Error Field Penetration Research Articles

Quantification of locked mode instability triggered by a change in confinement

Abstract This work presents the first analysis of the disruptive locked mode (LM) triggered by the dynamics of a confinement change. It shows that, under certain conditions, the LM threshold during the transient is significantly lower than expected from steady states. We investigate the sensitivity to a controlled n = 1 error field (EF) activated prior to the L-H transition in the COMPASS tokamak, at q 95 ∼ 3, β N ∼ 1, and using EF coils on the high-field side of the vessel. A threshold for EF penetration subsequent to the L-H transition is identified, which shows no significant trend with density or applied torque, and is an apparent consequence of the reduced intrinsic rotation of the 2/1 mode during this transient phase. This finding challenges the assumption made in theoretical and empirical works that natural mode rotation can be predicted by global plasma parameters and urges against using any parametric EF penetration scaling derived from steady-state experiments to define the EF correction strategy in the entire discharge. Furthermore, even at EFs below the identified penetration threshold, disruptive locking of sawtooth-seeded 2/1 tearing modes is observed after about 30% of L-H transitions without external torque.

Overview of recent experimental results on the EAST Tokamak

Since the last IAEA-FEC in 2021, significant progress on the development of long pulse steady state scenario and its related key physics and technologies have been achieved, including the reproducible 403 s long-pulse steady-state H-mode plasma with pure radio frequency (RF) power heating. A thousand-second time scale (∼1056 s) fully non-inductive plasma with high injected energy up to 1.73 GJ has also been achieved. The EAST operational regime of high β P has been significantly extended (H 98y2 > 1.3, β P ∼ 4.0, β N ∼ 2.4 and n e/n GW ∼ 1.0) using RF and neutral beam injection (NBI). The full edge localized mode suppression using the n = 4 resonant magnetic perturbations has been achieved in ITER-like standard type-I ELMy H-mode plasmas with q 95 ≈ 3.1 on EAST, extrapolating favorably to the ITER baseline scenario. The sustained large ELM control and stable partial detachment have been achieved with Ne seeding. The underlying physics of plasma-beta effect for error field penetration, where toroidal effect dominates, is disclosed by comparing the results in cylindrical theory and MARS-Q simulation in EAST. Breakdown and plasma initiation at low toroidal electric fields (<0.3 V m−1) with EC pre-ionization is developed. A beneficial role on the lower hybrid wave injection to control the tungsten concentration in the NBI discharge is observed for the first time in EAST suggesting a potential way toward steady-state H-mode NBI operation.

Error field penetration in J-TEXT tokamak based on two-fluid drift-MHD model

An externally generated resonant magnetic perturbation can induce complex non-ideal MHD responses in their resonant surfaces. We have studied the plasma responses using Fitzpatrick’s improved two-fluid model and program LAYER. We calculated the error field penetration threshold for J-TEXT. In addition, we find that the island width increases slightly as the error field amplitude increases when the error field amplitude is below the critical penetration value. However, the island width suddenly jumps to a large value because the shielding effect of the plasma against the error field disappears after the penetration. By scanning the natural mode frequency, we find that the shielding effect of the plasma decreases as the natural mode frequency decreases. Finally, we obtain the m/n = 2/1 penetration threshold scaling on density and temperature.

Error-field penetration thresholds in ohmically heated ITER and SPARC plasmas

The critical n = 1, n = 2, and n = 3 error-field amplitudes needed to trigger error-field penetration in ITER and SPARC, steady-state, ohmically heated plasmas are calculated using a standard asymptotic matching approach. The calculation incorporates plasma impurities, trapped particles, the bootstrap current, and neoclassical poloidal flow-damping. The energy confinement time is specified by the neo-Alcator scaling law in the low-density linear Ohmic confinement (LOC) regime and by the ITER-89P L-mode scaling law in the high-density saturated Ohmic confinement (SOC) regime. The response of the plasma in the inner region is calculated using a linearized version of the four-field model. At the normal operating electron number density, diamagnetic levels of rotation are found to be sufficient to protect ITER and SPARC ohmically heated plasmas from m=2/n=1 error-field penetration. On the other hand, SPARC, and especially ITER, ohmically heated plasmas may be vulnerable to n &amp;gt; 1 error-field penetration. ITER and SPARC ohmically heated plasmas are also slightly more susceptible to error-field penetration when the electron fluid at the rational surface rotates in the ion diamagnetic direction, rather than the electron diamagnetic direction. At electron number densities that are sufficiently low that the plasma lies in the LOC confinement regime, the error-field penetration threshold increases with increasing density. However, as soon as the electron number density becomes large enough that the plasma enters the SOC regime, the increase in the error-field penetration threshold with increasing density levels off.

The effect of plasma beta on error-field penetration in radio-frequency wave heated plasmas in EAST

The plasma-beta effect on the n = 1 resonant magnetic perturbation (RMP) field penetration in purely radio-frequency (RF) wave heated discharges has been investigated in EAST. The experimental results show that the dependence of the threshold RMP coil current for field penetration, , on the total absorbed power P tot scales as approximately , indicating that the error-field tolerance is improved with increasing RF power. This is benefited by the increased electron perpendicular flow dominated by a counter-current electron diamagnetic flow with increasing RF power. However, theoretical scaling in cylindrical geometry overestimates the power index. Assuming an additional term for the normalized beta in the scaling, it is shown that the fitted from the experimental observation is around −1, indicating a degradation effect of plasma beta. To clarify the underlying physics of the plasma-beta effect that was not included in the theoretical scaling in cylindrical geometry, the MARS-Q code with full toroidal geometry is employed for simulation of nonlinear field penetration (Liu et al 2013 Phys. Plasmas 20 042503). The MARS-Q simulation results reproduce the dependence well, and hence the P tot scaling of the threshold current in experimental observations. The main reason for this is that the net total torque, which is mainly contributed by the neoclassical toroidal viscosity (NTV), increases with increasing plasma . The results demonstrate that the nonlinear toroidal coupling effect via NTV torque plays an important role in determining field penetration, even in cases with relatively low , which is far less than the no-wall beta limit.

Influence of anomalous perpendicular transport on linear tearing mode dynamics in tokamak plasmas

The analysis of a previous paper [A. Cole and R. Fitzpatrick, Phys. Plasmas 13, 032503 (2006)] that maps out all of the two-fluid response regimes of a linear tearing layer interacting with an externally generated resonant magnetic perturbation, in a large aspect-ratio tokamak plasma, is generalized to take into account realistic levels of perpendicular particle transport. A new response-regime map is obtained that differs substantially, in many respects, from the old one. The improved analysis is first employed to find all of the two-fluid growth-rate regimes of a non-interacting low-mode-number tearing mode in a large aspect-ratio tokamak plasma. The analysis is then used to determine the scaling of the error-field penetration threshold with machine parameters in large aspect-ratio tokamak plasmas.

Density scaling of error field penetration in radio-frequency-dominant heating plasmas in the EAST tokamak

The density scaling of n = 1 error field penetration is investigated under radio-frequency (RF)-dominant heated L-mode discharges in the EAST tokamak. It is found that the density scaling of the threshold field strength for error field penetration in lower-hybrid current drive (LHCD) plasmas is about , where b r represents the error field amplitude. The results show a weaker density dependence compared to that observed in the previous ohmic heated discharges (Wang et al 2018 Nucl. Fusion 58 056024). For a better understanding of the density scaling, it is compared with field penetration theories, and it is found that it lies in the Waelbroeck regime. The observed scaling is consistent with that evaluated with the magnetohydrodynamic (MHD) theory on error field penetration, for which all the physical parameters are determined experimentally. Due to the density dependence of LHCD heating efficiency, the stronger negative correlation between density and temperature results in a weaker density scaling in these LHCD plasmas. Using realistic parameters under LHCD and ohmic heating as input, respectively, the numerical results based on a reduced MHD model reproduce well the scaling from the error field penetration theory and the observations. Besides, the density scaling in various tokamak operational regimes is also numerically investigated. This provides an excellent validation of MHD theory on error field penetration in the RF-dominant heated L-mode discharges.

Toroidal field and q95 scalings on error field penetration in EAST

Toroidal field and q95 scalings of error field penetration are investigated with n = 1 resonant magnetic perturbation coil in EAST. The toroidal field scalings of error field penetration thresholds under fixed q95 are about in both ohmically and lower hybrid wave heated plasmas, where br21 is the vacuum error field at the q = 2/1 rational surface and BT is the toroidal field. These scalings indicate a favorable tolerance on error field in ITER. To make clear the underlying physics on toroidal field scaling, the theoretical analysis is given. By subtituting penetration related scaling parameters into the theory, the obtained theoretical scalings are consistent with the experimental observations using the vacuum penetration thresholds. To further investigate penetration threshold in larger operation region, the q95 scaling on penetration threshold with has also been observed. The rational surface radius rs and magnetic shear s, which are crucial to q95 scaling, are included in the theoretical analysis. The theoretical analysis is also consistent with the experimental scalings using the vacuum penetration thresholds. Moreover, the obtained theoretical scalings are easy to compare with experimental scalings. These theoretical analyses will stimulate the extrapolation of error field tolerance towards future reactors.

Nonlinear modeling of the scaling law for the error field penetration threshold

The scaling law for the error field (EF) penetration threshold is predicted numerically based on non-linear single-fluid and two-fluid modeling using the TM1 code. The simulated penetration threshold of radial magnetic field br at the plasma edge is scaled to the electron density ne, temperature Te, viscous time , toroidal field Bt and the natural frequency ω in the form of by scanning these parameters separately. Here, αn, αT, , αB and are the scaling coefficients on ne, Te, , Bt and ω, respectively. Single-fluid modeling shows that the 3/2 EF threshold scales as , which is similar with the analytical scaling law in both the Rutherford and visco-resistive regimes. However, two-fluid modeling shows that the scaling law differs significantly in particular regarding the dependence on plasma rotation. In detail, the scaling coefficient αn on density decreases from 0.67 to 0.56 and αT on temperature decreases from 0.67 to 0.32, while on viscous time is around -0.45 and αB on toroidal field decreases slightly from -1.15 to -1, when the ratio between plasma rotation frequency ωE and diamagnetic drift frequency ω*e varies from 0 to 10. Scans of the plasma rotation reveals that the penetration threshold linearly depends on the perpendicular electron flow frequency (or natural frequency) , and there is a minimum in the required field amplitude when . In addition, the enduring mystery of non-zero penetration threshold at zero plasma natural frequency in EF experiments is resolved by two-fluid simulations. We find that the very small island and smooth bifurcation in EF penetration near zero frequency is hard to detect in the experiment, leading to a finite penetration threshold within the capability of the experimental measurements.

Triggering of Neoclassical Tearing Mode by Error Field Penetration

Triggering of Neoclassical Tearing Mode by Error Field Penetration

Density scaling on n = 1 error field penetration in ohmically heated discharges in EAST

Density scaling of error field penetration in EAST is investigated with different n = 1 magnetic perturbation coil configurations in ohmically heated discharges. The density scalings of error field penetration thresholds under two magnetic perturbation spectra are and , where br is the error field and ne is the line averaged electron density. One difficulty in understanding the density scaling is that key parameters other than density in determining the field penetration process may also be changed when the plasma density changes. Therefore, they should be determined from experiments. The estimated theoretical analysis ( in lower density region and in higher density region), using the density dependence of viscosity diffusion time, electron temperature and mode frequency measured from the experiments, is consistent with the observed scaling. One of the key points to reproduce the observed scaling in EAST is that the viscosity diffusion time estimated from energy confinement time is almost constant. It means that the plasma confinement lies in saturation ohmic confinement regime rather than the linear Neo-Alcator regime causing weak density dependence in the previous theoretical studies.

Active stabilization of error field penetration via control field and bifurcation of its stable frequency range

An active stabilization effect of a rotating control field against an error field penetration is numerically studied. We have developed a resistive magnetohydrodynamic code ‘AEOLUS-IT’, which can simulate plasma responses to rotating/static external magnetic field. Adopting non-uniform flux coordinates system, the AEOLUS-IT simulation can employ high magnetic Reynolds number condition relevant to present tokamaks. By AEOLUS-IT, we successfully clarified the stabilization mechanism of the control field against the error field penetration. Physical processes of a plasma rotation drive via the control field are demonstrated by the nonlinear simulation, which reveals that the rotation amplitude at a resonant surface is not a monotonic function of the control field frequency, but has an extremum. Consequently, two ‘bifurcated’ frequency ranges of the control field are found for the stabilization of the error field penetration.

The non-thermal origin of the tokamak low-density stability limit

DIII-D plasmas at very low density exhibit the onset of n = 1 error field (EF) penetration (the ‘low-density locked mode’) not at a critical density or EF, but instead at a critical level of runaway electron (RE) intensity. Raising the density during a discharge does not avoid EF penetration, so long as RE growth proceeds to the critical level. Penetration is preceded by non-thermalization of the electron cyclotron emission, anisotropization of the total pressure, synchrotron emission shape changes, as well as decreases in the loop voltage and bulk thermal electron temperature. The same phenomena occur despite various types of optimal EF correction, and in some cases modes are born rotating. Similar phenomena are also found at the low-density limit in JET. These results stand in contrast to the conventional interpretation of the low-density stability limit as being due to residual EFs and demonstrate a new pathway to EF penetration instability due to REs. Existing scaling laws for penetration project to increasing EF sensitivity as bulk temperatures decrease, though other possible mechanisms include classical tearing instability, thermo-resistive instability, and pressure-anisotropy driven instability. Regardless of the first-principles mechanism, known scaling laws for Ohmic energy confinement combined with theoretical RE production rates allow rough extrapolation of the RE criticality condition, and thus the low-density limit, to other tokamaks. The extrapolated low-density limit by this pathway decreases with increasing machine size and is considerably below expected operating conditions for ITER. While likely unimportant for ITER, this effect can explain the low-density limit of existing tokamaks operating with small residual EFs.

Error field penetration and locking to the backward propagating wave

In this letter, we investigate error field penetration, or locking, behavior in plasmas having stable tearing modes with finite real frequencies ωr in the plasma frame. In particular, we address the fact that locking can drive a significant equilibrium flow. We show that this occurs at a velocity slightly above v=ωr/k, corresponding to the interaction with a backward propagating tearing mode in the plasma frame. Results are discussed for a few typical tearing mode regimes, including a new derivation showing that the existence of real frequencies occurs for viscoresistive tearing modes, in an analysis including the effects of pressure gradient, curvature, and parallel dynamics. The general result of locking to a finite velocity flow is applicable to a wide range of tearing mode regimes, indeed any regime where real frequencies occur.

On the Transition Regime of Nonlinear Error Field Penetration in Toroidal Plasmas**supported by the National Magnetic Confinement Fusion Science Program of China (Nos. 2014GB124001 and 2013GB102000) and National Natural Science Foundation of China (Nos. 11322549, 11275043 and 11275080)

The error field penetration is numerically studied in the frame of the visco-resistive magnetohydrodynamics (MHD) model. A transition scaling is obtained to link the Rutherford and Waelbroeck regimes in the nonlinear phase of error field penetration process. Furthermore, a transition density scaling of [br/BT]crit ∼ ne½ is obtained in accord with recent experimental observations in the J-TEXT tokamak.

Measurements of the toroidal torque balance of error field penetration locked modes

Detailed measurements from the DIII-D tokamak of the toroidal dynamics of error field penetration locked modes under the influence of slowly evolving external fields, enable study of the toroidal torques on the mode, including interaction with the intrinsic error field. The error field in these low density Ohmic discharges is well known based on the mode penetration threshold, allowing resonant and non-resonant torque effects to be distinguished. These m/n = 2/1 locked modes are found to be well described by a toroidal torque balance between the resonant interaction with n = 1 error fields, and a viscous torque in the electron diamagnetic drift direction which is observed to scale as the square of the perturbed field due to the island. Fitting to this empirical torque balance allows a time-resolved measurement of the intrinsic error field of the device, providing evidence for a time-dependent error field in DIII-D due to ramping of the Ohmic coil current.

Growth and decay of runaway electrons above the critical electric field under quiescent conditions

Extremely low density operation free of error field penetration supports the excitation of trace-level quiescent runaway electron (RE) populations during the flat-top of DIII-D Ohmic discharges. Operation in the quiescent regime allows accurate measurement of all key parameters important to RE excitation, including the internal broadband magnetic fluctuation level. RE onset is characterized and found to be consistent with primary (Dreicer) generation rates. Impurity-free collisional suppression of the RE population is investigated by stepping the late-time main-ion density, until RE decay is observed. The transition from growth to decay is found to occur 3–5 times above the theoretical critical electric field for avalanche growth and is thus indicative of anomalous RE loss. This suggests that suppression of tokamak RE avalanches can be achieved at lower density than previously expected, though extrapolation requires predictive understanding of the RE loss mechanism and magnitude.

On error field penetration processes in magnetic island mode locking

Error field penetration processes in magnetic island mode locking with the time-varying and fixed boundary perturbations are investigated numerically by using a two-dimensional resistive magnetohydrodynamic model in slab geometry. The evolution of various poloidal torques on the rational surface in the processes is analyzed in detail. In particular, three different states with the fixed boundary perturbations, viz. below the threshold (nearly locked regime), on the threshold (just locked regime), and above the threshold (strongly locked regime), are discussed and compared with the physical processes of the Rutherford regime.

Error-field penetration in reversed magnetic shear configurations

Error-field penetration in reversed magnetic shear (RMS) configurations is numerically investigated by using a two-dimensional resistive magnetohydrodynamic model in slab geometry. To explore different dynamic processes in locked modes, three equilibrium states are adopted. Stable, marginal, and unstable current profiles for double tearing modes are designed by varying the current intensity between two resonant surfaces separated by a certain distance. Further, the dynamic characteristics of locked modes in the three RMS states are identified, and the relevant physics mechanisms are elucidated. The scaling behavior of critical perturbation value with initial plasma velocity is numerically obtained, which obeys previously established relevant analytical theory in the viscoresistive regime.

Nonlinear error-field penetration in low density ohmically heated tokamak plasmas

A theory is developed to predict the error-field penetration threshold in low density, ohmically heated, tokamak plasmas. The novel feature of the theory is that the response of the plasma in the vicinity of the resonant surface to the applied error-field is calculated from nonlinear drift-MHD (magnetohydrodynamical) magnetic island theory, rather than linear layer theory. Error-field penetration, and subsequent locked mode formation, is triggered once the destabilizing effect of the resonant harmonic of the error-field overcomes the stabilizing effect of the ion polarization current (caused by the propagation of the error-field-induced island chain in the local ion fluid frame). The predicted scaling of the error-field penetration threshold with engineering parameters is , where br is the resonant harmonic of the vacuum radial error-field at the resonant surface, BT the toroidal magnetic field-strength, ne the electron number density at the resonant surface and R0 the major radius of the plasma. This scaling—in particular, the linear dependence of the threshold with density—is consistent with experimental observations. When the scaling is used to extrapolate from JET to ITER, the predicted ITER error-field penetration threshold is (br/BT)crit ∼ 5 × 10−5, which just lies within the expected capabilities of the ITER error-field correction system.