions were expelled from the center at a sawtooth crash, leaving a hollow minority density profile w7x. At low m, the transmission through the absorption layer ŽEq. Ž1.. decreases with increasing m, due to the increasing thickness of the resonance layer. At high m, the transmission increases with increasing m, due to degradement of P. A 30 % decrease in m at the sawtooth crash is required to produce the decrease in P L shown in the left-hand side of Fig. 6 Žlow m case.. A 50 % decrease in m would be required to produce the increase in PL seen during high m.
411
during H-mode Ž n e s 3 = 10 20 my3, Te s 3 keV.. An independent measurement of the minority temperature is required to quantitatively verify the theory. Not only can the transmission factor T change significantly during a sawtooth cycle, as shown in Fig. 6, but also the antenna loading, which is inferred from measurements of the forward and reflected power, can change by as much as a factor of 2 in 0.1 ms at a sawtooth crash. Evidently the coupling of the fast wave to the plasma is affected by changes in the plasma core. The high-m data provides crucial support for the minority-ejection hypothesis. The low-m data could be explained either by variations in m Žthe minorityejection hypothesis., or by supposing that T H varied similarly to Te during a sawtooth cycle, which it is likely to do. This variation in T H would not produce the sawtooth variation in P L seen at high-m. Acknowledgements The authors acknowledge useful discussions with Dr. E. Lomon and Dr. E. Marmar. This work was supported by the US Department of Energy under Contracts No. DE-AC02-78ET51013 and DE-FC0299ER54512.
7. Discussion The dependence of the transmission factor on minority concentration is well-predicted by theory and code ŽFig. 5.. FELICE does a better job than the theory, which requires a surprisingly high minority temperature to predict even the qualitative dependence. The minority temperature is approximately w8x TH s Te q
P 3n H
ts .
Ž 6.
Here P is the power density flowing into the minority, and ts is the slowing-down time of minority ions. Assuming slowing down on electrons, the minority temperature in Alcator is estimated to be TH s Te q
3 keV m
Ž 7.
References w1x M. Porkolab et al., in: Plasma Physics and Controlled Nuclear Fusion ŽProc. 15th IAEA Conf. Seville 1994., Vol. 1 IAEA, Vienna, 1995, p. 123. w2x J. Reardon, Ph.D. thesis, June 1999, Massachusetts Institute of Technology, Cambridge, MA 02139. w3x M. Brambilla, Nucl. Fus. 28 Ž1988. 549. w4x Y. Takase et al., in: Fusion Engineering, Proc. 14th IEEErNPSS Symp. San Diego 1991, Vol. 1, IEEE, Piscataway, NJ, 1992, p. 118. w5x M. Porkolab, Plasma Heating by Fast Magnetosonic Waves in Tokamaks, in: Advances in Plasma Physics, T.H. Stix Symposium, AIP Conference Proceedings 314, N. Fisch ŽEd.., AIP, New York, 1994. w6x L.L. Lao, H.St. John, R.D. Stambaugh, A.G. Kellman, W. Pfeiffer, Nucl. Fus. 25 Ž1985. 1611. w7x L.-G. Eriksson, T. Hellsten, U. Willen, Nucl. Fus. 33 Ž1988. 1037. w8x T.H. Stix, Nucl. Fus. 15 Ž1975. 737.