Control of Neo-classical tearing mode (NTM) in advanced scenarios

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1 FIRST CHENGDU THEORY FESTIVAL Control of Neo-classical tearing mode (NTM) in advanced scenarios Zheng-Xiong Wang Dalian University of Technology (DLUT) Dalian, China Chengdu, China, 28 Aug, 2018

2 Outline Control methods of NTM Modeling & code we used NTM in RMS scenarios ECCD control of NTM in RMS Multiple-helicity NTM ECCD control of M-H NTM

3 Control methods of NTM 1. Remove seeds for NTM 2. Shear flow stabilization 3. Externally applied helical field (RMP) 4. Microwave current drive (ECCD) 5. Synergetic effects

4 Control methods of NTM Shear flow stabilization Rotation Profile Suppression of island Linearly, flow shear changes linear instability property. Nonlinearly, strong rotation shear suppresses islands. J.L. Wang et al NF 2017

5 Control methods of NTM Externally applied helical field (RMP) RMP amplitude island width Evolution of RMP, width and phase RMP is applied in phase region Suppression of NTMs and accelerating mode rotation by a modulated RMP. Completely suppressed ; or substantially Q. Hu and Q. Yu NF 2016

6 Control methods of NTM Microwave current drive (ECCD) unmodulated modulated ECCD modulation in the O-point Replace missing bootstrap current Comparison between unmodulated and modulated ECCD deposition M. Maraschek et al, PRL (2007)

7 Control methods of NTM Synergetic effects in DIII-D (a), Suppressing the locked mode (b) Increase of electron density (c) Increase of energy confinement time First control the locking phase by RMP, and then suppress locked island by ECCD F. A. Volpe et al, PRL (2015)

8 Outline Control methods of NTM Modeling & code we used NTM in RMS scenarios ECCD control of NTM in RMS Multiple-helicity NTM ECCD control of M-H NTM

9 Reduced MHD equations 1, z SA j jb Ez0, t u 1 2 u, j, z j R u, t p 2 2 p, // // p p S0, t u p S A E S j j j S b f 1 z0 A 0 b0 p B r 2 0 p0, and are the magnetic flux, vorticity and pressure, respectively. // a f j rdr / j rdr b 0 b0 0 z0 a : bootstrap current fraction A Modeling & code we used magnetic Reynolds number, Parallel transport coefficient, Code, MDC R A Reynolds number Perpendicular transport coefficient 9

10 Modeling & code we used The net EC drive current: j = j 1 + j 2 Yu s EC driven current transport model Yu Q. et al. POP 7 (2000) : : the thermal velocity : parallel velocity of the resonant electrons : collision rates A model for the spatiotemporal evolution of the EC driven current density J ECCD in singlefluid MHD is proposed by Westerhof and Pratt. Two major effects in establishing the EC driven current in fluid model a) parallel force term in the electron momentum balance equation b) modification of the electron-ion momentum exchange term E. Westerhof et al. Physics of Plasmas 21 (2015) 10

11 Modeling & code we used EC source used in this model is both radially and poloidally localized with Gaussian distributions centered at any point we need in the poloidal plane. EC current can be switched on and off any time we need. 11

12 Modeling & code we used Deposition of EC current after 1.0 ms With stationary magnetic island With rotating magnetic island With stationary island, steady current structure emerges, which fills the magnetic islands and follows the flux surfaces. With rotating island, the distribution region of the current is broader and the peak value is lower. 12

13 Outline Control methods of NTM Modeling & code we used NTM in RMS scenarios ECCD control of NTM in RMS Multiple-helicity NTM ECCD control of M-H NTM

14 NTM in RMS scenarios Equ parameters: q- profiles a/ R 0.25, 0 Large r s rs rs 2 rs Intermediate r s rs rs 2 rs Small r s rs rs 2 rs

15 NTM in RMS scenarios Nonlinear evolution for small rs f_b=0 1 DTM MR Ohm Source E S j j z0 A 0 b0 Evolution of kinetic energy f_b=0 Evolution of q-profile System enters a quasi-saturation state, similar to the Rutherford saturation.

16 NTM in RMS scenarios Nonlinear evolution for small rs Evolution of q- profile f_b=0.3 Evolution of kinetic energy f_b=0.6 f_b=0.6 For f_b=0.3, rational surfaces move inwards and then outwards, followed by oscillation. For f_b=0.6, rational surfaces move inwards and then disappear, followed by decay. Evolution of q-profile

17 NTM in RMS scenarios Nonlinear evolution for small rs f_b=0.6 First, m/n=9/3 mode appears And then island chains of m/n=9/3 and m/n=6/2 modes are merging together. Afterward, m/n=3/1 mode becomes dominant through the nonlinear mode coupling Evolution of kinetic energy Finally, no island appears in the decay phase

18 NTM in RMS scenarios Nonlin evolution for intermediate r s Perturbation on r_s1 is stabilized. Perturbation on r_s2 is destabilized. Explosive bursts effectively brought forward. Eigenfunction profiles Evolution of kinetic energy

19 NTM in RMS scenarios Nonlinear evolution for large rs f_b=0.6 Evolution of kinetic energy Linear eigenfunction High bs current induces bursts Islands on r_s2 is greatly destabilized. Full reconnection state is obained. Perturbation on r_1 is stabilized

20 Outline Control methods of NTM Modeling & code we used NTM in RMS scenarios ECCD control of NTM in RMS Multiple-helicity NTM ECCD control of M-H NTM

21 ECCD control of NTM in RMS Safety factor profile inner outer The q-profile with large separation Δr s = A radially uniform rotation profile with ω 0 =0.01 is applied in rotation case. Other typical parameters: a/ R S A R

22 ECCD control of NTM in RMS The baseline case of J_b destabilization Kinetic energy Island width The saturated island width of fb=0.3 is larger than that of fb=0. The explosive burst occurs at fb=0.6, which is previously observed only in intermediate separation cases for fb=0. 22

23 ECCD control of NTM in RMS The magnetic island width in the outer rational surface f_b=0 The ECCD has an evident stabilizing effect in both static and rotation cases. The saturated width gradually decreases with increasing ECCD. With sufficient ECCD, the TM can be completely suppressed. 23

24 ECCD control of NTM in RMS The influence of radial misalignments f_b=0 The radial misalignment can change the effectiveness of ECCD. Applying ECCD slightly inward deviate from the initial rational surface can attain a better stabilizing effect. There are two main reasons One is that the reversed shear can induce a strong zonal magnetic field and makes the outer rational surface move slightly inward. The other is that the outer magnetic island is greatly deformed through the interaction with the inner one. 24

25 ECCD control of NTM in RMS Temporal evolution of the island width w/o rotation f_b=0.3 w/o rotation During the early time after turning on ECCD, the island width decreases as normal. After a while, the island width increases instead with the so-called phase flip occurring. Soon after that, the explosive burst happens. 25

26 ECCD control of NTM in RMS f_b=0.3 w/o rotation t 2 t 3 The fine structure of the island Magnetic surfaces become fluctuating due to strong zonal magnetic field. phase flip occurs as ECCD aims at the X-point. The burst is induced by the synergistically driven force of ECCD and NTM. 26

27 ECCD control of NTM in RMS Putting forward the turn-on time of ECCD f_b=0.3 w/o rotation w rotation The influence of radial misalignments The NTM is completely suppressed with sufficiently large ECCD. The power of ECCD needed to completely suppress NTM in rotation cases is larger than static cases. w/o rotation w rotation A small inward movement can enhance the stabilizing effect in both cases. In rotation cases, saturated width becomes larger with the inward movement. 27

28 ECCD control of NTM in RMS Putting forward the turn-on time of ECCD f_b=0.6 w/o rotation w rotation The explosive burst can be effectively suppressed through enhancing the power of ECCD. For rotation cases, the explosive burst can be delayed with deficient ECCD. The influence of radial misalignments w/o rotation w rotation A small inward movement of ECCD can enhance the stabilizing effect. In rotation cases, saturated island width becomes larger with the inward movement. 28

29 Outline Control methods of NTM Modeling & code we used NTM in RMS scenarios ECCD control of NTM in RMS Multiple-helicity NTM ECCD control of M-H NTM

30 Multiple-helicity NTM Current, pressure and safety factor profiles Linear Spectra r Except for the m/n=2/1 mode with the linear instability parameter >0, the classical tearing modes with m/n=3/2 are linearly stable <0. Initial plasma perturbations from the core and boundary region are applied for the m/n=3/2 mode in the following nonlinear results. f b The plasma rotation is considered by setting. d V0 d 0( r) 0r(1 r) r 30

31 Neo-classical tearing mode Seeds from core region The magnetic island width grows up when the initial perturbation is larger than a critical value, which is consistent with the theory and simulation of the meta-stable NTMs. seed t saturated Two w/ t=0 points are, respectively, the critical seed island width and saturated island width, which are the corresponding solutions of the modified Rutherford equation. w (a) Evolution of magnetic islands (b) Growth rate of island VS width

32 Multiple-helicity NTM Evolution of island widths of 2/1 and 3/2 NTMs in the multiple helicity simulation fb=0.3 SH, 2/1 MH, 2/1 Time history of pressure profile and snapshots of pressure perturbations ( a) 10 1 SH, 3/2 MH, 3/2 t t When the magnetic island width of 2/1 NTM exceeds that of 3/2 NTM, the 3/2 NTM is gradually suppressed due to the competition among NTMs with different helicities. The pressure perturbation near the 3/2 surface decreases very fast and gradually merges into the pressure perturbation of 2/1 NTM, accompanied by the reduced 3/2 magnetic islands. 32

33 Multiple-helicity NTM Seeds from core region Although its linear growth rate increases by increasing the plasma rotation strength Ω, the saturated island width of 2/1 NTM decreases with increasing Ω with fixed plasma rotation m/n=2/1 m/n=2/1 m/n=3/2 The 3/2 and 2/1 NTMs could coexist in the saturation stage, which is qualitatively different from the case without plasma rotation, due to the weak stabilizing effect of 2/1 NTM on 3/2 NTM for large fixed Ω. m/n=3/2 t Evolution of island widths of 2/1 and 3/2 modes in presence of rotation. L. Wei, Z. X. Wang, J. Wang Nucl Fusion (2016) 33

34 Neo-classical tearing mode Seeds from boundary ( a) Penetration of RMP or error field will induce the driven reconnection on the resonant surface. Magnetic island seeded by the driven reconnection can excite the NTM with negative. As the amplitude of boundary perturbation on the plasma boundary increases, the mode with < 0 will gradually change from the drivenreconnection state to the NTM state. seed ( b) w (a) Evolution of magnetic islands (b) Growth rate of island VS width saturated

35 Multiple-helicity NTM Evolution of island widths of 2/1 and 3/2 NTMs w/o rotation Multiple Helicity, fb=0 Single Helicity, fb=0.3 m/n=2/1 Multiple Helicity, fb=0.3 m/n=2/ m/n=2/ m/n=3/ m/n=3/2 m/n=3/ t t t The magnetic islands induced by the driven reconnection triggered 3/2 NTM are gradually suppressed because of the competition effect of 2/1 NTMs, when the magnetic island width of 2/1 NTM exceeds that of 3/2 NTM. The m/n=2/1 spontaneous NTM makes the 3/2 mode transfer from the driven reconnection triggered NTM state back to the driven reconnection state with small magnetic islands. 35

36 Multiple-helicity NTM Seeds from boundary The nonlinear interaction between 3/2 and 2/1 NTMs with large Ω is almost the same as that without plasma rotation. Unfixed plasma rotation The linearly stable 3/2 tearing mode becomes unstable due to the destabilizing effect of rotation shear. The shear flow triggered 3/2 NTM still can be suppressed by the relatively large 2/1 magnetic perturbation due to the competition among NTMs. t L. Wei, Z. X. Wang, J. Wang Nucl Fusion (2016) 36

37 Multiple-helicity NTM Seeds from boundary The shielding effect of plasma rotation on the 3/2 magnetic perturbation at the plasma boundary is observed. Even though the linear growth rates of both 3/2 and 2/1 modes increase with increasing Ω, the stabilizing effect of 2/1 NTM on 3/2 NTM due to the nonlinear interaction between NTMs becomes weak as Ω increases. with fixed plasma rotation t Evolution of island widths of 2/1 and 3/2 modes in presence of rotation. 37

38 Poincaré plots of magnetic field lines in a poloidal cross section Nonlinear coupling of 2/1 and 3/2 modes inevitably results in the magnetic stochasticity between 2/1 and 3/2 rational surfaces. Multiple-helicity NTM ( a ) ( b) Five islands are well located near the 5/3 rational surface in the early nonlinear phase, when 3/2 magnetic islands are comparable to 2/1 magnetic islands. () c ( d) 3/2 NTM is gradually suppressed by the 2/1. 38

39 Outline Control methods of NTM Modeling & code we used NTM in RMS scenarios ECCD control of NTM in RMS Multiple-helicity NTM ECCD control of M-H NTM

40 ECCD control of M-H NTM Safety factor profile The monotonic safety factor q-profile is adopted. A radially uniform rotation profile with ω 0 =0.01 is applied in the rotation cases. Other typical parameters: a/ R and 1 6 S A R 10 40

41 ECCD control of M-H NTM The temporal evolution of magnetic island widths f 0.3 b The 2/1 NTM can suppress the 3/2 NTM to some extent. The suppression is due to the competition among different helicity NTMs. When the 2/1 island grows large enough to reach the 3/2 rational surface, the 2/1 island can change the perpendicular transport of 3/2 island. 41

42 The baseline case ECCD control of M-H NTM The magnetic island evolution of 2/1 SH NTM with ECCD 2/1 island can be effectively suppressed by ECCD in both cases. To achieve the same effect, the required ECCD power is larger in rotation cases. steady distributions of EC driven current static cases rotation cases The directions of the EC current are opposite to each other in static cases. The directions of the EC driven current are the same in rotation case. 42

43 ECCD control of M-H NTM In static cases The temporal evolution of magnetic island widths with ECCD With relatively low ECCD, as 2/1 island width decreases, the 3/2 island will grow again and then reach saturation. With sufficiently large ECCD to completely suppress the 2/1 island, the 3/2 island can also be suppressed. 43

44 In rotation cases ECCD control of M-H NTM The temporal evolution of magnetic island widths with ECCD With relatively low ECCD, as 2/1 island width decreases, the 3/2 island will grow again and then reach saturation. With sufficiently large ECCD to completely suppress the 2/1 island, the 3/2 island can also be suppressed. Further increasing ECCD, 2/1 can be suppressed in a short time. And 3/2 has a little rise first and then is suppressed. 44

45 In rotation cases ECCD control of M-H NTM The island evolution with ECCD turned on at different time For I cd /I p =1.43%, the 3/2 can be barely influenced when turning on ECCD early. For I cd /I p =7.14%, the 3/2 can be suppressed no matter what time the ECCD is turned on. 45

46 ECCD control of M-H NTM The island evolution with different transport coefficient // and // / = // / = // / = With increasing parallel transport coefficient, influence on 3/2 is reduced. After 2/1 is suppressed, the 3/2 can saturate in a relatively high state. With increasing parallel transport coefficient, ECCD power required to completely suppress 2/1 NTM become larger. 46

47 ECCD control of M-H NTM // / = Due to the large parallel coefficient, the 3/2 can saturate with a relatively large island width after 2/1 is suppressed. The 3/2 can be suppressed with another ECCD aiming at the 3/2 rational surface. 47

48 References Z.X. Wang*, T. Liu et al, "Control of multi-helicity NTMs by ECCD in tokamak plasmas" submitted to Nucl. Fusion (2018) T. Liu, Z.X. Wang* et al, "Suppression of explosive bursts triggered by NTM in RMS tokamak plasmas via ECCD " Nucl. Fusion 58, (2018) J.L. Wang, Z.X. Wang* et al, "Control of neo-classical DTMs by differential poloidal rotation in RMS tokamak plasmas" Nucl. Fusion 57, (2017) Cover articles L. Wei, Z.X. Wang* et al, "Nonlinear evolution of multi-helicity NTMs in rotating tokamak plasmas" Nucl. Fusion 56, (2016) Z.X. Wang*, L. Wei et al, "Nonlinear evolution of NTM in RMS tokamak plasmas" Nucl. Fusion (2015) Cover articles & Highlights L. Wei and Z.X. Wang*, "Nonlinear evolution of DTMs in tokamak plasmas via multiple helicity simulation" Nucl. Fusion 54, (2014)

49 Thank you very much! 49

50 ECCD control of NTM in RMS The steady distributions of the EC driven current f_b=0 The EC current has a steady distribution of the island structure. For static island in (a) and (b), the directions of the EC driven current inside island are opposite to each other. For rotary island in (c) and (d), the directions are the same, but the distributions are different. 50

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