Development of plasma sources for Dipole Research EXperiment(DREX)

Dipole Research EXperiment（DREX） is a new terrella device as part of the Space Plasma Environment Research Facility（SPERF） for laboratory studies of space physics relevant to the inner magnetospheric plasmas. Adequate plasma sources are very important for DREX to achieve its scientific goals. According to different research requirements, there are two density regimes for DREX. The low density regime will be achieved by an electron cyclotron resonance（ECR） system for the ‘whistler/chorus＇ wave investigation, while the high density regime will be achieved by biased cold cathode discharge for the desired ‘Alfvén＇ wave study. The parameters of ‘whistler/chorus＇ waves and ‘Alfvén＇ waves are determined by the scaling law between space and laboratory plasmas in the current device. In this paper, the initial design of these two plasma sources for DREX is described. Focus is placed on the chosen frequency and operation mode of the ECR system which will produce relatively low density ‘artificial radiation belt＇ plasmas and the seed electrons, followed by the design of biased cold cathode discharge to generate plasma with high density.

Explicit structure-preserving geometric particle-in-cell algorithm in curvilinear orthogonal coordinate systems and its applications to whole-device 6D kinetic simulations of tokamak physics

Explicit structure-preserving geometric particle-in-cell(PIC)algorithm in curvilinear orthogonal coordinate systems is developed.The work reported represents a further development of the structure-preserving geometric PIC algorithm achieving the goal of practical applications in magnetic fusion research.The algorithm is constructed by discretizing the field theory for the system of charged particles and electromagnetic field using Whitney forms,discrete exterior calculus,and explicit non-canonical symplectic integration.In addition to the truncated infinitely dimensional symplectic structure,the algorithm preserves exactly many important physical symmetries and conservation laws,such as local energy conservation,gauge symmetry and the corresponding local charge conservation.As a result,the algorithm possesses the long-term accuracy and fidelity required for first-principles-based simulations of the multiscale tokamak physics.The algorithm has been implemented in the Sym PIC code,which is designed for highefficiency massively-parallel PIC simulations in modern clusters.The code has been applied to carry out whole-device 6 D kinetic simulation studies of tokamak physics.A self-consistent kinetic steady state for fusion plasma in the tokamak geometry is numerically found with a predominately diagonal and anisotropic pressure tensor.The state also admits a steady-state subsonic ion flow in the range of 10 km s-1,agreeing with experimental observations and analytical calculations Kinetic ballooning instability in the self-consistent kinetic steady state is simulated.It is shown that high-n ballooning modes have larger growth rates than low-n global modes,and in the nonlinear phase the modes saturate approximately in 5 ion transit times at the 2%level by the E×B flow generated by the instability.These results are consistent with early and recent electromagnetic gyrokinetic simulations.

Influence of Superathermal Electrons oll Central Plasma Relaxation Oscillations during Localized Electron Cyclotron Heating on the HL-1M Tokamak

During initial studies of ECRH in the HL-1M tokamak, non-standard central MHD activities,such as saturated sawtooth, partially saturated sawtooth, double sawtooth, and the strong m = 1 bursts have been observed while changing the heating location, the ECRH power, the plasma density. Complete suppression of sawtooth is achieved for the duration of the ECRH, when the heating power is applied on the high-field side of low-density plasma, and exceeds a threshold value of power. The m = 1 bursts riding on the ramp phase of sawtooth can only be excited when the ECRH location is near the q = 1 surface on the high field side. The conditions under which the various relaxation activities are produced or suppressed are described. Experimental results imply that the energetic electrons generated during ECRH are responsible for the modification/or stabilization/or excitation of the instability. Near the q = 1 surface, the passing electrons play the role of reducing the shear and tending to stabilize the sawtooth activity, while the barely-trapped electrons play the role of enhancing or driving an internal kink instability.

Analysis of D_α(H_α) spectrum emitted in front of the limiter in HT-7

In order to understand the recycling and emission processes of hydrogen atoms in HT 7, spectral profiles of the Dα（Hα） line emitted in front of the limiter have been observed with a high-resolution spectrometer and simulated by using the neutral particle transport code DEGAS 2. The results show that four processes are necessary to interpret the Dα（Hα） line shape： 1） atom desorption, 2） molecular dissociation, 3） particle reflection, and 4） charge-exchange. The products of the first two processes are cold atoms which emit photons near the peak of Dα（Hα） line shape, and those from the last two are warm atoms contributing to the blue side of the spectrum. For a typical ohmic discharge （shot 68520 ne（0） ≈ 3× 10^19 m^-3. these components contribute 32%, 15%, 32% and 21%, respectively. Dα（Hα） line shapes under different plasma parameters are also discussed in this paper.

Structure-preserving geometric particle-in-cell methods for Vlasov-Maxwell systems

Recent development of structure-preserving geometric particle-in-cell （PIC） algorithms for Vlasov-Maxwell systems is summarized. With the arrival of 100 petaflop and exaflop computing power, it is now possible to carry out direct simulations of multi-scale plasma dynamics based on first-principles. However, standard algorithms currently adopted by the plasma physics community do not possess the long-term accuracy and fidelity required for these large-scale simulations. This is because conventional simulation algorithms are based on numerically solving the underpinning differential （or integro-differential） equations, and the algorithms used in general do not preserve the geometric and physical structures of the systems, such as the local energy-momentum conservation law, the symplectic structure, and the gauge symmetry. As a consequence, numerical errors accumulate coherently with time and long-term simulation results are not reliable. To overcome this difficulty and to harness the power of exascale computers, a new generation of structure-preserving geometric PIC algorithms have been developed. This new generation of algorithms utilizes modem mathematical techniques, such as discrete manifolds, interpolating differential forms, and non-canonical symplectic integrators, to ensure gauge symmetry, space-time symmetry and the conservation of charge, energy-momentum, and the symplectic structure. These highly desired properties are difficult to achieve using the conventional PIC algorithms. In addition to summarizing the recent development and demonstrating practical implementations, several new results are also presented, including a structure-preserving geometric relativistic PIC algorithm, the proof of the correspondence between discrete gauge symmetry and discrete charge conservation law, and a reformulation of the explicit non-canonical symplectic algorithm for the discrete Poisson bracket using the variational approach. Numerical examples are given to verify the advantages of the structure- preserving geometric PIC algorithms in comparison with the conventional PIC methods.

EXCITATION OF HIGH-N TOROIDAL SHEAR ALFVEN MODE DUE TO ALPHA-PARTICLE RIPPLE LOSSES IN TOKAMAKS\

The alpha-particle effects on high-n toroidal shear Alfven mode are investigated analytically.The mode can be driven to unstable when the alpha-particles have an anisotropic distribution function due to ripple losses in tokamaks.The growth rates of the instability in both“fast”and "slow"plasma heating cases are calculated,and the conditions for the excitation of the modes are also studied.

Nonlinear Simulations of Coalescence Instability Using a Flux Difference Splitting Method

A flux difference splitting numerical scheme based on the finite volume method is applied to study ideal/resistive magnetohydrodynamics. The ideal/resistive MHD equations are cast as a set of hyperbolic conservation laws, and we develop a numerical capability to solve the weak solutions of these hyperbolic conservation laws by combining a multi-state Harten-Lax-Van Leer approximate Riemann solver with the hyperbolic divergence cleaning technique, high order shock-capturing reconstruction schemes, and a third order total variance diminishing Runge-Kutta time evolving scheme. The developed simulation code is applied to study the long time nonlinear evolution of the coalescence instability. It is verified that small structures in the instability oscillate with time and then merge into medium structures in a coherent manner. The medium structures then evolve and merge into large structures, and The physics of this interesting nonlinear dynamics this trend continues through all scale-lengths is numerically analyzed.

Verification of Gyrokinetic Particle of Turbulent Simulation of Device Size Scaling Transport

Verification and historical perspective are presented on the gyrokinetic particle simulations that discovered the device size scaling of turbulent transport and indentified the geometry model as the source of the long-standing disagreement between gyrokinetic particle and continuum simulations.

Discovering exact,gauge-invariant,local energy–momentum conservation laws for the electromagnetic gyrokinetic system by high-order field theory on heterogeneous manifolds

Gyrokinetic theory is arguably the most important tool for numerical studies of transport physics in magnetized plasmas.However,exact local energy–momentum conservation laws for the electromagnetic gyrokinetic system have not been found despite continuous effort.Without such local conservation laws,energy and momentum can be instantaneously transported across spacetime,which is unphysical and casts doubt on the validity of numerical simulations based on the gyrokinetic theory.The standard Noether procedure for deriving conservation laws from corresponding symmetries does not apply to gyrokinetic systems because the gyrocenters and electromagnetic field reside on different manifolds.To overcome this difficulty,we develop a high-order field theory on heterogeneous manifolds for classical particle-field systems and apply it to derive exact,local conservation laws,in particular the energy–momentum conservation laws,for the electromagnetic gyrokinetic system.A weak Euler–Lagrange(EL)equation is established to replace the standard EL equation for the particles.It is discovered that an induced weak EL current enters the local conservation laws,and it is the new physics captured by the high-order field theory on heterogeneous manifolds.A recently developed gauge-symmetrization method for high-order electromagnetic field theories using the electromagnetic displacement-potential tensor is applied to render the derived energy–momentum conservation laws electromagnetic gauge-invariant.

ENERGETIC PARTICLE STABILIZATION OF m=1 INTERNAL KINK MODE IN TOKAMAKS

The stability of m=1 internal kink mode in a tokamak plasma with an anisotropic energetic particle component has been analyzed using the generalized energy principle.It is found that employing barely trapped energetic particles can significantly improve the stability properties.

Magnetic Configuration Effects on Fast Ion Losses Induced by Fast Ion Driven Toroidal Alfvén Eigenmodes in the Large Helical Device

Beam-ion losses induced by fast-ion-driven toroidal Alfven eigenmodes （TAE） were measured with a scintillator-based lost fast-ion probe （SLIP） in the large helical device （LHD）. The SLIP gave simultaneously the energy E and the pitch angle X=arccos（v///v） distribution of the lost fast ions. The loss fluxes were investigated for three typical magnetic configurations of Rax-vac=3.60 m, 3.75 m. and 3.90 m, where Rax-vac is the magnetic axis position of the vacuum field. Dominant losses induced by TAEs in these three configurations were observed in the E/X regions of 50-190 keV/40°, 40-170 keV/25°, and 30-190 keV/30°, respectively. Lost-ion fluxes induced by TAEs depend clearly on the amplitude of TAE magnetic fluctuations, Rax-vac and the toroidal field strength Bt. The increment of the loss fluxes has the dependence of （bTAE/Bt）s. The power s increases from s = 1 to 3 with the increase of the magnetic axis position in finite beta plasmas.

Simulation of ECCD and ECRH for SUNIST

1 Introduction Interaction of radio-frequency wave with plasma in magnetic confinement devices has been a very important discipline of plasma physics. To approach more realistic description of wave-plasma interaction in a time scale longer than the kinetic time scales bounce-average is needed. The long time evolution of the kinetic distribution can be treated by Fokker-Planck equation. The behavior of the plasma and the most interesting macroscopic effects are obtained by balancing the diffusion term with a collision term.

Modeling of Stochastic Magnetic Perturbation by RWMEF-Coils on NSTX

A 3-D field line integration code, TRIP3D has been modified to model stochastic magnetic perturbation produced by a resistive wall mode, error field （ RWMEF ） coil in the NSTX tokamak with very low aspect ratio. The RWMEF-coil has two turns, which may produce stochastic fields with the toroidal mode number of n = 1 or 3. In this study, it is found that the stochastic field of n = 3 is larger than that of n=-1 for the same coil current. Two divertor discharges with lower single null （ LSN ） and double null （ DN ） configurations in the NSTX have been modeled with different RWMEF-coil currents and toroidal modes.

A Nonlinear PIC Algorithm for High Frequency Waves in Magnetized Plasmas Based on Gyrocenter Gauge Kinetic Theory

Numerical methods based on gyrocenter gauge kinetic theory are suitable for first principle simulations of high frequency waves in magnetized plasmas.Theδf gyrocenter gauge PIC simulation for linear rf wave has been previously realized.In this paper we further develop a full-f nonlinear PIC algorithm appropriate for the nonlinear physics of high frequency waves in magnetized plasmas.Numerical cases of linear rf waves are calculated as a benchmark for the nonlinear GyroGauge code,meanwhile nonlinear rf-wave phenomena are studied.The technique and advantage of the reduction of the numerical noise in this full-f gyrocenter gauge PIC algorithm are also discussed.

ISSDE:基于第一性原理随机微分方程的碰撞等离子体隐式模拟

开发一种适用于求解含库仑碰撞等离子体随机微分方程(SDE)的第一性原理隐式模拟程序——Implicit Stratonovich Stochastic Differential Equations (ISSDE).该程序基于Fokker-Planck(FP)方程与Stratonovich SDE的等价性理论,通过精确求解Stratonovich SDE达到对FP方程的高效第一性原理计算的目标.ISSDE采用隐式格式保证求解的数值稳定性,同时可以保证粒子碰撞过程的能量守恒.ISSDE基于C++语言开发,具有标准接口和灵活的可扩展模组.通过模拟电子束在非磁化和磁化致密等离子体中的慢化过程验证ISSDE的正确性,并展示该程序在碰撞等离子体模拟中的应用.

Simulation of mode conversion at the magnetopause

Two-dimensional(2-D)and three-dimensional(3-D)hybrid simulations are carried out for mode conversion from fast mode compressional wave to kinetic Alfvn waves(KAWs)at the inhomogeneous magnetopause boundary.For cases in which the incident fast wave propagates in the xz plane,with the magnetopause normal along x and the background magnetic field pointing along z,the 2-D (xz)simulation shows that KAWs with large wave number kxρi～1 are generated near the Alfve′n resonance surface,whereρi is the ion Larmor radius.Several nonlinear wave properties are manifest in the mode conversion process.Harmonics of the driver frequency are generated.As a result of nonlinear wave interaction,the mode conversion region and its spectral width are broadened.In the 3-D simulation,after this first stage of the mode conversion to KAWs with large kx,a subsequent generation of KAW modes of finite ky is observed in the later stage,through a nonlinear parametric decay process.Since the nonlinear cascade to ky can lead to massive transport at the magnetopause,the simulation results provide an effective transport mechanism at the plasma boundaries in space as well as laboratory plasmas.

Geometric field theory and weak Euler-Lagrange equation for classical relativistic particle-field systems

A manifestly covariant, or geometric, field theory of relativistic classical particle-field systems is devel- oped. The connection between the space-time symmetry and energy-momentum conservation laws of the system is established geometrically without splitting the space and time coordinates; i.e., space- time is treated as one entity without choosing a coordinate system. To achieve this goal, we need to overcome two difficulties. The first difficulty arises from the fact that the particles and the field reside on different manifolds. As a result, the geometric Lagrangian density of the system is a function of the 4-potential of the electromagnetic fields and also a functional of the particles＇ world lines. The other difficulty associated with the geometric setting results from the mass-shell constraint. The standard Euler-Lagrange （EL） equation for a particle is generalized into the geometric EL equation when the mass-shell constraint is imposed. For the particle-field system, the geometric EL equation is further generalized into a weak geometric EL equation for particles. With the EL equation for the field and the geometric weak EL equation for particles, the symmetries and conservation laws can be established geometrically. A geometric expression for the particle energy-momentum tensor is derived for the first time, which recovers the non-geometric form in the literature for a chosen coordinate system.

Electromagnetic High Frequency Gyrokinetic Particle-in-Cell Simulation

Using the gyrocenter-gauge kinetic theory,an electromagnetic version of the high frequency gyrokinetic numerical algorithm for particle-in-cell simulation has been developed.The new algorithm,being an alternative to a direct Lorentz-force simulation,offers an efficient way to simulate the dynamics of plasma heating and current drive with radio frequency waves.Gyrokinetic formalism enables separation of gyrocenter and gyrophase motions of a particle in a strong magnetic field.From this point of view,a particlemay be viewed as a combination of a slow gyrocenter and a quickly changing Kruskal ring.In this approach,the nonlinear dynamics of high frequency waves is described by the evolution of Kruskal rings based on first principles physics.The efficiency of the algorithm is due to the fact that the simulation particles are advanced along the slow gyrocenter orbits,while the Kruskal rings capture fast gyrophase physics.Moreover,the gyrokinetic formalism allows separation of the cold response from kinetic effects in the current,which allows one to use much smaller number of particles than what is required by a direct Lorentz-force simulation.Also,the new algorithm offers the possibility to have particle refinement together with mesh refinement,when necessary.To illustrate the new algorithm,a simulation of the electromagnetic low-hybrid wave propagating in inhomogeneous magnetic field is presented.