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Characteristic of slide away discharges in the KSTAR tokamak
Physics Letters A 376 (2012) 3638–3640
Contents lists available at SciVerse ScienceDirect
Physics Letters A www.elsevier.com/locate/pla
Characteristic of slide away discharges in the KSTAR tokamak Z.Y. Chen a,b,∗ , W.C. Kim b , S.W. Yoon b , A.C. England b , K.D. Lee b , J.W. Yoo b , Y.K. Oh b , J.G. Kwak b , M. Kwon b a
State Key Laboratory of Advanced Electromagnetic Engineering and Technology, College of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China b National Fusion Research Institute, Daejeon, 305-333, Republic of Korea
a r t i c l e
i n f o
Article history: Received 19 June 2012 Received in revised form 26 October 2012 Accepted 27 October 2012 Available online 1 November 2012 Communicated by C.R. Doering Keywords: Runaway electron Slide away ADR
a b s t r a c t Low density slide away discharges with anomalous Doppler resonance (ADR) effects have been observed in the KSTAR tokamak. When the line averaged electron density was lower than 0.6 × 1019 m−3 , the discharges went into the slide-away regime with relaxations in the electron cyclotron emission due to the ADR effects which transferred the runaway electron energy from parallel to perpendicular motion. The suppression of the ADR effects has been achieved by electron cyclotron resonance heating which enhanced the perpendicular energy of electrons and led to an isotropization of the electron distribution function. © 2012 Elsevier B.V. All rights reserved.
1. Introduction In tokamak plasmas below a critical density [1] and under the influence of the longitudinal electric field, the initially Maxwellian electron distribution function forms a runaway tail. Above a certain threshold, runaway electron beam instabilities (REBIs) can be excited [2–4]. The distribution becomes unstable due to the anomalous Doppler resonance (ADR) effects, which causes pitch angle scattering of runaway electrons (REs) [5,6]. The empirical condition for the ADR effects to occur in a runaway discharge is the ratio of the electron plasma frequency to the electron cyclotron frequency ω pe /ωce < 0.3 [4]. This was satisfied in TFR, T-6, TM-3, Alcator, ASDEX and HT-7 low density discharges [7–12]. This regime is characterized by a large suprathermal electron population, low density, low loop voltage and oscillations in perpendicular energy related parameters such as electron cyclotron emission (ECE) [10–12]. The slide-away regime is usually accompanied by ADR events. The general resonant condition is ωk − nωce = k v with ωk the wave frequency, k the wave number parallel to the magnetic field, n the harmonic number, ωce the electron cyclotron frequency and v the electron velocity [4–6]. Owing to the decrease in the cyclotron frequency of relativistic REs, the runaway
*
Corresponding author at: State Key Laboratory of Advanced Electromagnetic Engineering and Technology, College of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China. Fax: +82 42 879 5209. E-mail address: [email protected] (Z.Y. Chen). 0375-9601/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physleta.2012.10.043
electrons and waves are coupled. It causes pitch angle scattering of the REs. For runaway electrons, the longitudinal energy is much larger than their transverse energy, v ∼ c. The resonance condition leads to nωce ≈ ω(1 − N ) < 0. Thus n must be negative. In the case of negative n, it corresponding to anomalous Doppler interaction. For negative n in the ADR effect, longitudinal energy of the electron is converted into transverse energy [5]. The characteristics of electron cyclotron resonance heating (ECRH) and electron cyclotron current drive (ECCD) to deposit power or current in a localized controllable way make these techniques applicable to plasma heating, and maintenance of desired current profiles and stabilization of magnetohydrodynamic (MHD) instabilities [13,14]. The ECRH mainly increases the perpendicular energy of resonant electrons. Since the REBIs occur mainly due to the fact that an electric field created a runaway tail in the longitudinal direction, ECRH may be used to control the REBIs by changing the electron distribution function by increasing the perpendicular energy of electrons. This could lead to an isotropization of the electron distribution function. When the ECRH power is high enough, it will result in suppression of runaway population due to a large drop of loop voltage. In the KSTAR tokamak, slide-away discharges have been observed in low density discharges. The effect of ECRH on the REBI has been investigated. In Section 2 the experimental conditions and diagnostics are presented. The behaviors of REBI and suppression of REBI by ECRH are described in Section 3. The discussion of experimental results is presented in Section 4. Finally Section 5 contains the summary.
Z.Y. Chen et al. / Physics Letters A 376 (2012) 3638–3640
Fig. 1. Waveforms of slide-away discharge No. 3800. (a) is the plasma current, (b) the line-averaged electron density, (c) the loop voltage and the critical voltage (2π REc ), (d) the center ECE emission intensity. The two inlays in (d) is time trace of center ECE emission intensity just before and during flat-top phase.
2. Experimental setup The Korea Superconducting Tokamak Advanced Research (KSTAR) system is a full superconducting, medium-sized tokamak device [15]. The KSTAR tokamak machine parameters include a major radius of R = 1.8 m and a minor radius of a = 0.5 m. An ECRH system with 110 GHz was available for the KSTAR 2010 experiment. A 280 GHz single-channel horizontal millimeter-wave interferometer system was installed for plasma electron density measurements in KSTAR. The electron temperature was measured by an ECE radiometer which covered the frequency range of 110–196 GHz with 1 GHz steps. Formation of low energy REs electrons could result in substantial enhancement of the downshifted ECE. In slide away discharges the ECE signals were used to monitor the generation of REs and the ADR effects. 3. Experimental results In the KSTAR tokamak, when the line averaged electron density was lower than 0.6 × 1019 m−3 , the discharges went into the slide away regime. For B T = 2 T, this corresponds to the ratio ω pe /ωce = 0.4 in the core. The threshold of ω pe /ωce for a slide away discharge in KSTAR is about 30% higher than other machines which have a threshold of about 0.3. A typical slide away discharge at B T = 2 T, plasma current of about 400 kA, and line averaged electron density of about 0.35 × 1019 m−3 is shown in Fig. 1. Due to the low electron density, the discharge went into a slide away regime at about 0.5 s, after which the ECE signal amplitude increased strongly due to the presence of a large population of low energy REs. All of the ECE signals showed inverted sawtooth like oscillations after the discharge went into the slide away regime, as shown in Fig. 1 which is the characteristic of ADR events. The ratio of ω pe /ωce was about 0.3 in the core in this discharge. During the phase of plasma current ramp up, the ECE oscillation amplitude was about 5% as shown in Fig. 1 inlay zoom from 0.92 s to 1.0 s. The period of ADR events was about 4 ms. When the discharge reached flat-top, the ECE amplitude increased to 10%–12%, and the period increased to about 15 ms as shown in Fig. 1 inlay zoom from 1.2 s to 1.28 s. Since the ECRH can modify the electron distribution function in the perpendicular direction, it can be used to control the run-
3639
Fig. 2. Waveforms of slide-away discharge No. 3700 with ECRH. (a) is the plasma current and the ECRH power, (b) the line-averaged electron density, (c) the loop voltage and the critical voltage (2π REc ), (d) the center ECE emission intensity. The three inlays in (d) indicates the behaviors of ECE just before and during the ECRH, at the time of ECRH power switch off, and in the recovered slide away phase.
away electron beam driven instabilities. ECRH with power of about 200 kW deposited on-axis was switched on from 1.0 s to 2.0 s in a slide away discharge as shown in Fig. 2. In this discharge, the plasma current was about 380 kA, with B T = 2 T, and line averaged electron density about 0.5 × 1019 m−3 . The discharge went into the slide away regime at about 0.3 s. Before the ECRH phase, the ECE signal remained stationary with ADR events. The period of an ADR events was about 5 ms with 5% amplitude in oscillations. After the injection of ECRH power, the ECE signal decreased significantly to about one fourth of the initial amplitude, and the ADR events disappeared, with development of strong sawtooth activity. The ADR events in ECE disappeared when the ECRH power ramped up to about 150 kW, apparent the threshold of ECRH power for suppression of the ADR effects in these conditions. The sawtooth activities appeared following the suppression of the ADR effects. The conversion of the ADR events to sawtooth activities was finished in 20 ms. After the termination of the ECRH power, the ECE signal decreased again, which indicates that the electron temperature decreased and the low energy runaway population was quenched. Since the plasma density was low enough for the discharge to be converted into the slide away regime, the discharge went into the slide away regime again at about 2.3 s as indicated by the increase of ECE and the emergence of the ADR effects. The center ECE just before and after the termination of the ECRH is shown in Fig. 2 inlay zoom. It is found that the sawtooth activities became much weaker after the termination of ECCD power. In about 200 ms, the sawtooth activities disappeared and the ADR effects became obvious in 300 ms. The discharge finally went into a pure slide away regime as shown in inlay zoom of ECE from 2.92 s to 3.0 s. The period and amplitude are similar to that before the ECRH phase. 4. Discussion There is a critical energy for the runaway beam to undergoing ADR effects [3]. The critical energy for the ADR events to occur is much higher than the threshold energy of electrons to runaway. As a consequence of the ADR events, runaway electrons with a parallel energy slightly higher than the critical energy were pitch angle scattered into perpendicular energy. Their total energy then reduced due to the enhancement of electron cyclotron emission
3640
Z.Y. Chen et al. / Physics Letters A 376 (2012) 3638–3640
losses. It may lead to a barrier to a further increase in the runaway energy. Because the runaways are accelerated continually, this whole process repeats, so that the ADR events have a recurrent character: the ECE oscillations periodically flash and attenuate. The change of oscillation amplitude and period just at the beginning of the flat-top phase was possibly due to the decrease of loop voltage. With lower loop voltage, the electrons need more time to acquire the critical energy for the ADR effects to occur. The period of an ADR event is much larger than that in other machines, which have periods on the order of 1 ms [7–12]. The parallel electric field was about 0.1 V/m during the slide away phase in the HT-7 tokamak [11]. The parallel electric field was about 0.04 V/m during the slide away phase in the KSTAR tokamak. Thus the period of the ADR events is larger in KSTAR. In the FTU experiment [16], the electric field was decreased to below the threshold electric field ( E c =
e 3 ne ln Λ ) 4π ε02 me c 2
for runaway
generation by high power ECRH. In this case the synchrotron radiation loss was included in the calculation of threshold electric field for runaway generation which increased the threshold electric field. The runaway population does not appear when the electric field is small than the threshold electric field. Though high power ECRH can quench the runaway population by reducing the toroidal electric field below the threshold electric field E c for runaway generation [16], the ECRH power in this experiment was only 200 kW which could not quench the runaway population by a small drop of loop voltage. The electric field is much higher than the threshold electric field as shown in Fig. 2. The suppression of the ADR events could have occurred due to the modification of the electron distribution function by ECRH. The free energy source which drives REBIs is the distortion of the plasma electron distribution function by the applied electric field. The distribution became unstable owing to the ADR effects. The ECRH enhanced the perpendicular energy of electrons which could lead to an isotropization of the electron distribution function. In this case, the free energy source which drives REBIs decreased. Thus the REBIs can be suppressed by the ECRH. The suppression of the ADR events is likely to coincide with the suppression of low energy runaway population also as indicated by the drop of ECE signal. No measurement of the current density profile or q profile was available in these experiments, however results from theory [17] and other devices [18,19] help to interpret the present observations. Stabilization of sawtooth activity is expected to result from a decrease of current density at the magnetic axis and corresponding increase of q0 above 1, as would occur when ECCD is turned off. When the ECCD power is turned off, the fast electron population will slow down to thermal electrons. Thus the non-inductive current fraction will disappear. When the ECCD power is turned off, the resonance absorption between the waves and the thermal electrons disappeared. This will lead to a decrease of the electron temperature. Since the ECCD increased the perpendicular energy of electrons, it will increase the synchrotron radiation loss of fast electron pop-
ulation. Thus the threshold electric field for runaway generation will increase. On the other hand, the toroidal electric field will decrease due to the resonance absorption of wave power by thermal electrons which results in increase of electron temperature. So the ECCD has two benefits on the runaway suppression. 5. Summary In KSTAR tokamak, slide-away discharges have been observed in low density discharges with line averaged electron density nec < 0.6 × 10−19 m−3 . In the slide away regime, the ADR effects were observed in the ECE signals. The ADR events transfer energy from parallel to perpendicular motion. The ADR effect in the flat top phase had larger amplitude in oscillations and a larger period compared to that in the current ramp up phase. The ECRH was demonstrated to be effective in the suppression of the ADR effects in slide away discharges. About 150 kW ECRH power was enough to convert the slide away discharge into a normal discharge in KSTAR. The suppression of the ADR effects with ECRH is possibly due to the modification of electron distribution function and quenching of low energy runaway population. The ECRH enhanced the perpendicular energy of electrons which could lead to an isotropization of the electron distribution function. The discharge went into the slide away regime again in a few hundred ms after the ECRH phase. The ECRH provides us with a new way to suppress the REBIs. Acknowledgements It is a pleasure to acknowledge the assistance of KSTAR group. This work was partially supported by the National Natural Science Foundation (Nos. 11005090 and 11275079) and the National Magnetic Confinement Fusion Science Program (Nos. 2009GB104003 and 2011GB109001) of China. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]
M.N. Rosenbluth, S.V. Putvinski, Nucl. Fusion 37 (1997) 1355. H. Knoepfel, et al., Nucl. Fusion 19 (1979) 785. B.B. Kadomtsev, et al., Zh. Eksp. Teor. Fiz. 53 (1967) 2025. V.V. Parail, O.P. Pogutse, Nucl. Fusion 18 (1978) 303. P. Brossier, Nucl. Fusion 18 (1978) 1069. J.R. Martin-Solis, et al., Phys. Plasmas 9 (2002) 1667. J.M. Rax, et al., Europhys. Lett. 15 (1991) 497. T.F.R. Equipe, Nucl. Fusion 16 (1976) 473. V.S. Vlasenkov, et al., Nucl. Fusion 13 (1973) 509. V.V. Alikaev, et al., Sov. J. Plasma Phys. 1 (1975) 303. A.A.M. Oomens, et al., Phys. Rev. Lett. 36 (1976) 255. Z.Y. Chen, et al., Chin. Phys. Lett. 24 (2007) 3195. G. Fussmann, et al., Phys. Rev. Lett. 47 (1981) 1004. C. Gormezano, et al., Nucl. Fusion 47 (2007) S285. R.A. James, et al., Phys. Rev. A 45 (1992) 8783. G.S. Lee, et al., Nucl. Fusion 41 (2001) 1515. J.R. Martin-Solis, et al., Nucl. Fusion 44 (2004) 974. C.C. Petty, et al., Nucl. Fusion 42 (2002) 1366. C. Angioni, et al., Nucl. Fusion 43 (2003) 455.
Contents lists available at SciVerse ScienceDirect
Physics Letters A www.elsevier.com/locate/pla
Characteristic of slide away discharges in the KSTAR tokamak Z.Y. Chen a,b,∗ , W.C. Kim b , S.W. Yoon b , A.C. England b , K.D. Lee b , J.W. Yoo b , Y.K. Oh b , J.G. Kwak b , M. Kwon b a
State Key Laboratory of Advanced Electromagnetic Engineering and Technology, College of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China b National Fusion Research Institute, Daejeon, 305-333, Republic of Korea
a r t i c l e
i n f o
Article history: Received 19 June 2012 Received in revised form 26 October 2012 Accepted 27 October 2012 Available online 1 November 2012 Communicated by C.R. Doering Keywords: Runaway electron Slide away ADR
a b s t r a c t Low density slide away discharges with anomalous Doppler resonance (ADR) effects have been observed in the KSTAR tokamak. When the line averaged electron density was lower than 0.6 × 1019 m−3 , the discharges went into the slide-away regime with relaxations in the electron cyclotron emission due to the ADR effects which transferred the runaway electron energy from parallel to perpendicular motion. The suppression of the ADR effects has been achieved by electron cyclotron resonance heating which enhanced the perpendicular energy of electrons and led to an isotropization of the electron distribution function. © 2012 Elsevier B.V. All rights reserved.
1. Introduction In tokamak plasmas below a critical density [1] and under the influence of the longitudinal electric field, the initially Maxwellian electron distribution function forms a runaway tail. Above a certain threshold, runaway electron beam instabilities (REBIs) can be excited [2–4]. The distribution becomes unstable due to the anomalous Doppler resonance (ADR) effects, which causes pitch angle scattering of runaway electrons (REs) [5,6]. The empirical condition for the ADR effects to occur in a runaway discharge is the ratio of the electron plasma frequency to the electron cyclotron frequency ω pe /ωce < 0.3 [4]. This was satisfied in TFR, T-6, TM-3, Alcator, ASDEX and HT-7 low density discharges [7–12]. This regime is characterized by a large suprathermal electron population, low density, low loop voltage and oscillations in perpendicular energy related parameters such as electron cyclotron emission (ECE) [10–12]. The slide-away regime is usually accompanied by ADR events. The general resonant condition is ωk − nωce = k v with ωk the wave frequency, k the wave number parallel to the magnetic field, n the harmonic number, ωce the electron cyclotron frequency and v the electron velocity [4–6]. Owing to the decrease in the cyclotron frequency of relativistic REs, the runaway
*
Corresponding author at: State Key Laboratory of Advanced Electromagnetic Engineering and Technology, College of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China. Fax: +82 42 879 5209. E-mail address: [email protected] (Z.Y. Chen). 0375-9601/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physleta.2012.10.043
electrons and waves are coupled. It causes pitch angle scattering of the REs. For runaway electrons, the longitudinal energy is much larger than their transverse energy, v ∼ c. The resonance condition leads to nωce ≈ ω(1 − N ) < 0. Thus n must be negative. In the case of negative n, it corresponding to anomalous Doppler interaction. For negative n in the ADR effect, longitudinal energy of the electron is converted into transverse energy [5]. The characteristics of electron cyclotron resonance heating (ECRH) and electron cyclotron current drive (ECCD) to deposit power or current in a localized controllable way make these techniques applicable to plasma heating, and maintenance of desired current profiles and stabilization of magnetohydrodynamic (MHD) instabilities [13,14]. The ECRH mainly increases the perpendicular energy of resonant electrons. Since the REBIs occur mainly due to the fact that an electric field created a runaway tail in the longitudinal direction, ECRH may be used to control the REBIs by changing the electron distribution function by increasing the perpendicular energy of electrons. This could lead to an isotropization of the electron distribution function. When the ECRH power is high enough, it will result in suppression of runaway population due to a large drop of loop voltage. In the KSTAR tokamak, slide-away discharges have been observed in low density discharges. The effect of ECRH on the REBI has been investigated. In Section 2 the experimental conditions and diagnostics are presented. The behaviors of REBI and suppression of REBI by ECRH are described in Section 3. The discussion of experimental results is presented in Section 4. Finally Section 5 contains the summary.
Z.Y. Chen et al. / Physics Letters A 376 (2012) 3638–3640
Fig. 1. Waveforms of slide-away discharge No. 3800. (a) is the plasma current, (b) the line-averaged electron density, (c) the loop voltage and the critical voltage (2π REc ), (d) the center ECE emission intensity. The two inlays in (d) is time trace of center ECE emission intensity just before and during flat-top phase.
2. Experimental setup The Korea Superconducting Tokamak Advanced Research (KSTAR) system is a full superconducting, medium-sized tokamak device [15]. The KSTAR tokamak machine parameters include a major radius of R = 1.8 m and a minor radius of a = 0.5 m. An ECRH system with 110 GHz was available for the KSTAR 2010 experiment. A 280 GHz single-channel horizontal millimeter-wave interferometer system was installed for plasma electron density measurements in KSTAR. The electron temperature was measured by an ECE radiometer which covered the frequency range of 110–196 GHz with 1 GHz steps. Formation of low energy REs electrons could result in substantial enhancement of the downshifted ECE. In slide away discharges the ECE signals were used to monitor the generation of REs and the ADR effects. 3. Experimental results In the KSTAR tokamak, when the line averaged electron density was lower than 0.6 × 1019 m−3 , the discharges went into the slide away regime. For B T = 2 T, this corresponds to the ratio ω pe /ωce = 0.4 in the core. The threshold of ω pe /ωce for a slide away discharge in KSTAR is about 30% higher than other machines which have a threshold of about 0.3. A typical slide away discharge at B T = 2 T, plasma current of about 400 kA, and line averaged electron density of about 0.35 × 1019 m−3 is shown in Fig. 1. Due to the low electron density, the discharge went into a slide away regime at about 0.5 s, after which the ECE signal amplitude increased strongly due to the presence of a large population of low energy REs. All of the ECE signals showed inverted sawtooth like oscillations after the discharge went into the slide away regime, as shown in Fig. 1 which is the characteristic of ADR events. The ratio of ω pe /ωce was about 0.3 in the core in this discharge. During the phase of plasma current ramp up, the ECE oscillation amplitude was about 5% as shown in Fig. 1 inlay zoom from 0.92 s to 1.0 s. The period of ADR events was about 4 ms. When the discharge reached flat-top, the ECE amplitude increased to 10%–12%, and the period increased to about 15 ms as shown in Fig. 1 inlay zoom from 1.2 s to 1.28 s. Since the ECRH can modify the electron distribution function in the perpendicular direction, it can be used to control the run-
3639
Fig. 2. Waveforms of slide-away discharge No. 3700 with ECRH. (a) is the plasma current and the ECRH power, (b) the line-averaged electron density, (c) the loop voltage and the critical voltage (2π REc ), (d) the center ECE emission intensity. The three inlays in (d) indicates the behaviors of ECE just before and during the ECRH, at the time of ECRH power switch off, and in the recovered slide away phase.
away electron beam driven instabilities. ECRH with power of about 200 kW deposited on-axis was switched on from 1.0 s to 2.0 s in a slide away discharge as shown in Fig. 2. In this discharge, the plasma current was about 380 kA, with B T = 2 T, and line averaged electron density about 0.5 × 1019 m−3 . The discharge went into the slide away regime at about 0.3 s. Before the ECRH phase, the ECE signal remained stationary with ADR events. The period of an ADR events was about 5 ms with 5% amplitude in oscillations. After the injection of ECRH power, the ECE signal decreased significantly to about one fourth of the initial amplitude, and the ADR events disappeared, with development of strong sawtooth activity. The ADR events in ECE disappeared when the ECRH power ramped up to about 150 kW, apparent the threshold of ECRH power for suppression of the ADR effects in these conditions. The sawtooth activities appeared following the suppression of the ADR effects. The conversion of the ADR events to sawtooth activities was finished in 20 ms. After the termination of the ECRH power, the ECE signal decreased again, which indicates that the electron temperature decreased and the low energy runaway population was quenched. Since the plasma density was low enough for the discharge to be converted into the slide away regime, the discharge went into the slide away regime again at about 2.3 s as indicated by the increase of ECE and the emergence of the ADR effects. The center ECE just before and after the termination of the ECRH is shown in Fig. 2 inlay zoom. It is found that the sawtooth activities became much weaker after the termination of ECCD power. In about 200 ms, the sawtooth activities disappeared and the ADR effects became obvious in 300 ms. The discharge finally went into a pure slide away regime as shown in inlay zoom of ECE from 2.92 s to 3.0 s. The period and amplitude are similar to that before the ECRH phase. 4. Discussion There is a critical energy for the runaway beam to undergoing ADR effects [3]. The critical energy for the ADR events to occur is much higher than the threshold energy of electrons to runaway. As a consequence of the ADR events, runaway electrons with a parallel energy slightly higher than the critical energy were pitch angle scattered into perpendicular energy. Their total energy then reduced due to the enhancement of electron cyclotron emission
3640
Z.Y. Chen et al. / Physics Letters A 376 (2012) 3638–3640
losses. It may lead to a barrier to a further increase in the runaway energy. Because the runaways are accelerated continually, this whole process repeats, so that the ADR events have a recurrent character: the ECE oscillations periodically flash and attenuate. The change of oscillation amplitude and period just at the beginning of the flat-top phase was possibly due to the decrease of loop voltage. With lower loop voltage, the electrons need more time to acquire the critical energy for the ADR effects to occur. The period of an ADR event is much larger than that in other machines, which have periods on the order of 1 ms [7–12]. The parallel electric field was about 0.1 V/m during the slide away phase in the HT-7 tokamak [11]. The parallel electric field was about 0.04 V/m during the slide away phase in the KSTAR tokamak. Thus the period of the ADR events is larger in KSTAR. In the FTU experiment [16], the electric field was decreased to below the threshold electric field ( E c =
e 3 ne ln Λ ) 4π ε02 me c 2
for runaway
generation by high power ECRH. In this case the synchrotron radiation loss was included in the calculation of threshold electric field for runaway generation which increased the threshold electric field. The runaway population does not appear when the electric field is small than the threshold electric field. Though high power ECRH can quench the runaway population by reducing the toroidal electric field below the threshold electric field E c for runaway generation [16], the ECRH power in this experiment was only 200 kW which could not quench the runaway population by a small drop of loop voltage. The electric field is much higher than the threshold electric field as shown in Fig. 2. The suppression of the ADR events could have occurred due to the modification of the electron distribution function by ECRH. The free energy source which drives REBIs is the distortion of the plasma electron distribution function by the applied electric field. The distribution became unstable owing to the ADR effects. The ECRH enhanced the perpendicular energy of electrons which could lead to an isotropization of the electron distribution function. In this case, the free energy source which drives REBIs decreased. Thus the REBIs can be suppressed by the ECRH. The suppression of the ADR events is likely to coincide with the suppression of low energy runaway population also as indicated by the drop of ECE signal. No measurement of the current density profile or q profile was available in these experiments, however results from theory [17] and other devices [18,19] help to interpret the present observations. Stabilization of sawtooth activity is expected to result from a decrease of current density at the magnetic axis and corresponding increase of q0 above 1, as would occur when ECCD is turned off. When the ECCD power is turned off, the fast electron population will slow down to thermal electrons. Thus the non-inductive current fraction will disappear. When the ECCD power is turned off, the resonance absorption between the waves and the thermal electrons disappeared. This will lead to a decrease of the electron temperature. Since the ECCD increased the perpendicular energy of electrons, it will increase the synchrotron radiation loss of fast electron pop-
ulation. Thus the threshold electric field for runaway generation will increase. On the other hand, the toroidal electric field will decrease due to the resonance absorption of wave power by thermal electrons which results in increase of electron temperature. So the ECCD has two benefits on the runaway suppression. 5. Summary In KSTAR tokamak, slide-away discharges have been observed in low density discharges with line averaged electron density nec < 0.6 × 10−19 m−3 . In the slide away regime, the ADR effects were observed in the ECE signals. The ADR events transfer energy from parallel to perpendicular motion. The ADR effect in the flat top phase had larger amplitude in oscillations and a larger period compared to that in the current ramp up phase. The ECRH was demonstrated to be effective in the suppression of the ADR effects in slide away discharges. About 150 kW ECRH power was enough to convert the slide away discharge into a normal discharge in KSTAR. The suppression of the ADR effects with ECRH is possibly due to the modification of electron distribution function and quenching of low energy runaway population. The ECRH enhanced the perpendicular energy of electrons which could lead to an isotropization of the electron distribution function. The discharge went into the slide away regime again in a few hundred ms after the ECRH phase. The ECRH provides us with a new way to suppress the REBIs. Acknowledgements It is a pleasure to acknowledge the assistance of KSTAR group. This work was partially supported by the National Natural Science Foundation (Nos. 11005090 and 11275079) and the National Magnetic Confinement Fusion Science Program (Nos. 2009GB104003 and 2011GB109001) of China. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]
M.N. Rosenbluth, S.V. Putvinski, Nucl. Fusion 37 (1997) 1355. H. Knoepfel, et al., Nucl. Fusion 19 (1979) 785. B.B. Kadomtsev, et al., Zh. Eksp. Teor. Fiz. 53 (1967) 2025. V.V. Parail, O.P. Pogutse, Nucl. Fusion 18 (1978) 303. P. Brossier, Nucl. Fusion 18 (1978) 1069. J.R. Martin-Solis, et al., Phys. Plasmas 9 (2002) 1667. J.M. Rax, et al., Europhys. Lett. 15 (1991) 497. T.F.R. Equipe, Nucl. Fusion 16 (1976) 473. V.S. Vlasenkov, et al., Nucl. Fusion 13 (1973) 509. V.V. Alikaev, et al., Sov. J. Plasma Phys. 1 (1975) 303. A.A.M. Oomens, et al., Phys. Rev. Lett. 36 (1976) 255. Z.Y. Chen, et al., Chin. Phys. Lett. 24 (2007) 3195. G. Fussmann, et al., Phys. Rev. Lett. 47 (1981) 1004. C. Gormezano, et al., Nucl. Fusion 47 (2007) S285. R.A. James, et al., Phys. Rev. A 45 (1992) 8783. G.S. Lee, et al., Nucl. Fusion 41 (2001) 1515. J.R. Martin-Solis, et al., Nucl. Fusion 44 (2004) 974. C.C. Petty, et al., Nucl. Fusion 42 (2002) 1366. C. Angioni, et al., Nucl. Fusion 43 (2003) 455.