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Reversed Magnetic Shear (RMS) in Fusion Plasmas

Updated 17 November 2025

Reversed Magnetic Shear (RMS) configurations are magnetic equilibria featuring non-monotonic q-profiles with negative magnetic shear regions that enable refined turbulence suppression.
They are achieved through manipulating current drive and plasma rotation, which form internal transport barriers and regulate MHD instabilities in advanced fusion scenarios.
RMS enhances confinement and energetic particle control by optimizing q-profile structures, thereby supporting steady-state, high-performance tokamak operation.

Reversed Magnetic Shear (RMS) configurations are magnetic equilibria in toroidal confinement systems, primarily tokamaks and stellarators, in which the radial profile of the safety factor $q(r)$ exhibits a non-monotonic behavior—typically a local minimum at some intermediate radius. This produces regions where the local magnetic shear $\hat s(r) = \frac{r}{q}\frac{dq}{dr}$ is negative. RMS provides fundamentally altered stability and transport properties, influencing the formation of internal transport barriers (ITBs), energetic particle dynamics, nonlinear turbulent behavior, and magnetohydrodynamic (MHD) instabilities. RMS is a cornerstone of advanced steady-state fusion scenarios due to its role in high bootstrap current fractions and enhanced confinement.

1. Magnetic Shear Reversal: Definitions and Generation Mechanisms

In conventional positive-shear tokamaks, $q(r)$ rises monotonically from center to edge, with $\hat s>0$ everywhere. RMS profiles are constructed so that $q(r)$ has a central or off-axis maximum, a distinct minimum $q_{\min}$ at radius $r_{\min}$ , and increases again toward the plasma boundary, yielding $\hat s<0$ for $r<a$ with $a$ the minor radius (Nakamura, 16 May 2024). The local reversal is realized by manipulating the current profile (current ramp-up, off-axis current drive via neutral beams (NBCD), lower hybrid current drive (LHCD), or helicon current drive (HCD)), by localized toroidal rotation (Li et al., 2021), or through turbulent self-organization (Volčokas et al., 6 Feb 2025).

Key conditions for RMS formation include sharp bumps in the parallel current profile $J_{\parallel}(r)$ and sufficient local peaking in the rotation profile in high- $\beta$ regimes. The Grad–Shafranov equilibrium including toroidal rotation yields the criterion

$\dfrac{d\ln\langle J_{\parallel}\rangle}{d\psi}\gtrsim \mathcal{O}(1)$

which, for a strong edge rotation, naturally induces $dq/d\psi < 0$ and thus RMS. High $\beta$ amplifies this effect, making RMS more accessible in advanced scenarios (Li et al., 2021).

2. Transport Barriers and Turbulent Transport Suppression

RMS regions are closely associated with robust internal transport barriers (ITBs), which manifest as steep gradients of temperature and density, sharply reduced local turbulent diffusivity $\chi_{i,e}$ , and enhanced confinement. Nonlinear gyrokinetic simulations demonstrate that RMS elevates the nonlinear critical gradient $z_c^{\mathrm{NL}}=(R/L_{T_e})_{\rm crit,nonlin}$ for electron-temperature-gradient (ETG)-driven turbulence by nearly a factor of three over the linear threshold $z_c^{\rm lin}$ (Peterson et al., 2011). Thus, electron heat transport remains suppressed until gradients reach $z_c^{\mathrm{NL}}$ , sustaining high core temperatures and low heat loss.

In addition, RMS configurations with stepped $q$ profiles at low-order rationals (turbulence-generated) yield extended regions of near-zero shear, where eddies elongate along field lines, enhancing parallel interaction and reducing radial transport—a feedback mechanism that triggers ITB formation even at modest $\beta$ (Volčokas et al., 6 Feb 2025). This self-organized staircase of $q$ -plateaus acts as a series of quasi-transport barriers.

3. MHD Stability: Effects on Resistive Wall Modes and Kinks

RMS affects the stability landscape for macroscopic MHD modes, especially resistive wall modes (RWMs), kinks, ballooning modes, neoclassical tearing modes (NTMs), and double tearing modes (DTMs) (Nakamura, 16 May 2024, Wan et al., 11 Jan 2024, Wan et al., 1 Sep 2025). Analytic and simulation studies reveal:

Increasing core reversal strength (more negative $s_{\rm core}$ ) destabilizes the $n=1$ RWM, broadening the unstable $\beta_N$ window and raising the rotation stabilization threshold (Wan et al., 1 Sep 2025). The critical rotation frequency required for suppression follows $\Omega_c \propto |s_{\min}|^{0.5\mbox{--}0.7}$.
A widened zero-shear plateau near the edge acts to stabilize RWMs, except when the flat- $q$ region approaches a low-order rational (Wan et al., 11 Jan 2024). Positive shear at the edge is always stabilizing.
DTMs become prominent when two nearby rational surfaces occur in the RMS region (e.g., $q_{\min}\rightarrow 2$ ), potentially leading to rapid reconnection unless mitigated by central electron heating (Nakamura, 16 May 2024).
RMS suppresses NTMs by maintaining $q_{\min}\gtrsim 2$ , helping avoid the $m/n=2/1$ and $3/2$ tearing thresholds.

4. Alfvénic Activity and Energetic Particle Physics

RMS alters the spectrum of Alfvénic and energetic particle modes. The local minimum of the shear-Alfvén continuum supports discrete Reversed Shear Alfvén Eigenmodes (RSAEs) localized near $q_{\min}$ (Wang et al., 2020). The interplay between weak local shear and energetic particle (EP) drive results in:

RSAEs with broad, global radial structure and strong nonperturbative EP-induced growth rates and frequency shifts (up to 10% of mode frequency), as observed and simulated in hybrid MHD-gyrokinetic codes (Wang et al., 2020).
Nonlinear saturation occurs via radial EP convection and decoupling rather than local trapping, with EP transport over wide regions and non-adiabatic frequency chirping.
Nonlinear RSAE decay into low-frequency Alfvén modes (LFAMs) via three-wave coupling produces core-localized $\alpha$ -channeling: spontaneous RSAE $\rightarrow$ (RSAE + LFAM) with LFAM Landau damping heating core fuel ions (Wei et al., 2022, Qiu et al., 2023). This process is efficient for future reactors with a dense core-localized RSAE spectrum (due to small $\alpha$ orbits near $q_{\min}$ ).

5. Microinstabilities and Double-Well Potential Structure

For ion temperature gradient (ITG) driven turbulence, RMS produces unique kinetic features (Jia et al., 10 Nov 2025). The generalized eigenmode equation, transformed to a Schrödinger-type ODE, reveals:

In RMS, the effective radial "potential" for ITG modes acquires a double-well shape, with wells centered on rational surfaces where $q(r)$ achieves local minima. This leads to degeneracy between even and odd parity eigenstates when wells are well separated—both types can be excited in turbulence.
The maximum ITG growth rate is achieved when the two wells slightly overlap; increasing separation (deeper RMS) restores isolated wells and lower growth.
Mode drive resonates with the average magnetic drift frequency, remaining the principal instability mechanism but with spatial trapping set by RMS geometry.
Comparison with global gyrokinetic simulations (GTC) confirms quantitative accuracy of this reduced model for both normal and RMS cases.

6. Magnetic Topology, Particle-Orbit Effects, and Transport Barriers

RMS fundamentally modifies magnetic topology for both field lines and full particle orbits (Ogawa et al., 2016, del-Castillo-Negrete et al., 2014), with critical consequences for transport:

The shearless ("nontwist") surface at $q'(r_*)=0$ acts as an internal transport barrier (ITB) for both field lines and, in an energy and pitch–angle dependent manner, for particles.
Reversed-shear fields produce twin magnetic islands for each rational $(m,n)$ , with separatrix reconnection phenomena and the formation of shearless Cantori, which act as partial transport barriers and quasi-static islands regardless of complete surface destruction by stochasticity (del-Castillo-Negrete et al., 2014).
Numerical studies show particle ITBs can persist even when field-line ITBs are broken by stochasticity; their effectiveness depends on orbit energy and pitch angle, with finite-Larmor-radius and drift effects modulating transport permeability (Ogawa et al., 2016).
Radial heat pulse propagation in RMS is orders of magnitude slower than in monotonic $q$ profiles for comparable field stochasticity, confirming robust transport barrier properties even in fully chaotic regions.

7. Practical Implementation, Stability Optimization, and Reactor Implications

Experimental and simulation evidence from DIII-D, JT-60U, ASDEX Upgrade, JET, PBX-M, COMPASS-D, and reactor studies (ARIES-RS/AT, SSTR) indicates that RMS profiles are pivotal for achieving high-performance steady-state operation (Nakamura, 16 May 2024). Essential features for optimization include:

Maintaining $q_{\min}\in(2,3)$ and avoiding strong rational resonances in the core to suppress MHD/AE instability (Varela et al., 2019).
Employing off-axis NBI deposition to prevent energetic particle gradient peaks at $q_{\min}$ and operating in weak resonance regimes for beam ions.
Exploiting turbulence-induced staircase $q$ profiles for passive barrier formation, supplementing with advanced current drive and central heating for sustainability.
Ensuring edge positive shear and broad zero-shear edge plateaus for RWM stabilization; active feedback and sufficient rotation are often required for wall-modes.
High poloidal and normalized beta ($\beta_p\sim0.5\mbox{--}1.2$, $\beta_N\sim2\mbox{--}4$), broad current profiles, and robust bootstrap fractions ( $f_{BS}>0.75$ ) are engineered through RMS.

Challenges remain, particularly coupling high-power RF at reactor densities and sustaining sufficient rotation for wall-mode control at large radius. Nevertheless, RMS is the dominant paradigm for non-inductive, high-confinement, and stable tokamak fusion operation.

Table: Key Effects of RMS on Mode Stability and Transport

RMS Feature	Main Effect	Confinement/Stability Consequence
Negative core shear	Raises ETG/ITG nonlinear critical gradients	Suppressed turbulent transport, ITBs
$q$ staircase profile	Extends zero-shear regions near rationals	Passive formation of multiple transport barriers
Core-localized RSAEs	Nonlinear decay to LFAM, efficient $\alpha$ -channeling	Direct fuel ion heating, enhances burn
Twin rational islands	Shearless Cantori/barrier formation	Slow radial transport, robust trapping
RWM stabilization	Edge positive shear, rotation thresholds	Active/passive control required for stability

In summary, RMS configurations alter magnetic, kinetic, and transport properties in ways that enable advanced operational regimes. Implementation requires precise control of $q(r)$ profiles through equilibrium shaping, current drive, localized heating, and turbulence management, with ongoing research into optimal barrier placement, energetic particle management, and stability control (Volčokas et al., 6 Feb 2025, Nakamura, 16 May 2024, Wan et al., 1 Sep 2025).