Electron Cyclotron Current Drive Research Articles

Efficient ECCD non-inductive plasma current start-up, ramp-up, and sustainment for an ST fusion reactor

The elimination of the need for an Ohmic heating solenoid may be the most impactful design driver for the realization of economical compact fusion tokamak reactor systems. However, this would require fully non-inductive start-up and current ramp-up from zero plasma current and low electron temperature of sub-keV to the full plasma current of ∼10–15 MA at 20–30 keV electron temperature. To address this challenge, an efficient solenoid-free start-up and ramp-up scenario utilizing a low-field-side-launched extraordinary mode at the fundamental electron cyclotron harmonic frequency (X–I) is proposed, which has more than two orders of magnitude higher electron cyclotron current drive (ECCD) efficiency than the conventional ECCD for the sub-keV start-up regime. A time dependent model was developed to simulate the start-up scenarios. For the Spherical Tokamak Advanced Reactor (STAR) (Menard et al 2023 Next-Step Low-Aspect-Ratio Tokamak Design Studies (IAEA)), it was found that to fully non-inductively ramp-up to 15 MA, it would take about 25 MW of EC power at 170 GHz. Because of the relatively large plasma volume of STAR, radiation losses must be considered. It is important to make sure that high Z impurities are kept sufficiently low during the early current start-up phase where the temperature is sub-keV range. Since the initial current ramp up takes place at a factor of ten lower density compared to the sustained regimes, it is important to transition into a higher bootstrap fraction discharge at lower density to minimize the ECCD power requirement during the densification. For the sustainment phase an array of eight gyrotron launchers with a total of about 60 MW of fundamental O-mode was found to be sufficient to provide the required axis-peaked external current drive. High efficiencies between 19–57 kA MW−1 were found with optimal aiming, and these were resilient to small changes in aiming angles and density and temperature profiles.

Neoclassical tearing mode stabilization by electron cyclotron current drive in EAST tokamak experiments

The stabilization of the m/n= 2/1 neoclassical tearing mode (NTM) by electron cyclotron current drive (ECCD) has been carried out in EAST H-mode discharges, where m/n is the poloidal/toroidal mode number. The experimental results are reported for the first time in this paper. To facilitate the experimental study, the magnetic island (NTM) is generated by a sufficiently large amplitude of the externally applied resonant magnetic perturbation (RMP). After switching off the RMP, the NTM exists due to the bootstrap current perturbation, with the magnetic island width being about 5 cm for the local equilibrium bootstrap current fraction being larger than 10%. By applying the localized ECCD later, the NTM is fully suppressed if the radial misalignment between the magnetic island and the ECCD location is sufficiently small. The stabilizing effect depends on both the radial misalignment and the applied electron cyclotron wave power. More importantly, it is found that the NTM can be avoided when applying ECCD earlier during the ramp-up phase of the RMP amplitude, if ECCD is localized around the O-point of the magnetic island, indicating an efficient way for avoiding locked modes that can lead to the major disruptions of tokamak plasmas.

Systematic numerical analysis of ECCD exploring injection conditions with high CD efficiency and current profile controllability in JA DEMO

Systematic Electron Cyclotron Current Drive (ECCD) simulations were performed in JA DEMO plasma (Te=34keV and ne=1.0×1020m−3 at the center) for various injection conditions of EC waves, including wave frequency, injection direction and injection position. Different injection positions surrounding the plasma are comprehensively scanned, including midplane and upper launch on the high/low field side (HFS/LFS) of the plasma. Numerical results indicated that higher harmonic absorptions deteriorate the ECCD efficiency regardless of injection positions. High ECCD efficiencies for each injection position were obtained when avoiding higher harmonic absorptions. The maximum ECCD efficiency of 46kA/MW was obtained for upper LFS launch with an optimal frequency and direction. An important finding from the systematic analysis is that such an efficient ECCD exceeding 40kA/MW is expected for a wide range of injection positions of upper and midplane LFS launch. This result is favorable for fusion reactor design, indicating flexibility in EC port arrangement for efficient ECCD. Current profile controllability in JA DEMO was also discussed in two injection cases: the upper LFS launch and the conventional midplane LFS launch. Driven current density profiles with various injection angles from each injection position successfully cover the regions from the center to mid-radius of the plasma, where external current drive is required to achieve a weak reversed shear. Furthermore, sufficient ECCD efficiencies of 35–46kA/MW at the upper LFS launch and of 35–43kA/MW at the midplane LFS launch are obtained.

Effects of edge-localized electron cyclotron current drive on edge-localized mode suppression by resonant magnetic perturbations in DIII-D

According to recent DIII-D experiments (Logan et al 2024 Nucl. Fusion 64 014003), injecting edge localized electron cyclotron current drive (ECCD) in the counter-plasma-current (counter-I p) direction reduces the n = 3 resonant magnetic perturbation (RMP) current threshold for edge-localized mode (ELM) suppression, while co-I p ECCD during the suppressed ELM phase causes a back transition to ELMing. This paper presents nonlinear two-fluid simulations on the ECCD manipulation of edge magnetic islands induced by RMP using the TM1 code. In the presence of a magnetic island chain at the pedestal-top, co-I p ECCD is found to decrease the island width and restore the initially degraded pedestal pressure when its radial deposition location is close to the rational surface of the island. With a sufficiently strong co-I p ECCD current, the RMP-driven magnetic island can be healed, and the pedestal pressure fully recovers to its initial ELMing state. On the contrary, counter-I p ECCD is found to increase the island width and further reduce the pedestal pressure to levels significantly below the peeling-ballooning-mode limited height, leading to even stationary ELM suppression. These simulations align with the results from DIII-D experiments. However, when multiple magnetic island chains are present at the pedestal-top, the ECCD current experiences substantial broadening, and its effects on the island width and pedestal pressure become negligible. Further simulations reveal that counter-I p ECCD enhances RMP penetration by lowering the penetration threshold, with the degree of reduction proportional to the amplitude of ECCD current. For the ∼1 MW ECCD in DIII-D, the predicted decrease in the RMP penetration threshold for ELM suppression is approximately 20%, consistent with experimental observations. These simulations indicate that edge-localized ECCD can be used to either facilitate RMP-driven ELM suppression or optimize the confinement degradation.

Influence of electron cyclotron current drive on the transition between normal sawteeth and the stationary state

The transition between normal sawteeth and a sawtooth-free stationary state after electron cyclotron current drive (ECCD) deposition has been numerically investigated by the CLT code. The periods of normal sawteeth decrease if co-ECCD deposits inside the initial q=1 surface and increase when co-ECCD deposits outside the q=1 surface. When co-ECCD deposits in the vicinity of the q=1 surface, the normal sawteeth can be converted into a stationary state, during which sawteeth are completely prevented. The stationary state can also be converted into normal sawteeth if co-ECCD is injected just outside the q=1 surface. The mechanism of the transition between normal sawteeth and sawtooth-free stationary states is then discussed.

Enhancement of ECCD by the current condensation effect for stabilizing large magnetic islands caused by neoclassical tearing modes in tokamak plasmas

The radio frequency current condensation effect reported in Reiman and Fisch (2018 Phys. Rev. Lett. 121 225001) is modeled in the nonlinear resistive magnetohydrodynamic code. A series of numerical investigations have been performed to investigate the enhancement of electron cyclotron current drive (ECCD) by the current condensation effect during the control of neoclassical tearing mode (NTM) in tokamak plasmas. In the numerical model, both the parallel transport and the perpendicular transport of electron temperature are considered. The EC driven current and driven perturbed electron temperature can nonlinearly evolve within the given magnetic configuration and eventually reach saturation states. The input power threshold of ECCD and the fold bifurcation phenomenon are numerically verified via nonlinear simulations. The numerical results show good agreements with the analytical results. Moreover, spatial distributions of EC current for the two solutions at different condensed level are displayed. The control effectiveness of ECCD for large NTM islands has been evaluated while considering the current condensation effect. While taking into account current condensation effect, for a sufficiently large input power, a larger island can be more effectively stabilized than a smaller one, which suggests a reassessment of the previous idea that the ECCD should always be turned on as early as possible. The potential physics mechanism behind the ECCD control have all been discussed in detail. Furthermore, the condensation effect is found to have favorable effects on the radial misalignment of ECCD. In the consideration of the situation for extremely localized control needs, a highly peaked heating profile is adopted to verify that the fold bifurcation phenomenon still exists and the current condensation effect can still take effect in this extreme condition.

Inter-discharge optimization for fast, reliable access to ASDEX Upgrade advanced tokamak scenario

Rapid inter-discharge simulation and optimization using the RAPTOR code have allowed the development of a reliable and reproducible early heating strategy for an advanced tokamak (AT) scenario on ASDEX Upgrade. Solving for electron heat and current diffusion in RAPTOR with ad-hoc formulas for heat transport and electron cyclotron current drive (ECCD) efficiency is found to robustly recover the coupled dynamics of Te and q, while maintaining model parameters fixed for all discharges. The pedestal top boundary condition in pre-shot simulations is set by a newly derived scaling law for the electron pressure at ρ = 0.8, using a data set of previous AT discharges. RAPTOR simulations have allowed to develop an understanding of the onset of 3/2 tearing modes, which were observed to have a detrimental impact on confinement when low magnetic shear conditions are present at the rational surface during the high-β phase. Delaying the NBI heating, by a specific time interval found via simulations, has led to avoiding these modes. A non-linear optimization scheme has been applied to optimize the ECCD deposition radii to reach a stationary state with qmin>1 at the beginning of the flat-top phase, while ensuring a non-zero magnetic shear at q = 1.5 throughout the high-β phase, and has been successfully tested in experiment. However, further experiments, aiming for qmin>1.5 , have highlighted limitations of the present feedforward control approach in the presence of shot-to-shot variations that are not included in the applied model. Application of real-time model-based control is proposed to overcome model-reality mismatches in future work.

Modelling of energetic particle drive and damping effects on TAEs in AUG experiment with ECCD

The impact of electron cyclotron current drive (ECCD)-driven current on toroidicity-induced Alfvén eigenmodes (TAEs) in experiments on the AUG tokamak is investigated numerically. The dynamical evolution of the plasma profiles and equilibria are modelled with European transport solver, while ion cyclotron resonance heating-accelerated H-minority ions exciting TAEs are assessed with the PION code. TAEs, their drive and damping are computed with the codes CASTOR and CASTOR-K. In the set of discharges analysed, two groups of TAEs are observed, differing in frequency and radial location. Experimental observations show that when counter-ECCD is applied the higher frequency group of approximately 150 kHz is suppressed, while the lower frequency modes of 125 kHz are amplified. When co-ECCD is applied, depending on the location of the ECCD current deposition layer, both groups of TAE can be suppressed. Numerical calculations of energetic particle drive and thermal plasma damping show that neither one effect could explain the variety of the experimental observations. The fine balance between the drive, sensitive to the TAE position, and the radiative and continuum damping effects could only explain the experiment if the effects are considered all together.

Effects of the resonance modification by electron cyclotron current drive on the linear and nonlinear dynamics of energetic particle driven magnetohydrodynamics modes in Heliotron J

This study investigates the effects of electron cyclotron current drive (ECCD) on the linear and nonlinear dynamics of energetic-particle (EP)-driven magnetohydrodynamics (MHD) instability (mode) in Heliotron J (HJ), using MEGA, a nonlinear hybrid EP-MHD simulation code. The effects of ECCD are included through the modification of the equilibrium magnetic field. Five MHD equilibria with plasma currents () of −2.00, −1.00, 0.00, 0.50, and 1.00 kA are considered, where negative and positive represent counter and co-ECCD, respectively. To account for the EP finite charge-exchange loss observed in HJ, a bump-on-tail velocity distribution is assumed for EP. The study finds that the stabilization trends in terms of the linear growth rate () are qualitatively similar to the FAR3D linear simulation and experimental results. In addition to the enhancements of the local magnetic shear and continuum damping by ECCD as proposed in previous studies, the study suggests that changes in the linear EP and shear Alfvén wave resonance are another important factor, especially for the mode. The study shows that in the currentless equilibrium, the high-velocity toroidicity-induced resonance between the mode and the co-passing EP () has the highest EP energy transfer rate, but is located slightly below the NBI injection velocity. The co-ECCD and cntr-ECCD can shift this resonance into higher and lower velocity regions, respectively. This can lead to resonance removal for co-ECCD, while cntr-ECCD can initially increase the number of resonant EPs for a small value of shift. If the shift of the resonance by cntr-ECCD is sufficiently large, the study observes stabilization due to the reduction in the EP population in the low-velocity region. The study also finds that changes in resonance affect nonlinear dynamics such as EP transport and frequency chirping. The convective transport of the co- and counter-passing EPs can be controlled, which can only be achieved for energetic-particle-mode due to the asymmetry in the resonance velocity between co- and cntr-passing EPs. The changes in the frequency chirping from the downward chirping branch to the upward chirping branch can also be explained by the changes in the resonance velocity caused by ECCD.

Access to stable, high pressure tokamak pedestals using local electron cyclotron current drive

Experiments on the DIII-D tokamak demonstrate that edge localized mode (ELM) stability can be manipulated using localized electron cyclotron current drive (ECCD) in conjunction with resonant magnetic perturbations (RMPs). The injection of counter-plasma-current edge ECCD reduces the RMP amplitude required to suppress ELMs and bifurcates the pedestal into a high-confinement regime with 7 kPA pedestal pressure. This is the first time such a high confinement regime has been accessed through the bifurcation from the ballooning stability branch predicted by existing models. These observations are consistent with modeled ECCD manipulation of magnetic islands induced by the RMPs.

Application of linear electron Bernstein current drive models in reactor-relevant spherical tokamaks

Electron Bernstein current drive (EBCD) systems in spherical tokamaks are sensitive to plasma and launch conditions, and therefore require large parametric scans to optimise their design. One particular bottleneck in the simulation workflow is quasilinear modelling of current drive efficiency. Linear adjoint models are an attractive alternative, offering a speed-up compared to quasilinear codes. While linear models are well-tested and commonly used for electron cyclotron current drive (ECCD), they have seen little use in EBCD modelling. In this work, variants of the linear model are applied to EBCD and compared to quasilinear results in a reactor-relevant plasma, i.e. Spherical Tokamak for Energy Production (STEP). This comparison reveals it is important to accurately model the collision operator and finite Larmor radius effects in the linear model. When done properly, good agreement is found with quasilinear calculations, at least for normalised minor radii ρ < 0.7 and at low power densities. The power density threshold for quasilinear effects during EBCD is found to be significantly lower than that of ECCD. This is attributed to the much lower group velocity of the electron Bernstein wave (EBW). Thus, the linear model is only valid for EBCD modelling at low power densities (e.g. 1 MW launched EBW power in STEP). This may be satisfied in present-day experimental devices, but certainly not in reactors targeting non-inductive operation.

Effects of toroidally-distributed-divertor biasing on scrape-off-layer (SOL) current drive, divertor particle flux and fast electron confinement in the QUEST spherical tokamak

A novel divertor biasing by four biasing plates distributed toroidally (TDDB) on the upper divertor target plate is applied to low density tokamak plasmas started-up by 28 GHz 2nd harmonic electron cyclotron current drive (ECCD) in a quasi-double null configuration of the QUEST spherical tokamak (ST). In the ST plasmas of line averaged electron density < > ∼0.7–1 × 1018 m−3, about 20%–40% of the current driven by ∼85 V sawtooth bias voltage reaches the lower divertor plate along the biased scrape-off-layer (SOL) flux tube as the SOL current . The fact is noticeably lower than indicates an appreciable leakage of parallel current from the biased SOL flux tube. The leakage currents in the toroidal and radial directions are confirmed by detection of them using the unbiased plates in the TDDB experiments. From the ion saturation current density profile obtained by a divertor Langmuir probe array, the fall-off lengths of divertor particle flux are estimated together with the strike line position. Total particle flux to the upper divertor, evaluated by the integrated ion saturation current density profile is reduced by up to 45% during positive biasing of the TDDB, depending on the position of the strike line to the biased plate. In addition, the TDDB also induces a noticeable loss of fast electrons produced by ECCD, leading to an ∼2% reduction in the maximum toroidal current of the ST plasma compared to a shot without the TDDB. Reduction of the divertor particle flux and enhancement of the fast electron losses are thought to be dominantly caused by E drift induced by the TDDB. In the present experimental conditions, the effects of magnetic perturbations produced by the SOL currents on the fast electron losses can be neglected because of a too small SOL current.

Direct preemptive stabilization of neoclassical tearing modes by electron cyclotron current drive in the DIII-D low-torque ITER baseline scenario

We report the first preemptive direct stabilization of neoclassical tearing modes (NTMs) in DIII-D low-torque ITER baseline scenario plasmas by electron cyclotron waves. These experiments strongly support that the observed stabilization is achieved by replacing the missing bootstrap current in the island by electron cyclotron current drive (ECCD). These plasmas (with and without ECCD) are stable to 2,1 NTMs when the differential rotation between the q = 1 and q = 2 surfaces () is sustained above a critical value ( kHz), but those evolving to low differential rotation () routinely develop a disruptive 2,1 island at the time and frequency of a sawtooth precursor. Preemptive, local and direct stabilization by ECCD is tested by scanning the current drive amplitude and location inside and outside of the q = 2 rational surface shot by shot. Analysis of only low differential rotation time windows, i.e. when stabilization from is absent, shows focused ECCD at q = 2 prevents the onset of 2,1 NTMs. These results are important, as they give the first demonstration of disruptive NTM control by ECCD in the plasma scenario planned for ITER.

The Formation and Stationary Maintenance of Peaked Pressure Profiles in Turbulent Tokamak Plasmas

The theoretical model for increasing peaking of radial distribution of plasma thermal energy and plasma energy confinement time improvement due to the formation of current profiles those provide the increased value of the safety factor qb at the outer plasma boundary is considered. The model for the formation and stationary maintenance of the peaked current density profiles those ensure the maintenance of plasma column equilibrium state with increased qb value and conservation of q0=1 at the magnetic axis is developed. The model is based on the significant ramp down of the Iind current maintained by the inductor with simultaneous central ECR heating and electron cyclotron current drive (ECCD) switching on. It is shown by the computer simulations of the self-consistent time evolution of turbulent plasma for the conditions of T-10 and T-15MD tokamaks that in the shot scenarios with three- or four-fold decrease in the Iind current at the ECRH stage of shots it was achieved an approximately two-fold enhancement of the electron and ion temperatures at the axis of the plasma column as compared to the standard shots with the same heating powers.

The Formation and Stationary Maintenance of Peaked Pressure Profiles in Turbulent Tokamak Plasmas

The theoretical model for increasing peaking of radial distribution of plasma thermal energy and plasma energy confinement time improvement due to the formation of current profiles those provide the increased value of the safety factor {{q}_{b}} at the outer plasma boundary is considered. The model for the formation and stationary maintenance of the peaked current density profiles those ensure the maintenance of plasma column equilibrium state with increased {{q}_{b}} value and conservation of {{q}_{0}} approx 1 at the magnetic axis is developed. The model is based on the significant ramp down of the {{I}_{{{text{ind}}}}} current maintained by the inductor with simultaneous central ECR heating and electron cyclotron current drive (ECCD) switching on. It is shown by the computer simulations of the self-consistent time evolution of turbulent plasma for the conditions of T-10 and T-15MD tokamaks that in the shot scenarios with three- or four-fold decrease in the {{I}_{{{text{ind}}}}} current at the ECRH stage of shots it was achieved an approximately two-fold enhancement of the electron and ion temperatures at the axis of the plasma column as compared to the standard shots with the same heating powers.

Investigation of electron cyclotron wave absorption and current drive in CFETR hybrid scenario plasmas

The investigation of electron cyclotron (EC) wave absorption and current drive has been performed for the China Fusion Engineering Test Reactor (CFETR) hybrid scenarios using the TORAY code. To achieve the physics goal of the EC system in CFETR, a total of four wave frequency values and nine locations of launching antennas have been considered, and the injection poloidal and toroidal angles have been scanned systematically. The electron cyclotron current drive (ECCD) efficiency of the 170 GHz EC system is quite low due to the wave-particle interactions being located at the low-field side. To optimize the ECCD efficiency, the wave frequency is increased up to 221–250 GHz, which leads to the power being deposited at the high-field side. The off-axis ECCD efficiency can be significantly enhanced by launching EC waves from the top window and injecting them towards the high-field side. The optimized ECCD efficiency at ρ = 0.32 and at ρ = 0.4 is 2.9 and 2.2 times that of 170 GHz, respectively.

Optimization of X-mode electron cyclotron current drive in high-electron-temperature plasma in the EAST tokamak

A discharge with electron temperature up to 14 keV has been achieved in EAST. Analysis of the electron cyclotron current drive (ECCD) efficiency at high electron temperature under EAST parameters is presented using C3PO/LUKE code. Simulation results show that the ECCD efficiency of X-mode increases with central electron temperature up to 10 keV and then starts to decrease above 10 keV, at a specific magnetic field and toroidal angle. The efficiency degradation is due to the presence of the third harmonic extraordinary (X3) downshifted absorption at the low field side (LFS); even the cold resonance of X3 mode is located outside the plasma. As the electron temperature increases from 5 to 20 keV, the X3 absorption increases from 0.9% to 96.4%. The trapping electron effect at the LFS produces a reverse Ohkawa current. The competition between the Fisch–Boozer current drive and the Ohkawa current drive results in a decrease in ECCD efficiency. ECCD efficiency optimization is achieved through two methods. One is to increase the toroidal angle, leading to X2 mode predominating again over X3 mode and the electron resonance domain of X2 mode moving far from the trapped/passing boundary. The second one is to increase the magnetic field to move away the X3 resonance layer from the plasma, hence less EC power absorbed by X3 mode.

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Magnetic island produced in toroidal magnetic confinement plasma has a three-dimensional helical structure because of the rotational transform, especially the equilibrium magnetic surface of the stellarator is three-dimensional helical structure. Thus, the formation and instability of the magnetic island of the Stellarator is a typical issue of the three-dimensional physics and is also one of the key topics of the physics research of the Stellarator. Magnetic islands and related tearing mode physics are major issues in stellarator. The non-inductively current drive, i.e. electron cyclotron current drive (ECCD) can be used as one of the approaches to adjusting the rotational transform, and hence, affecting the generation of magnetic islands. In this study, we use an additional toroidal magnetic field to generate &lt;i&gt;m&lt;/i&gt;/&lt;i&gt;n&lt;/i&gt; = 5/2 magnetic islands in the low-&lt;i&gt;β&lt;/i&gt; operation on the Chinese First Quasi-axisymmetric Stellarator (CFQS) so that the influence of the bootstrap current is negligible. Then, we investigate the suppression mechanism of magnetic islands in low-&lt;i&gt;β&lt;/i&gt; plasma by using the HINT code. It is found that in the case of the constant current, when the current direction is positive, with the increase of current, the width of island increases. When the direction of current is reversed, the island is suppressed when the current is larger than 6 kA. The main reason is that the rotational transform is away from &lt;i&gt;ι&lt;/i&gt;/2π = 0.4 rational surface and the &lt;i&gt;m&lt;/i&gt;/&lt;i&gt;n&lt;/i&gt;=5/2 magnetic island does not meet the resonance conditions. In the case of local current profile, the magnetic island width decreases as a result of the enhanced magnetic shear at &lt;i&gt;ι&lt;/i&gt;/2π = 0.4 rational surface. Moreover, effects of the direction and the amplitude of the current on the suppression of magnetic islands are also discussed in more detail.

Investigation of electron cyclotron current drive efficiency on the J-TEXT tokamak

Electron cyclotron current drive (ECCD) efficiency research is of great importance for the neoclassical tearing mode (NTM) stabilization. Improving ECCD efficiency is beneficial for the NTM stabilization and the ECCD power threshold reduction. ECCD efficiency has been investigated on the J-TEXT tokamak. The electron cyclotron wave (ECW) power scan was performed to obtain the current drive efficiency. The current drive efficiency is derived to be approximately η 0 = (0.06–0.16) × 1019 A m−2 W−1 on the J-TEXT tokamak. The effect of the residual toroidal electric field has been included in the determination of the current drive efficiency, which will enhance the ECCD efficiency. At the plasma current of I p = 100 kA and electron density of n e = 1.5 × 1019 m−3, the ratio of Spitzer conductivity between omhic (OH) and ECCD phases is considered and the experimental data have been corrected. The correction results show that the current drive efficiency η 1 caused by the fast electron hot conductivity decreases by approximately 79%. It can be estimated that the driven current is approximately 24 kA at 300 kW ECW power.

Investigation of the effectiveness of ‘multi-harmonic’ electron cyclotron current drive in the non inductive EXL-50 ST

The fully non-inductive spherical tokamak EXL-50, built and operated by the ENN private limited company, has routinely achieved high current drive efficiency of ∼ 1 A/W in only ECRH powered experiments. We have numerically investigated the effectiveness of multiple electron cyclotron resonance (ECR) harmonics in generating such a high efficiency of electron cyclotron current drive (ECCD) in non-inductive plasma start-up. The Fokker-Planck equation is numerically solved to obtain the electron distribution function, under the steady state of relativistic nonlinear Coulomb collision and quasi-linear diffusion operators, for calculating plasma current driven by the injected EC waves. Multi-pass absorption simulations, done with the CQL3D code for extra-ordinary EC waves, demonstrate over 1 A/W efficiency in current for a relatively low density (∼ 2 × 1018 m −3), and low temperature (∼ 100 eV) plasma, consistent with the experimental results observed on EXL-50. Systematic scanning of different ECR harmonics in simulation has revealed that the multi-harmonic resonance interaction in EXL-50 plays a pivotal role in generating the energetic electron tail responsible for the current.