Reduced kinetic model for ion temperature gradient instability in tokamaks with reversed magnetic shear

Abstract

Using the averaged magnetic drift model and a first-order finite Larmor radius (FLR) expansion, the eigenvalue equation for the ion temperature gradient (ITG) mode in tokamak plasmas is reduced to a Schrödinger-type differential equation. By invoking generalized translational invariance, the model is extended to reversed magnetic shear (RMS) configurations and benchmarked against global gyrokinetic simulations from GTC, showing good quantitative agreement. The analysis reveals a characteristic double-well potential unique to RMS profiles, which gives rise to the degeneracy between the lowest-order even and first-order odd eigenmodes when the two potential wells are sufficiently separated radially. The ITG instability is also found to resonate with the magnetic drift frequency, and its maximum growth occurs when the two rational surfaces are slightly separated. These results provide new physical insight into ITG mode behavior under reversed magnetic shear and offer a compact, accurate theoretical framework that bridges simplified analytic models and global simulations.

Figures (10)

• Figure 1: (a) Real frequency and (b) growth rate of the ITG mode as functions of $k_{\theta}\rho_{i}$. Blue and orange lines correspond to the GTC simulation and the reduced model results, respectively.
• Figure 2: (a) Potential well (solid lines), mode structure (filled circles), and q-profile (green dashed line) of the eigenvalue equation eq:newModel for the CBC parameters. (b) Full potential well (solid lines), together with the second-order (dashed lines) and fourth-order (filled circles) Taylor expansions of the potential well for the same parameters. Blue and orange lines represent the real and imaginary parts of the potential well, respectively.
• Figure 3: Eigenvalue (Real frequency $\omega_{r}$ and growth rate $\gamma$) trajectories in the complex plane with respect to different parameter scans. Solid lines represent the kinetic integral model shown here as references. Filled circles represent the Weber form equation eq:weberEq
• Figure 4: Radial mode structures for normal shear (a,c) and RMS (b,d), (a,b) represent ideal translational invariance and generalized translational invariance while (c,d) represent the GTC simulation results correspondingly.
• Figure 5: (a) Real frequency (solid lines) and growth rate (dashed lines) of the ITG dispersion relation calculated using the first four orders of the finite Larmor radius (FLR) expansion shown in blue, orange, green, and red lines, respectively. (b) Dispersion relation comparison between the first-order FLR expansion and GTC simulation results, where the GTC results for different toroidal mode numbers (n) are represented by blue, orange, and green filled circles.