Locking of tearing modes by error field in J-TEXT Tokamak

1. Locking of tearing modes by error field in J-TEXT Tokamak Tao XU Qiming HU, Xiwei HU Qingquan YU College of Electric and Electronic Engineering, Huazhong University of Science and Technology

2. Contents 1. Background 2. Basic Equations 3.Modeling Results 4. Conclusion Page 2 Page 2

3. 1. Background Page 3 Error field are generated primarily by field-coil misalignments and nonaxisymmetric coil-feeds. Considerable theoretical [1-8] and experimental [9-12] effort has been done on the interaction of small resonant helical magnetic field errors with neoclassical tearing modes (NTM) in tokamaks. The Locking threshold was found to be very small, typically bra/Bt∼10⁻⁴-10⁻³, where brais the radial component of the error field at the plasma edge r=a, and Bt is the toroidal magnetic field. Page 3

4. The magnetic reconnection can be driven by error field, which result in the formation of locked magnetic islands in even intrinsically tearing stable plasmas. The locking of neoclassical tearing modes by error field degrade the plasma confinement. In order to avoid these excitation, we will study the interaction of error field with tearing mode in J-TEXT tokamak. • Because the 2/1 tearing modes can lead to a disruption , we will discuss it mainly in this paper.

5. 2. Basic equations In this paper, large aspect ratio tokamak plasmas (ε=a/R≪1, where ε, a, R are the inverse aspect ratio, the minor and the major radii, respectively) are considered. The equilibrium toridal magnetic field is Btet. The purturbed error field is expressed in term

9. 3 Modeling results3.1 Locking of tearing mode by error field • In this subsection, we will study the interaction of the error field with m/n=2/1 magnetic island. We will use the J-TEXT discharge 1011914, for this discharge a large data set was available. The boundary is chosen as ψb=1.2×10⁻⁵(aBt), the initial magnetic island width is about 0.01a. Te₀=0.8kev, S=8.7×10⁶, χ∥=1.9×10⁹(a²/τR), X⊥≈μ≈0.6(a²/τR). jb= 2.5×10⁻⁴(Bt/μ₀a), ne=1.14×10¹⁹m⁻³, τR=0.15 s, the initial rotatin angle frequency is ω₀=5.6×10⁴ s⁻¹.

10. Three cases are examined: one is the case with superposition of error field, and with bootstrap current, 'with error field'; the second is the case with superposition of error field, and without bootstrap current, 'without bootstrap'; the third is the case without error field and without bootstrap current, 'without error field'.

13. 3.2 The time for the magnetic island to be locked • For a given system, once the error field amplitude is larger than a critical value ψc, the magnetic island will eventually be locked as shown in Figures 1 and 2. The stronger the error field is, the less time is required for the magnetic island to be locked. Figure 3 shows the relation between the required time for mode locking and theerror field amplitude, assuming the island width starts to grow from 0.01a. In figure 3, the input parameters are: Te=0.8Kev, S=7.6×10⁶, χ∥=1.5×10⁹(a²/τR), χ⊥≈μ≈0.8(a²/τR), jb= 3×10⁻⁴(Bt/μ₀a), τR =0.15 s, ne=1.5×10¹⁹m⁻³. Figure 3 shows two case: the first case is ω₀=4×10⁴ s⁻¹, the second case: ω₀=2×10⁴ s⁻¹. where ω0 is the mode frequency without the error field.The critic value of error field is ψc=3.65×10⁻⁶ (aBt) for the first case, and ψc=1.2×10⁻⁶ (aBt) for the second case. The time t→∞ for the magnetic island to be locked as error field ψ→ψc.

15. 3. 3The threshold for mode locking • We are interested in the dependence of the threshold on the plasma rotation. Numerical simulations have been carried out for m/n=2/1 mode in J-TEXT. In figure 4 J-TEXT input parameters are: S=1.19×10⁷, χ∥=4.5×10⁹ (a²/τR), μ≈χ⊥≃1.1 (a²/τR), Te=1Kev, ne=1.14×10¹⁹m⁻³, jb= 3×10⁻⁴(Bt/μ₀a). • Figure 4 shows the mode locking threshold versus the island angular rotation frequency ω.

17. In figure 5, input parameters are: S=7.6×10⁶, χ∥=1.5×10⁹ (a²/τR), ne=1.5×10¹⁹m⁻³, μ≈χ⊥≃0.8 (a²/τR), jb= 3×10⁻⁴(Bt/μ₀a) • Figure 5 shows the threshold ψ_{threshold} for mode excitation changed with plasma viscosity μ in the 2/1 resonant surface. • Figure 5 shows that • We also get

21. 4. Conclusion • In summary, we have found the mode locking threshold, equation (11), for J-TEXT tokamak plasmas. The threshold is proportional to μ^0.5 and S^(−2). We have also found that faster rotating plasmas are more resistant towards mode locking. • In order to research the effect of the helical field on tearing modes, saddle coils will be installed in J-TEXT tokamak soon. The mode locking threshold will be studied in future experiments and compared to our theoretical results.

22. Thanks Page 22