TBD
Understanding the formation of large-scale structures in weakly magnetized plasmas represents a crucial step towards developing predictive design capabilities for E×B devices dedicated to investigating fundamental plasma physics phenomena. MISTRAL is such a device based at PIIM laboratory to study plasmas in cross-field configuration (E⊥B). The formation of coherent rotating structures in MISTRAL is supposed to be due to an interplay between various instabilities and the E×B flow. However, a definitive understanding of which instabilities are accountable for their emergence and the specific triggers involved remains elusive. An experimental investigation of MISTRAL plasmas has been performed to lay the basis for the theoretical modeling. A two-fluid model has been developed to discuss the linear stability of rotating plasma columns. Prior works have demonstrated that rotating plasma columns are susceptible to centrifugal flute modes. However, most of the existing models rely on the low-frequency approximation (LFA), which holds true when the instability frequency and equilibrium flow frequency are considerably smaller than the ion-cyclotron frequency. This assumption is challenged in numerous laboratory plasma devices, including weakly magnetized plasma columns like MISTRAL. To address this limitation, a radially global dispersion relation describing the centrifugal instability without the LFA has been derived and linear stability analysis is performed. A comparison has been made between the results obtained using the dispersion relation with the radially local approximation and those obtained using the radially global dispersion relation. This comparison revealed the non-applicability of the local solution to MISTRAL-like plasma systems. Due to the high fraction of neutrals in the present plasma system, the model is further extended to include the effects due to ion-neutral collisions. In this first step, the ion-neutral collision frequency is assumed to be small as compared to the ion-cyclotron frequency. The dispersion relation is then solved with finite ion-neutral collisionality and the linear stability analysis is conducted.
In magnetic confinement fusion plasmas, many instabilities have a flute mode character. The field-aligned coordinates bring the benefit of efficient resolution of parallel mode structure along the magnetic field direction. However, the curvilinear coordinates make equations and codes more complex especially in high order PDE.
The Compile-time Symbolic Solver (CSS) is developed to solve PDEs and ODEs in finite difference method from vector equations directly. CSS is a general-purpose finite difference framework for generating finite difference codes easily and greatly reducing the risk of implementation mistakes.
For physics model, CSS supports arbitrary equations in arbitrary curvilinear coordinates and multiple boundaries for both PDEs and ODEs. For memory distribution, N-dimension distribution grids with hybrid TBB and MPI parallelization in arbitrary dimensions are implemented. For numerical method, CSS employs Method of Line in numerical difference with arbitrary grid points and offset. The N-dimension B-spline is implemented with arbitrary orders for pushing particles. CSS employs PARDISO to solve matrix problem and Runge–Kutta method for time advance. CSS is a C++20 template metaprogramming code which guarantee zero-overhead at runtime. Furthermore, the instruction optimization makes the codes generated by CSS much faster than usual codes.
We have used CSS to generate the Gyrokinetic-MHD Hybrid Code GMEC, 3D Field and the Particle calculation code FP3D and a fluid ITG code. For GMEC, we propose a new shifted metric method which is able to stabilize numerical instabilities and avoid the interpolation from MHD field-align grids to particle flux coordinate grids at the same time. The equilibriums can be analytical ones or numerical ones calculated by VMEC or DESC. We have used GMEC to simulate ballooning modes (IBM) with or without the diamagnetic drift term and tearing modes. The simulation results agree well with those of the eigenvalue code MAS. The n=20 IBM costs only 17 seconds using 448 cores. We have also used GMEC to simulate energetic particle-driven TAEs in a circular equilibrium and a CFETR equilibrium. The results of an n=3 TAE agree well with those of M3D-K code.
We have also used CSS to generate the test particle code FP3D for calculation of magnetic surfaces, rotation transform, particle orbits and neoclassical transport in both tokamaks and stellarators. We have used FP3D to simulate ripple losses in EAST tokamak and neoclassical transport coefficient in NCSX. The results are consistent with previous results. FP3D has been used in design and optimization of stellarators successfully.
[1] P. Y. Jiang, et al. CSS: Compile-time symbolic solver for finite difference method. To be submitted.
[2] P. Y. Jiang, et al. GMEC: Gyrokinetic-MHD Hybrid Code. To be submitted. [3] P. Y. Jiang, Z. C. Feng, G. D. Yu, and G. Y. Fu, FP3D: A code for calculating 3D magnetic field and particle motion. Submitted to POP.Accurately predicting lower hybrid current drive (LHCD) in the weak-damping regime is an outstanding challenge, which suggests important physics is missing in present-day ray-tracing/Fokker-Planck (RTFP) models. In this work, the impact of filamentary scrape-off layer (SOL) turbulence on LH waves is investigated using a new multi-scale scattering model. When coupled to an RTFP code, the resulting simulations of LHCD in Alcator C-Mod show RF power deposition profiles robustly peaked on-axis, leading to good agreement with experimental Motional Stark Effect and hard X-ray measurements. Therefore, it is shown that the rotation of the perpendicular wave-vector due to SOL turbulence is sufficient to bridge the discrepancy between simulation and experiment. Notably, this model predicts an asymmetric broadening of the transmitted wave-spectrum, which is attributed to full-wave scattering effects in the presence of spatially coherent turbulence. This asymmetry leads to rotation of incident power away from the plasma core when SOL densities are sufficiently high. RTFP modeling shows this effect plays a significant role in the anomalous drop in LHCD efficiency observed at high densities.
The multi-scale scattering model has two steps. (1) Single filament-wave interactions are solved in full-wave formalism using a Mie-scattering technique. (2) Multiple of these filament-wave interactions are modeled using the radiative transfer approximation, in which a photon’s scattering probability depends on the statistical properties of the filament population. The radiative transfer equation (RTE) is then solved using a Monte Carlo scattering term in a ray-tracing model, allowing for self-consistent coupling to RTFP codes. For verification and comparison against other models, the RTE is also solved in a simple slab geometry using a Markov chain. This model shows good agreement with ray-tracing in the Wentzel-Kramer-Brillouin (WKB) limit, and predicts greater, asymmetric scattering beyond the WKB limit. Good agreement is also found with numeric full-wave solutions at sufficiently low filament packing-fraction, which is consistent with the validity limit of the radiative transfer approximation.
It should be emphasized that this multi-scale scattering model retains many important full-wave effects while remaining computationally inexpensive, allowing fast parameter scans and inter-shot analysis. In addition, this model is highly applicable to the modeling of electron cyclotron wave scattering since the radiative transfer approximation is increasingly valid for waves at higher k.
B. Biswas et al., “Spectral broadening from turbulence in multiscale lower hybrid current drive simulations,” Nuclear Fusion, 63, 1 (2022).
B. Biswas et al., “A hybrid full-wave Markov chain approach to calculating radio-frequency wave scattering from scrape-off layer filaments,” Journal of Plasma Physics, 87, 5 (2021).
This is joint work with M. O'Neil, L. Greengard, and L.-M. Imbert-Gerard
Since the work of Sauter in 1931 it is known that quantum electrodynamics (QED) exhibits a so-called "critical" electromagnetic field scale, at which the quantum interaction between photons and macroscopic electromagnetic fields becomes nonlinear. One prominent example is the importance of light-light interactions in vacuum at this scale, which violates the superposition principle of classical electrodynamics. Furthermore, an electromagnetic field becomes unstable in this regime, as electron-positron pairs can be spontaneously created from the vacuum at the expenses of electromagnetic-field energy (Schwinger mechanism). Unfortunately, the QED critical field scale is so high that experimental investigations are challenging. One promising pathway to explore QED in the nonlinear domain with existing technology consists in the combination of modern (multi) petawatt optical laser systems with highly energetic particles. The suitability of this approach was first demonstrated in the mid-1990s at the seminal SLAC E-144 experiment. Since then, laser technology continuously developed, implying the dawn of a new era of strong-field QED experiments. For instance, the basic processes nonlinear Compton scattering and Breit-Wheeler pair production are expected to influence laser-matter interactions and in particular plasma physics at soon available laser intensities. Therefore, a considerable effort is being undertaken to include these processes into particle-in-cell (PIC) codes used for numerical simulations.
In the first part of the talk the most prominent nonlinear QED phenomena are presented and discussed on a qualitative level. Afterwards, the mathematical formalism needed for calculations with strong plane-wave background fields is introduced with an emphasize on fundamental concepts. Finally, the nonlinear Breit-Wheeler process is considered more in depth. In particular, the semiclassical approximation is elaborated, which serves as a starting point for the implementation of quantum processes into PIC codes.