Simulations of first-orbit losses of neutral beam injection(NBI) fast ions on EAST

Simulations of first-orbit losses of neutral beam injection(NBI) fast ions in the EAST tokamak have been studied in detail by using the orbit-following code GYCAVA and the NBI code TGCO. Beam ion losses with the wall boundary are smaller than those with the last closed flux surface boundary. In contrast to heat loads on the wall without radio frequency wave(RFW)antennas, heat loads on the wall with RFW antennas are distributed more locally near the RFW antennas. The direction of the toroidal magnetic field dramatically affects the final positions of lost fast ions, which is related to the magnetic drift. The numerical results on heat loads of beam ions corresponding to different toroidal magnetic fields are qualitatively consistent with the experimental results. Beam ion losses increase with the beam energy for the co-current NBIs and the counter-perpendicular NBI. We have studied the behavior of fast ions produced by a small section neutral beam(beamlet) by using the numerical tool NBIT. The distributions of the loss fraction of beamlet fast ions peaked near the edge of the beam section for the counter-current NBIs, and they are related to the injection angle. This indicates that the first-orbit losses can be reduced by changing the shape of beam cross section.     

Simulations of energetic alpha particle loss in the presence of toroidal field ripple in the CFETR tokamak

Energetic alpha particle losses with the toroidal field ripple and the Coulomb collision in the CFETR tokamak have been simulated by using the orbit-following code GYCAVA for the steady-state and hybrid scenarios. The effects of the outer boundary and the ripple amplitude on alpha particle losses have been investigated. The loss fractions and heat loads of alpha particles in the hybrid scenario are much smaller than those in the steady-state scenario for a significant ripple amplitude. Some alpha particles in the plasma core are lost due to the ripple stochastic transport for a large ripple amplitude parameter. The heat loads with the last closed flux surface boundary are different from those with the wall boundary for the CFETR tokamak, which can be explained by typical alpha particle orbits. Discrete heat load spots have been observed in alpha particle loss simulations, which is due to the ripple well loss. The transition of the lost alpha particle behavior from the ripple stochastic diffusion to the ripple well trapping has been identified in our CFETR simulations. The Coulomb collision effect is responsible for this transition.     

Numerical study on the loss of fast ions produced by minority ion cyclotron resonance heating in EAST

The classical prompt loss of fast ions produced by minority ion cyclotron resonance heating(ICRH)is studied by a guiding center orbit following code in the Experimental Advanced Superconducting Tokamak(EAST).It is found that the loss of fast ions produced by ICRH mainly appears in both ends of the resonance layer,while the loss of fast ions in the middle resonance layer is very small.The dominant fast loss comes from trapped ions,rather than from passing ions.Controlling the location of resonance layer at the plasma core may be more beneficial to the EAST tokamak ICRH.In addition,the loss distribution of fast ions is studied.The results show that the fast ions are mainly lost near the midplane in the poloidal direction,but almost uniformly in the toroidal direction.Moreover,we investigate the dependence of fast ion loss on the ICRH power.The simulation results show that the loss fraction of fast ions in both ends of the resonance region increases with the ion cyclotron range of frequencies(ICRF)power,but barely affects the loss of fast ions in the middle region.     

Effect of Plasma Rotation on Neutral Beam Heating and Current Drive in Tokamaks

For a rapidly rotating plasma, the effects of the resulting Doppler shift have to be included in the neoclassical theory of neutral beam heating, current drive, and plasma transport. In this paper, an improved simulation of neutral beam injection (NBI) and current drive in rotating plasmas is introduced. NBI is simulated using the Monte Carlo code NUBEAM along with the transport code ONETWO. The physical characteristics of heating and current drive for co- and counter-NBI are investigated for non-rotating, co-rotating, and counter-rotating plasmas, all of which can take place in the experiments. In general, it is found that rotation of the plasma can increase the NBI power deposition on the plasma electrons but has little effect on the ions. Moreover, plasma heating by co-NBI is more efficient than that by counter-NBI. For neutral beam current drive, because of the Doppler shift, co-rotation (counter-rotation) of the bulk plasma tends to decrease the co-NBI (counter-NBI) driven current. On the other hand, due to trapping and orbit loss of the fast ions, co-rotation (counter-rotation) has little effect on the counter-NBI (co-NBI) driven current. The results are applied to the forthcoming NBI heating and current drive experiments of the EAST tokamak and should also be useful in the design of experiments in ITER.     

Numerical Study on Ripple Loss of Neutral-Beam-Injected Fast Ions in EAST

A systematic comparative study on the behaviors and loss processes of energetic beam ions in the rippled toroidal field on Experimental Advanced Superconducting Tokamak (EAST) is carried out by numerical simulations. The predicted loss fractions of either co-injected or counter-injected neutral beam ions for typical EAST experiments are 9–16 %; while for low current experiments, the ripple loss domain is enlarged with the increase of the safety factor q, resulting in enhanced beam ions loss. In addition, Counter-injected ions give rise to more lost fractions in the relatively high-energy range, and fewer of them distribute into the core plasma region, which suggest that the co-injection scheme is somewhat preferable for plasma heating. Moreover, the total losses of energetic beam ions in both co-injection and counter-injection geometries are seen to be due entirely to the delayed losses owing to a synergistic effect of collisions and ripple. Finally, potential first wall damage appears to be avoidable for long pulse neutral beam injection scenarios.     

Symplectic Simulation of Fast Alpha Particle Radial Transport in Tokamaks in the Presence of TF Ripples and a Neoclassical Tearing Mode

A Hamiltonian guiding centre drift orbit code based on a symplectic integration algorithm, which enables the efficient calculation of particle trajectories and diffusion coefficients, is applied to fast alpha particle motion in magnetically perturbed tokamak plasmas. In particular, fast ion drift motion is examined in the presence of a stationary, low mode-number MHD magnetic perturbation in a toroidally rippled tokamak with circular flux surface. The main focus of our study is to investigate the dependence of the radial diffusion coefficient of energetic ions on their energy, on the perturbation strength and the localization of the perturbation. As expected, the resonance between bounce motion and toroidal field ripples plays a significant role in this context. For an ensemble of fast ions uniformly distributed in toroidal angle but with a given poloidal starting position their radial transport coefficient takes on higher values in the neighbourhood of resonance speeds and can exhibit there local minima, i.e. it shows an M-shaped speed dependence around resonances for sufficiently strong ripple perturbations. Expectedly, the addition of a modelled low-mode number neoclassical tearing mode perturbation will modify the pure ripple resonance structure of the radial diffusion coefficient. Depending on the strength and localization of the MHD mode it can cause enhancement or degradation of the radial ripple diffusion coefficient.     

中性束注入快离子初始分布的蒙特卡罗模拟

比较精确地模拟计算中性束注入（NBI）托卡马克等离子体的快离子初始分布是采用大规模数值模拟方法研究NBI快离子相关物理问题的首要任务。本文建立了NBI托卡马克等离子体的简化物理模型，采用蒙特卡罗方法自主开发了NBI应用程序。选取ASDEX Upgrade（AUG）托卡马克上切向注入和垂直注入两种情况为计算实例，分别模拟计算出NBI粒子被离子化的初始三维空间位置，并统计得出初始快离子的径向分布、极向角分布、环向角分布和投掷角分布，这些计算结果与国际上相关文献结果一致。     

快电子对快离子损失诊断测量的影响

基于闪烁体原理的快离子损失探针(Fast Ion Loss Detector,FILD),可以同时测量损失快离子的能量和pitch-angle的值,是核聚变装置中对高能粒子诊断的重要方式。根据先进实验超导托卡马克(Experimental Advanced Superconducting Tokamak,EAST)的发展需求,为了更好地对损失快离子行为进行研究,设计并安装了快离子损失诊断,且探测到在中性束加热条件下产生的损失快离子。同时,探测到在放电中产生的逃逸电子,以及低杂波注入时快电子产生X射线对快离子损失背景信号的影响。并且在H-mode放电时边界扰动也对快离子损失信号产生影响,这些探测到的现象都为不断升级损失诊断系统提供依据。     

Evaluation of NBI absorption and fast ion stored energy to improve thermal energy confinement time calculation in EAST

The absorption of neutral beam power and the fast ion stored energy in EAST plasmas with neutral beam injection(NBI)is analyzed to improve the calculation of thermal energy confinement time.The neutral beam power absorption and fast ion stored energy are systematically calculated using the TRANSP code,through the investigation of global parameters including plasma current,line averaged density and beam energy.Results have shown that scaling laws for the NBI absorption coefficient and fast ion energy rate are obtained through statistical analysis.A comparison of the confinement improvement factor H98y2 with these new scaling laws against those assuming fixed coefficients is given.     

Effects of ferromagnetic components on energetic ion confinement in ITER

By using a fully three dimensional magnetic field orbit-following Monte-Carlo code, the energetic ion confinement was investigated for the current conceptual design of the ferromagnetic components in ITER which will be employed for reducing the toroidal magnetic field (TF) ripple. The ferromagnetic insert is effective in the reference standard scenario with Q = 10 (Scenario No. 2) and steady state scenario with Q = 5 (Scenario No. 4) to improve the energetic ion confinement. Over-compensation appears at half of the full toroidal magnetic field and its effect becomes stronger when the quantity of the ferromagnetic insert is increased in order to more reduce the TF ripple at the full toroidal magnetic field. Though the current design is acceptable, whether to increase the ferromagnetic insert to achieve lower TF ripple amplitude at the full field operation depends on how prospected are possibilities of lower field operations. Planned test blanket modules do not induce large loss (<1%) at the full field in Scenario No. 4. At the half field, however, the loss reaches ∼10% for the alpha particles due to localized large TF ripple.     

Results of Predictive Fokker?CPlanck Modelling of NBI Deuterons in ITER

First an analytical formalism is presented for calculating the source distribution of ions generated by neutral beam injection (NBI) in tokamak plasmas. A general NBI ion source term, applicable to studies in the phase space up to 6 dimensions, is provided for neutral beams with finite thickness and divergence. Further, using this source term for the envisaged NBI in ITER, we carry out 3D Fokker?CPlanck modelling of the steady-state deuteron distribution function of NBI produced fast deuterons relaxing on bulk plasma components. For two basic ITER scenarios we demonstrate the poloidal profiles of the beam deuteron density, of the NBI generated current as well as of the NBI power deposition to bulk electrons and ions. Further, we evaluate the capability of gamma and NPA diagnostics of NBI ions in ITER and demonstrate the sensitivity of the distributions of NBI generated ions to different ITER operation scenarios.     

Symplectic Simulations of Radial Diffusion of Fast Alpha Particles in the Presence of Low-Frequency Modes in Rippled Tokamaks

The symplectic Hamiltonian guiding centre code which enables efficient calculation of charged particle trajectories and diffusion coefficients has been applied to fast ion motion in magnetically perturbed tokamak plasmas. Particularly fusion born alpha particle drift motion, in constant of motion space, is examined in the presence of low mode-number neoclassical tearing mode (NTM) perturbation in a toroidally rippled tokamak. The main focus of this study is to investigate the dependence of the radial diffusion coefficient of energetic ions on the perturbation strength and on the localization of the perturbation. The resonance between bounce motion and toroidal field ripples plays a significant role in this context. The presence of NTMs results in substantial enhancement of radial diffusion coefficient for passing particles. Depending on the strength and localization of the NTM it can cause enhancement or degradation of the radial ripple diffusion coefficient of trapped particles.     

The effect of local magnetic field perturbations on confinement of particles in an adiabatic magnetic trap

It has been observed in experiments on the Ogrenok adiabatic magnetic trap that loss of fast ions in the mirror and to the wall of the chamber occurs mainly in the region where the magnetic channel is located. The reason for the loss is scattering of ions by a local perturbation of the magnetic field produced by the magnetic channel. Measurements have been made of the dimensions of the perturbation region and the nature of the perturbation itself. It has been found that replacing the magnetic channel by an electrostatic channel produces a marked reduction in the fast ion current lost in the mirror and to the wall. There is no region here from which the ion loss predominantly occurs. Measurements were made of some of the parameters of the fast ion scattering by perturbations of this sort by setting up a dipole type adjustable local perturbation.     

The Effect of Externally Applied Resonant Magnetic Perturbations on Fusion Product Dynamics in Toroidal Plasmas: Numerical Simulation

The suppression of edge-localized modes by means of externally induced resonant magnetic perturbations (RMPs) has been investigated extensively on present-day tokamaks. In this paper we examine the modification of the loss of fusion born α-particles as effected by the application of RMPs in tokamak plasmas. This study was performed by means of test-particle simulations. To simplify the calculations we use a toroidal magnetic field model with circular magnetic flux surfaces. The transport properties of energetic α-particles are investigated during a 3 s time interval by tracing the test-particle ensemble with each particle trajectory following by integration of the full orbit equation. Three regimes of particle losses are identified during the evolution of the particle ensemble. A natural consequence of RMP excitation is the formation of magnetic islands together with stochastic magnetic layers at the plasma edge. The formation of these resonant magnetic field structures are associated with irregularities of the energetic α-particle orbits, which can substantially increase the loss of slowing down α-particles from the plasma periphery. At the same time the first orbit losses of fusion alphas are practically unaffected by RMPs.     

Study of first orbit losses of 1 MeV tritons using the Lorentz orbit code in the LHD

Shot-integrated measurement of the triton burnup ratio has been performed in the Large Helical Device. It was reported that the triton burnup ratio, defined as total DT neutron yield divided by total DD neutron yield, increases significantly in inward shifted configurations. To understand the magnetic configuration dependence of the triton burnup ratio, the first orbit loss fraction of 1 MeV tritons is evaluated by means of the Lorentz orbit code for various magnetic configurations. The first orbit loss of 1 MeV tritons is seen at t of less than 10-5 s and loss points of the triton are concentrated on the side of the helical coil case where the magnetic field is relatively weak. The significant decrease of the first orbit loss fraction by 15% is obtained with the inward shift of the magnetic axis position from 3.90 to 3.55 m. It is found that the decrease of first orbit loss is due to the reduction of the first orbit loss of transition and helically trapped tritons.     

Position-dependent charge-exchange and energy-loss processes for MeV He ions near a crystal surface

Inelastic interaction of fast ions at glancing angles of incidence on a low index crystal surface is described by the probabilities, which depend on the distance of the ion from the surface; the charge state and energy distributions of the scattered ions are found to result from position-dependent interactions along their trajectories in vacuum. A stochastic equation to describe the charge exchange and energy loss of specularly reflected ions is proposed. Taking account of ion scattering at surface steps, the theory is applied to derive the position-dependent probabilities of electron loss and electron capture of MeV ions from the observed charge state and energy distributions of the scattered ions at glancing angle incidence on the (100) surface of SnTe.     

A Monte Carlo computer code for evaluating energy loss of 10 keV to 10 MeV ions in amorphous silicon materials

The basic concepts of a computer simulation code for determining the energy loss of ions in the 10 keV to 10 MeV energy range in amorphous silicon materials were presented and discussed. Data obtained were found in good agreement with those obtained by using a SRIM programme. Electronic and nuclear energy losses were evaluated. Variation of the energy loss as a function of the incident ion energy were studied. This new computer code is a good tool for evaluating stopping powers of various materials for light and heavy ions.     

等离子体电流反向平衡位形中带电粒子运动的数值模拟研究

本文采用数值方法求解Grad-Shafranov方程获得CT-6B交流放电实验总电流过零时的平衡位形和磁场分布,进而结合粒子在磁场中的运动方程,模拟氘离子在该平衡位形中的运动轨迹,统计氘离子的损失率与损失位置。结果表明：总电流过零时刻的平衡位形为内外两侧电流反向平衡位形,在强、弱场侧各存在1个磁岛,电流在磁岛附近取极值;位于强场侧的粒子几乎不损失,弱场侧的粒子在径向位置很大时存在损失,越靠近边界损失率越高;损失位置基本上位于赤道面以下并在最底部达到极值;随初始角变大,氘离子轨迹由通行轨迹变成损失轨迹再向香蕉轨迹演变。     

Modelling of Small Size Divertor Tokamak Plasma Edge in the Higher Confinement Regime

A version of the B2SOLPS0.5.2D fluid transport code is the new version of B2SOLPS fluid transport code, which is suited technique to simulate the edge plasma of small size divertor tokamak in the H- regime. The results of simulation provide the following: (1) the radial electric field inside the transport barrier is consistent with the neoclassical nature of the radial electric field. (2) The absolute value of the radial electric field shear at inner side of internal transport barrier is small and consistent with the value of shear before the L–H transition, while the value of shear at barrier is significantly large. (3) As a result of strong radial electric field shear and strong barrier formation the diffusion coefficient reduced by factor ~3 with respect to L-mode while ion heat conductivity reduced by factor ~22 with respect to L-mode inside the barrier. (4) The toroidal (Parallel) flux is directed along co-current direction as L-mode but at inner side of barrier is significantly large in absolute value. (5) The radial profile of toroidal rotation in vicinity of transition layer is determined by the parameter δ (width of the transition layer) depending on the collisionality and anomalous diffusion coefficient.     

Ripple effect and impact of test blanket module by using RAFM steels on the plasma of ITER

The losses of high-energy particles from the plasma depend on the toroidal field (TF) ripple in Tokomak machine. TBM (test blanket module), using RAFM (reduced activation ferritic/martensitic) steels as structure material, impacts on TF ripple in International Thermonuclear Experimental Reactor (ITER). The aim in this paper was to investigate the impact of TBM on TF ripple in ITER. It was analyzed based on ANSYS code and the Chinese DFLL (Dual Function Lithium Lead)-TBM as instances of analysis. The results indicated the TF ripple was still beyond the acceptable level of ITER (δ_TF < 0.3%) while considering several kinds of configurations (different masses, different dimensions, and different distances to plasma) of the DFLL-TBM. The correction coil might be one way to further reduce the effect on ripple of TF, and the ferromagnetic inserts under TF coil need to continue optimized.