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In this study, hydrophobic quaternary ammonium intermediate was synthesized by epichlorohydrin (ECH) and oleamide propyl dimethyl tertiary amine (PKO). Sodium carboxymethylcellulose (CMC) was chemically modified by introducing a large number of hydrophobic quaternary ammonium branched chains to improve CMC’s salt resistance, thickening ability, and solubility. The quaternary ammonium salt structure can partially offset the compression double-layer effect of linear polymers in a low-price salt ion solution, which makes CMC more stretchable and helps it obtain a higher viscosity and greater drag-reduction performance. The experiment was mainly divided into three parts: Firstly, we performed an epichlorohydrin and oleic acid PKO reaction, generating an oleic acid chain quaternary ammonium chlorine atom intermediate. Secondly, the etherification reaction between intermediate –Cl and –OH groups of CMC was completed. Finally, the modified CMC was characterized by IR, SEM, and XPS, and the viscosity and the drag-reduction rate were evaluated. After CMC and the intermediate were reacted at a mass ratio of 9:1.8 at 80 °C for 5 h, the new CMC with enhanced thickening ability, salt resistance, and drag-reduction performance was obtained. We found that the apparent viscosity increased by 11%, the drag reduction rate increased by 3% on average, and the dissolution rate was also significantly accelerated, which was ascribed to the introduction of quaternary ammonium cation. Moreover, the oleic acid amide chain increased the repulsive force of the CMC chain to low-priced metal cations in solution and intermolecular repulsive force, which is beneficial to increase the viscosity, salt resistance, and drag-reduction performance.

We report the fabrication and testing of ultrafast response nonenzymatic glucose sensor based on the use of interlaced chain structure Au@CuS nanomaterial. The new Au@CuS nanomaterial was synthesized by a facile solvothermal method from L-cysteine、Cu(NO3)2·3H2O and Au Seeds without using additional surfactants or templates. The combination of Au and CuS solves the problems of poor electrical conductivity of CuS and the susceptibility of Au to toxicity, while the interlaced chain structure exposes more active sites to facilitate the diffusion of glucose molecules with a low resistance to increase the inter-electron transfer rate. The non-enzymatic Au@CuS-based glucose sensor showed a wide linear range with excellent sensitivity (5817.37 and 3629.78 μA mM−1cm−2), ultrafast response time (

The internal transport barrier (ITB) which is related to the fishbone instability has been observed on the Experimental Advanced Superconducting Tokamak (EAST) in ELMy H-mode discharges. An interpretation of the formation of the ITB on EAST tokamak is provided, based on both analytical and numerical calculations. The fishbone instability induces the redistribution of fast ions and leads to the accumulation of fast ions in a local region where the ITB is going to appear. Correspondingly, the gradients of fast ions are enhanced, where the ion temperature gradient (ITG) mode exists. Fast ions can interact with the ITG mode through the dilution, Shafranov shift and wave-particle resonance mechanisms. It is found that the ITG mode is stabilized by fast ions and the stabilizing effects are determined mainly by the density, temperature and their gradients of fast ions. The enhanced density and temperature gradients of fast ions lead to a stronger stabilizing effect on ITG mode. Compared with the stabilizing effect before the appearance of fishbone instability, the stabilization on ITG mode is enhanced after the fishbone instability, which is beneficial to the formation of the ITB.

The nonlinear evolution of the tearing mode instability with toroidal rotation is investigated using a three-dimensional toroidal geometry magnetohydrodynamic code (M3D). It is found that toroidal rotation plays a significantly stable role in reducing the width of magnetic island, which is independent of the direction of toroidal rotation. Compared with the stabilizing effect in the linear phase, the stabilizing effect of toroidal rotation is much stronger in the nonlinear phase. The magnetic island is almost suppressed by large enough rotation, even though the linear growth rate is weakly reduced in the linear phase. It is observed that the flow shear has a stabilizing effect, which is significant when the rotation frequency is large. However, it is shown that the magnitude of rotation plays a dominant role in stabilizing the magnetic island when the rotation frequency is small. The Coriolis force, rather than the centrifugal force, is found to play a dominant role in stabilizing the tearing mode in the nonlinear phase. When m / n = 3 / 2 and m / n = 2 / 1 tearing modes exist simultaneously, the sheared toroidal rotation is shown to effectively suppress the overlap of magnetic islands and field stochasticity caused by the coupling of neighboring islands.

The spatial structure and amplitude of the current induced by collisionless trapped-electron-mode (CTEM) turbulence are investigated by gyrokinetic simulations. It is shown that the barely passing electrons play a crucial role in determining the magnitude and direction of the current density. Two characteristic radial scales of the current density are found. The fine structure (a few ion Larmor radius) of the turbulence-induced current is observed near the rational surfaces. Furthermore, the mesoscale structure (tens of ion Larmor radii) of the turbulence-induced current related to the zonal flow shear is confirmed, especially for the high toroidal mode number (n) CTEM. For the strongly driven CTEM, the zonal flow shear effect on the turbulence-induced current is significant, while it is not visible for the weakly driven CTEM. We show that the magnitude of the CTEM turbulence-induced current density features a moderate local magnitude comparable to the bootstrap current density near rational surfaces, as demonstrated by nonlinear simulations with multi-n modes.

The dynamics of energetic particles and tearing modes and the interactions between them are of great significance for magnetically confined fusion plasmas. In this review, we focus on these issues in the context of tokamak plasmas. The interaction between energetic particles and tearing modes is considered from two perspectives: (i) the influence of energetic particles on tearing modes and (ii) the transport of energetic particles by tearing modes. The influence of energetic particles on tearing modes is described on the basis of a general dispersion relation for tearing modes. The effects of energetic particles are considered separately in the outer region and the island region of a tearing mode. The physics mainly results from the modification of the perturbed parallel current by energetic particles without wave–particle resonance. In addition, the resonance between energetic particles and tearing modes is also reviewed. For the transport of energetic particles, transport of both circulating and trapped energetic particles by tearing mode is reviewed. Our descriptions of physical phenomena here are based on an analytical approach, while the experiments and simulations are used to illustrate and confirm our results. Finally, a number of open issues are discussed.

Gyrokinetic simulations in the collisionless limit demonstrate the physical mechanisms and the amplitude of the current driven by turbulence. Simulation results show the spatio-temporal variation of the turbulence driven current and its connection to the divergence of the Reynolds stress and the turbulence acceleration. Fine structures (a few ion Larmor radii) of the turbulence induced current are observed near the rational surfaces with the arbitrary wavelength solver of the quasi-neutrality equation. The divergence of the Reynolds stress plays a major role in the generation of these fine structures. The so-called "spontaneous" current is featured with large local magnitude near the rational surfaces., Comment: 21pages, 20figures

Understanding and modeling fast-ion stabilization of ion-temperature-gradient (ITG) driven microturbulence have profound implications for designing and optimizing future fusion reactors. In this work, an analytic model is presented, which describes the effect of fast ions on ITG mode. This model is derived from a bounce-average gyro-kinetic equation for trapped fast ions and ballooning transformation for ITG mode. In addition to dilution, strong wave-fast-ion resonant interaction is involved in this model. Based on numerical calculations, the effects of the main physical parameters are studied. The increasing density of fast ions will strengthen the effects of fast ions. The effect of wave-particle resonance strongly depends on the temperature of fast ions. Furthermore, both increasing density gradient and the ratio of the temperature and density gradients can strengthen the stabilization of fast ions in ITG mode. Finally, the influence of resonance broadening of wave-particle interaction is discussed.

Based on the experimental parameters in the HL-2A tokamak, hybrid simulations have been carried out to investigate the linear stability and nonlinear dynamics of the beta-induced Alfvén eigenmode (BAE). It is found that the (m/n = 3/2) BAE is excited by co-passing energetic ions with q min = 1.5 in linear simulation, and the mode frequency is consistent with the experimental measurement. The simulation results show that the energetic ions β h, the injection velocity v 0, and orbit width parameter ρ h of energetic ions are important parameters determining the drive of BAE. Furthermore, the effect of q min (with the fixed shape of the q profile) is studied, and it is found that when q min ⩽ 1.5, the excited modes are BAEs, which are located near q = 1.5 rational surfaces; when q min > 1.5, the excited modes are similar to the reversed-shear Alfvén eigenmodes, which are mainly localized around q = q min surfaces. Nonlinear simulation results show that the nonlinear dynamics of BAE are sensitive to the EP drive. For the strongly driven case, firstly, redistribution and transport of energetic ions are trigged by 3/2 BAE, which raised the radial gradient of the distibution function of energetic ions near the q = 2 rational surface, and then an energetic particle mode (EPM) (m/n = 4/2) is driven in the nonlinear phase. Finally, these two instabilities triggered a significant redistribution of energetic ions, which results in the twice-repeated and mostlydownward frequency chirping of 3/2 BAE. For the weakly driven case, there are no 4/2 EPM being driven nor twice-repeated chirping in the nonlinear phase, since the radial gradient near q = 2 rational surface is small and almost unchanged.

The mechanism of rapid frequency chirping for neoclassical tearing modes (NTMs) is studied. Resonance between NTMs and trapped energetic ions can provide an additional torque to change the evolution of frequency. Whether the frequency rises or falls depends on the direction of island propagation. If the island propagates in the direction of ion diamagnetic drift, the frequency will be increased dramatically and rapidly. If the island propagates in the direction of electron diamagnetic drift, the frequency will be reduced to a lower value. The predicted chirping time is consistent with experimental results in DIII-D (Liu et al 2020 Nucl. Fusion 60 112009).

The mechanism of excitation of beta-induced Alfvén eigenmodes (BAEs) with magnetic islands larger than a threshold without energetic ions is studied. It is found that the nonlinear coupling between geodesic acoustic mode and magnetic islands can drive the pair of BAEs. The phase of BAEs to island should be π/2 to excite the BAEs and the magnetic island is larger than a threshold. The results are consistent with the experimental results shown in EAST(#86309). It implies that similar experimental results in other tokamaks, that BAEs excitation by magnetic islands without energetic ions, may be from the nonlinear coupling between islands and waves. It also implies that the existence of magnetic islands can make the excitation of BAEs easier in plasma with energetic ions, since the magnetic island can also increase the pressure gradient of energetic ions near the island separatrix. This predicts that BAEs may appear more frequently in the presence of magnetic islands in ITER.

The influence of trapped energetic ions (TEIs) on m / n = 2 / 1 low-frequency magnetohydrodynamic (MHD) instabilities with reversed shear profile is investigated by a global kinetic–MHD hybrid simulation. For low energetic-ion beta, TEIs have a stabilizing effect on the double tearing mode (DTM). When the energetic-ion beta is larger than a threshold, an energetic-particle-driven mode, the fishbone-like mode (FLM), is excited; that is, a mode transition from the DTM to the FLM occurs. The threshold increases with increasing resistivity, and the growth rate of the FLM is reduced by the presence of resistivity. In addition, the dependences on energetic-ion beta, gyroradius, and injection velocity of the effects of TEIs are studied systematically.

EAST has demonstrated its capability of long pulse operation using RF heating (LHCD and ICRF) in past experiments. One key issue to realize the long pulse H-mode experiments is to sustain the plasma current for steady state operation. Based on the calculations of the transport code ONETWO and its coupled RF code GENRAY, two scenarios have been proposed to achieve the 10 s H-mode plasma with Ip=400 kA, =4.5×1019 m−3, βN=2, and the 100 s H-mode plasma with Ip=280 kA, =3.5×1019 m−3, βN = 1.8 recently. The current drive of lower hybrid wave is an important issue in the two scenarios. An experimental result on lower hybrid current drive in H-mode plasmas on EAST is also presented.

The key issue of burning plasma in tokamak is the loss and confinement of the energetic particles, and one of the loss channels is the perturbation due to discrete toroidal field coils. The work investigated the α ripple loss of CFETR hybrid scenario with plasma transportation code TRANSP/NUBEAM and guiding center code ORBIT, which have considered the initial α distribution, classical steady state slowing down distribution and other models. The results of the work can give the information of the lost particles, including the lost position, fraction and localized heat load on the wall. The study reveals the heat load on CFETR is about 0.13 MW/m2, which is below the safety threshold of ITER, 0.5 MW/m2, and the paper also gives the direction to reduce the α ripple loss.

The effects of deeply trapped energetic ions (DTEIs) on the stability of tearing modes through stability criterion Δ ′ are studied. In contrast to the stabilizing adiabatic effect of background plasma pressure, the adiabatic contribution of the DTEI destabilizes due to the direct coupling between the bad curvature and asymmetrical pressure of energetic ions. When the orbit width is much larger than the island width, the nonadiabatic effect of the DTEI stabilizes, which counteracts the major destabilizing adiabatic contribution. DTEIs are shown to have a net destabilizing effect on the tearing mode. The main physics of destabilization of Δ ′ comes from the modification of the Mercier index.The effects of deeply trapped energetic ions (DTEIs) on the stability of tearing modes through stability criterion Δ ′ are studied. In contrast to the stabilizing adiabatic effect of background plasma pressure, the adiabatic contribution of the DTEI destabilizes due to the direct coupling between the bad curvature and asymmetrical pressure of energetic ions. When the orbit width is much larger than the island width, the nonadiabatic effect of the DTEI stabilizes, which counteracts the major destabilizing adiabatic contribution. DTEIs are shown to have a net destabilizing effect on the tearing mode. The main physics of destabilization of Δ ′ comes from the modification of the Mercier index.

In the last few years, long-pulse H-mode plasma discharges (with small edge-localized modes and normalized beta, β N ~ 1) have been realized at the Experimental Advanced Superconducting Tokamak (EAST). This paper reports on high-β N (>1.5) discharges in the 2015 EAST campaign. The characteristics of these H-mode plasmas have been presented in a database. Analysis of the experimental limit of β N has revealed several main features of typical discharges. Firstly, efficient, stable high heating power is required. Secondly, control of impurity radiation (partly due to interaction between the plasma and the in-vessel components) is also a critical issue for the maintenance of high-β N discharges. In addition an internal transport barrier (ITB) has recently been observed in EAST, introducing further improvement in confinement surpassing H-mode plasmas. ITB dynamics is another key issue for high-β N plasmas in EAST. Each of these features is discussed in this paper. Study and improvement of these issues could be considered as the key to achieving long-pulse high-β N operation with EAST.

The analytical approaches for nonlinear tearing mode have been reviewed. It is shown that Rutherford's model has triggered numerous studies on the nonlinear tearing mode. Its physical picture is clear meanwhile its mathematical method is ingenious but still puzzling to understand. It is trying to find how the 'nonlinear behavior' resulted from the linear equation by a nonlinear transform. It is indicated that Li's model for the tearing mode includes the linear growth, Rutherford's behavior and the new behavior. It was found that the quasilinear modification of magnetic field provided a new damping mechanism for nonlinear growth. The new behavior becomes dominant if the mode is weakly unstable. It is shown that many analytical methods have been developed to calculate the criterion parameter of the tearing mode. Li's instability criterion can cover the previous results in the limit cases.

The dynamics of magnetic islands including toroidal rotation in tokamaks is studied. It is found that the contribution of toroidal rotation to the dynamics of magnetic islands is mainly through the coupling of magnetic curvature with pressure and density. In the presence of toroidal rotation, pressure and density are poloidal asymmetric. Then, their coupling with magnetic curvature provides a perpendicular current, and a corresponding return parallel current is induced to affect the dynamics of magnetic islands. It is found that the effect of toroidal rotation depends on its magnitude, rather than the shear. It also depends on the relative magnitude of the island propagation frequency to sound frequency. When the Mach number is large enough, the effect of toroidal rotation is stabilizing and dramatic, and overcomes the contribution of polarization current, namely the onset threshold of NTMs increases. Further, it is also suggested that the toroidal rotation plays an important role in the stability of small scale magnetic islands.

Toroidal rotation has always existed in tokamak plasmas, and its Mach number can reach unity during neutral beam injection. Toroidal rotation can affect plasma equilibrium and magnetohydrodynamic instabilities significantly. Based on linearized equations including the toroidal rotation effect, the toroidal model derived by Glasser et al. [Phys. Fluids 18, 875 (1975)] is extended to include this effect, and a set of resistive equations including the toroidal rotation effect in the axi-symmetry toroidal geometry is derived. Based on these derived equations, the effect of toroidal rotation on tearing modes is considered, and the growth rate of tearing modes is obtained analytically. It is shown that the effect of toroidal rotation on tearing modes depends on both the direction of toroidal rotation flow and the sign of toroidal rotation flow shear. When they have the same sign, they play a role in stabilizing tearing modes, while when they have opposite signs, they have a destabilizing effect on tearing modes.

In addition to their effect on the linear stability of tearing modes, energetic particles can influence the nonlinear evolution of a magnetic island through an uncompensated cross field current due to the effect of charge separation when the orbit width of an energetic particle is much larger than the island width. The corresponding return parallel current may compensate the loss of bootstrap current in the magnetic island. This nonlinear effect depends on the island’s propagation frequency (the rotation frequency of the island relative to the plasma), the density gradient of energetic ions and magnetic shear. If the island’s propagation frequency is positive, the effect of the uncompensated current plays a stable role on neoclassical tearing modes. When the magnetic shear is sufficiently small, this effect becomes significant and can partially cancel or even overcome the destabilizing effect of the perturbed bootstrap current. In ITER this provides a possibility of using energetic ions to suppress the neoclassical tearing mode for the steady state and hybrid scenarios with weak magnetic shear.

In contrast with the stability effects of trapped energetic ions on tearing modes, the effects of circulating energetic ions (CEI) on tearing modes depend on the toroidal circulating direction, and are closely related to the momentum of energetic ions. CEI provide an additional source or sink of momentum to affect tearing modes. For co-CEI, tearing modes can be stabilized if the momentum of energetic ions is large enough. On the other hand, the growth of tearing modes can be enhanced by counter-CEI. Further, a possibility to suppress the island growth of neoclassical tearing modes by co-CEI is pointed out.

The onset threshold of neoclassical tearing modes with finite ion orbit width is studied. The evolution of neoclassical tearing modes including the effect of ion orbit is derived analytically. When ion orbit width is comparable to island width, the effect of ion orbit is significant. It would increase the island width needed to flatten pressure in the island, and reduce the amplitude of ion perturbed bootstrap current. It is found that ion orbit effect tends to increase the onset threshold βθonset for a given seed island. It also would increase the lowest threshold βθ,min and the corresponding marginal island width. It has important implications for the onset of neoclassical tearing modes with comparable ion orbit width and island width in International Thermonuclear Experimental Reactor.

An extended magnetohydrodynamic model including the effect of runaway current is developed and implemented in the M3D code. Based on this model, a simulation has been carried out to investigate the linear stability and the nonlinear evolution of the n = 1 resistive kink mode in the presence of runaway current. It is found that sawteeth oscillation is suppressed in a runaway plasma. The nonlinear evolution of the n = 1 mode only leads to a single sawtooth crash before reaching a new steady state axi-symmetric equilibrium with flattened current profile in the plasma core and q(0)>1.

Tearing mode stability analysis in the presence of circulating energetic ions (CEI) is studied in the reversed field pinch (RFP) magnetic configuration. In contrast to the minimal effect of precessional drift of CEI on tearing modes in tokamaks, the effect of precessional drift of CEI on tearing modes is important in the RFP. It is found that the effects of CEI on tearing modes in RFP depend on their toroidal circulating direction, and have a strong relation to the pressure gradient of CEI. For co-CEI, tearing modes can be stabilized if the pressure gradient of energetic ions is sufficiently large, which is qualitatively consistent with experimental results in the Madison Symmetric Torus.

Alfven eigenmodes in up-down asymmetric tokamak equilibria are studied by a new magnetohydrodynamic eigenvalue code. The code is verified with the NOVA code for the Solovev equilibrium and then is used to study Alfven eigenmodes in a up-down asymmetric equilibrium of the Experimental Advanced Superconducting Tokamak. The frequency and mode structure of toroidicity-induced Alfven eigenmodes are calculated. It is demonstrated numerically that up-down asymmetry induces phase variation in the eigenfunction across the major radius on the midplane.

A stability analysis of the circulating energetic ions (CEIs) on resistive wall mode is carried out in the reversed field pinch (RFP). In contrast to the minor resonant effects of CEI on resistive wall mode (RWM) in tokamak, the resonant interaction between RWM and CEI is important for high toroidal mode number in RFP with high beta value. The resonance provides an energy dissipation channel of free energy, and stabilizes RWM. As the fraction of CEI is large enough, the RWM is fully suppressed by CEI in the low plasma rotation, even vanishing rotation. Further, a possibility to suppress the RWM by CEI is suggested.

The effects of pressure gradient on the existence of global Alfven eigenmodes (GAE) in Reversed Field Pinch are studied by numerical calculation. It is found that GAEs near the plasma core can exist when pressure gradient is sufficiently large. The calculated mode frequency and structure are consistent with the experimental results in the Madison Symmetric Torus.

A magnetic field greatly affects the relaxation phenomena in a plasma when the particles’ thermal gyro-radii are smaller than the Debye length. Its influence on the temperature relaxation (TR) is investigated through consideration of binary collisions between charged particles in the presence of a uniform magnetic field within a perturbation theory. The relaxation times are calculated. It is shown that the electron-electron (e-e) and ion-ion (i-i) TR rates first increase and then decrease as the magnetic field grows, and the doubly logarithmic term contained in the electron-ion (e-i) TR rate results from the exchange between the electron parallel and the ion perpendicular kinetic energies.

The effects of energetic ions on stability of tearing mode are investigated by global kinetic/MHD hybrid simulations in a low beta tokamak plasma. The kinetic effects of counter circulating energetic ions from the non-adiabatic response are found to be strongly destabilizing while the effects from the adiabatic response are stabilizing. The net effect with both adiabatic and non-adiabatic contributions is destabilizing. On the other hand, the kinetic effects of co-circulating energetic ions from the non-adiabatic response are calculated to be weakly stabilizing while the corresponding adiabatic contribution is destabilizing for small energetic ion beta. The net effect is weakly stabilizing. The dependence of kinetic effects on energetic ion beta, gyroradius, and speed is studied systematically and the results agree in large part with the previous analytic results for the kinetic effects of circulating particles. For trapped energetic ions, their effects on tearing mode stability are dominated by the adiabatic response due to large banana orbit width and strong poloidal variation of particle pressure. The net effect of trapped energetic particles on tearing modes is much more destabilizing as compared to that of counter circulating particles at the same beta value.

The general time evolution of tearing mode due to electron viscosity μe from linear to nonlinear phase in the framework of electron magnetohydrodynamics (EMHD) is derived by quasilinear theory. Tearing mode grows exponentially in the linear phase and slows to an algebraic growth behavior Ψ1∝(μet)2/3 (Ψ1 is the magnetic flux) in the nonlinear phase. These two phases are separated by a transition during which the growth behavior is much different from that in the linear and nonlinear phases. It behaves as Ψ1∝μe5/8t1/2 approximately.

The dissipation mechanisms of reconnection and the pressure gradient effects on tearing mode with guide magnetic field are analyzed systematically by including the electron pressure tensor in electron magnetohydrodynamics. It is found that which dissipation mechanism dominates, either pressure-based dissipation or inertia-based dissipation, has a great relation with the relative scaling orders between the electron thermal Larmor radius and electron inertia skin depth. The effects of pressure gradient also depend on the relative magnitude between parallel and perpendicular equilibrium pressure gradients. When the pressure-based dissipation is dominant, the condition that pressure drives or suppresses tearing mode instability also depends on the relative magnitude between parallel and perpendicular equilibrium pressure gradients.

The general dispersion relation of tearing mode with pressure gradient effect in pair plasmas is derived analytically. If the pressure gradients of positron and electron are not identical in pair plasmas, the pressure gradient has significant influence at tearing mode in both collisionless and collisional regimes. In collisionless regime, the effects of pressure gradient depend on its magnitude. For small pressure gradient, the growth rate of tearing mode is enhanced by pressure gradient. For large pressure gradient, the growth rate is reduced by pressure gradient. The tearing mode can even be stabilized if pressure gradient is large enough. In collisional regime, the growth rate of tearing mode is reduced by the pressure gradient. While the positron and electron have equal pressure gradient, tearing mode is not affected by pressure gradient in pair plasmas.

The tearing mode instability with guide field gradient is investigated in electron magnetohydrodynamics. It is found that the guide field gradient has a significant influence in the inner region. The growth rates are derived analytically in small and large guide field gradient limits, respectively. When the guide field gradient is smaller than the magnetic field shear at the magnetic null plane, the growth rate of tearing mode instability is enhanced by the guide field gradient and has no oscillatory component. When the guide field gradient is larger than the magnetic field shear, the guide field gradient can destabilize tearing mode instability dramatically. In this case, the growth rate is proportional to the guide field gradient.

The general dispersion relation of collisionless reconnection instability due to electron viscosity μe in the whistler frequency is derived. In the framework of electron magnetohydrodynamics (EMHD), the evolution of magnetic reconnection instability is studied, and the linear growth rates are obtained. The scaling laws of the reconnection instability growth rate with respect to the electron viscosity in constant-ψ (used in the tearing mode) and low-k regimes are obtained, respectively, and compare with those obtained in standard magnetohydrodynamic theory. In the constant-ψ regime for “tearing-mode-like” instability, the growth rate is proportional to μe1∕4, while in the low-k regime, it is proportional to μe1∕8.