arXiv subjects

Huasheng Xie

Publications and source records attributed to Huasheng Xie.

At least 37 records · Page 2Linked to original sources

arXiv2025

A robust method for calculating plasma waves absorption in magnetized plasmas and its implementation in the BORAY ray-tracing code

This paper presents a robust numerical method for calculating the total absorption rate of electromagnetic waves in magnetized plasmas, capable of determining the absorption ratio among different plasma components. The method adopts Ronnmark's expressions for the plasma dispersion function, $Z(ζ)$, and the dielectric tensor, K, to overcome the convergence issues and computational inefficiency of the traditional Bessel function summation approach for evaluating the hot plasma dispersion relation, D, particularly at large $k_\perp$. It has been implemented and validated across multiple frequency regimes, including ion cyclotron (ICRF), lower hybrid (LHRF), and electron cyclotron (ECRF) ranges of frequencies, with results benchmarked against conventional $Z(ζ)$ and Bessel function expansions. Integrated into the BORAY ray-tracing code, the method uses expressions derived from the anti-Hermitian part of the dielectric tensor to compute absorption ratios. This work extends the ray-tracing framework, providing a more reliable tool for wave heating simulations.

physics.plasm-ph↗

arXiv2025

Developing a Linear Fluid Plasma Model with Accurate Kinetic Bernstein Waves: A First Step

Kinetic models provide highly accurate descriptions of plasma waves but involve complex integrals that are computationally expensive to solve. To facilitate a fluid-like treatment of the system, we propose rational approximations for both the plasma dispersion function in the parallel integral and the Bessel function in the perpendicular integral, ensuring that the system remains rational with respect to all three variables: wave frequency $ω$, parallel wavevector $k_\parallel$, and perpendicular wavevector $k_\perp$. By accurately approximating the Bessel function over a wide range of Larmor radius $ρ_{cs}$ values, from $k_\perpρ_{cs} \to 0$ to $k_\perpρ_{cs} \to \infty$, we present an initial attempt to incorporate kinetic Bernstein waves into a fluid model. As an application, we employ this model to analyze { electromagnetic plasma} wave propagation conditions (i.e., accessibility) by solving for the complex perpendicular wavevector $k_\perp$ using a matrix eigenvalue method with given input parameters. This work may contribute to studies of electron cyclotron resonance heating (ECRH) and ion cyclotron resonance frequency (ICRF) heating in magnetized confinement plasmas.

physics.plasm-ph↗

arXiv2025

Bremsstrahlung radiation power in non-Maxwellian plasmas

In plasmas, bremsstrahlung includes electron-ion (e-i) bremsstrahlung and electron-electron (e-e) bremsstrahlung. Bremsstrahlung radiation power loss is one of the most significant losses in fusion plasmas, which is more pronounced in higher temperature fusion. The factors that affect bremsstrahlung power include the mean electron energy and the electron velocity distribution shape. In this study, we systematically study the influence of the electron velocity distribution shape on the bremsstrahlung power with fixed total electron energy. It was found that the existing electron velocity distribution shapes have little effect on the bremsstrahlung power. In addition, by analyzing the bounds of bremsstrahlung power, we have provided the theoretical upper and lower bounds of e-i radiation. Our analysis reveals that the e-i bremsstrahlung power depends critically on the degree of energy distribution concentration. Specifically, in non-relativistic regimes, concentrated energy distributions enhance the radiation power, whereas in high-temperature relativistic regimes, such concentration suppresses it. This discrepancy arises from the distinct contributions of high-energy electron populations to radiation power across different energy regimes. For e-e bremsstrahlung, a similar dependence on energy concentration is observed. Furthermore, e-e radiation power exhibits additional sensitivity to the anisotropy of the electron velocity distribution function. These rules could provide a basis for reducing bremsstrahlung power losses in fusion plasmas.

physics.plasm-ph↗

arXiv2025

EFIT-mini: An Embedded, Multi-task Neural Network-driven Equilibrium Inversion Algorithm

Equilibrium reconstruction, which infers internal magnetic fields, plasmas current, and pressure distributions in tokamaks using diagnostic and coil current data, is crucial for controlled magnetic confinement nuclear fusion research. However, traditional numerical methods often fall short of real-time control needs due to time-consuming computations or iteration convergence issues. This paper introduces EFIT-mini, a novel algorithm blending machine learning with numerical simulation. It employs a multi-task neural network to replace complex steps in numerical equilibrium inversion, such as magnetic surface boundary identification, combining the strengths of both approaches while mitigating their individual drawbacks. The neural network processes coil currents and magnetic measurements to directly output plasmas parameters, including polynomial coefficients for $p'$ and $ff'$, providing high-precision initial values for subsequent Picard iterations. Compared to existing AI-driven methods, EFIT-mini incorporates more physical priors (e.g., least squares constraints) to enhance inversion accuracy. Validated on EXL-50U tokamak discharge data, EFIT-mini achieves over 98% overlap in the last closed flux surface area with traditional methods. Besides, EFIT-mini's neural network and full algorithm compute single time slices in just 0.11ms and 0.36ms at 129$\times$129 resolution, respectively, representing a three-order-of-magnitude speedup. This innovative approach leverages machine learning's speed and numerical algorithms' explainability, offering a robust solution for real-time plasmas shape control and potential extension to kinetic equilibrium reconstruction. Its efficiency and versatility position EFIT-mini as a promising tool for tokamak real-time monitoring and control, as well as for providing key inputs to other real-time inversion algorithms.

physics.plasm-ph↗

arXiv2025

Overview of EXL-50 Research Progress and Future Plan

XuanLong-50 (EXL-50) is the first medium-size spherical torus (ST) in China, with the toroidal field at major radius at 50 cm around 0.5T. CS-free and non-inductive current drive via electron cyclotron resonance heating (ECRH) was the main physics research issue for EXL-50. Discharges with plasma currents of 50 kA - 180 kA were routinely obtained in EXL-50, with the current flattop sustained for up to or beyond 2 s. The current drive effectiveness on EXL-50 was as high as 1 A/W for low-density discharges using 28GHz ECRH alone for heating power less than 200 kW. The plasma current reached Ip>80 kA for high-density (5*10e18m-2) discharges with 150 kW 28GHz ECRH. Higher performance discharge (Ip of about 120 kA and core density of about 1*10e19m-3) was achieved with 150 kW 50GHz ECRH. The plasma current in EXL-50 was mainly carried by the energetic electrons.Multi-fluid equilibrium model has been successfully applied to reconstruct the magnetic flux surface and the measured plasma parameters of the EXL-50 equilibrium. The physics mechanisms for the solenoid-free ECRH current drive and the energetic electrons has also been investigated. Preliminary experimental results show that 100 kW of lower hybrid current drive (LHCD) waves can drive 20 kA of plasma current. Several boron injection systems were installed and tested in EXL-50, including B2H6 gas puffing, boron powder injection, boron pellet injection. The research plan of EXL-50U, which is the upgrade machine of EXL-50, is also presented.

physics.plasm-ph↗

arXiv2025

Efficient Framework for Solving Plasma Waves with Arbitrary Distributions

Plasma, which constitutes 99\% of the visible matter in the universe, is characterized by a wide range of waves and instabilities that play a pivotal role in space physics, astrophysics, laser-plasma interactions, fusion research, and laboratory experiments. The linear physics of these phenomena is described by kinetic dispersion relations (KDR). However, solving KDRs for arbitrary velocity distributions remains a significant challenge, particularly for non-Maxwellian distributions frequently observed in various plasma environments. This work introduces a novel, efficient, and unified numerical framework to address this challenge. The proposed method rapidly and accurately yields all significant solutions of KDRs for nearly arbitrary velocity distributions, supporting both unstable and damped modes across all frequencies and wavevectors. The approach expands plasma species' velocity distribution functions using a series of carefully chosen orthogonal basis functions and employs a highly accurate rational approximation to transform the problem into an equivalent matrix eigenvalue problem, eliminating the need for initial guesses. The efficiency and versatility of this framework are demonstrated, enabling simplified studies of plasma waves with arbitrary distributions. This advancement paves the way for uncovering new physics in natural plasma environments, such as spacecraft observations in space plasmas, and applications like wave heating in fusion research.

physics.plasm-ph↗

arXiv2024

Bremsstrahlung Radiation Power in Fusion Plasmas Revisited: Towards Accurate Analytical Fitting

In fusion plasmas, where electron temperatures $T_e$ range from keV to hundreds of keV, Bremsstrahlung radiation constitutes a significant energy loss mechanism. While various thermal average fitting formulas exist in the literature, their accuracy is limited, particularly for $T_e \leq 20$ keV with error $>10\%$. Additionally, non-relativistic fitting formulas become invalid for $T_e \geq 50$ keV. The accurate calculation of Bremsstrahlung radiation is important for fusion gain study, especially of advanced fuels fusion. In this work, we develop new but still simple fitting formulas that are valid for electron temperatures ranging from small ($\lesssim0.1$ keV) to extreme relativistic range, with errors of less than 1\% even for high atomic number ions (e.g., $Z=30$), which could be sufficient for fusion plasma applications. Both electron-ion (e-i) and electron-electron (e-e) Bremsstrahlung radiations are considered. Both polynomial fitting with truncated ($t=k_BT_e/m_ec^2\leq10$) and one-fit-all formulas are provided. Additionally, we offer fitting formulas for e-i and e-e specifically for electron energies, which could prove useful in non-Maxwellian Bremsstrahlung radiation studies.

physics.plasm-ph↗

arXiv2024

Introduction to Fusion Ignition Principles: Zeroth Order Factors of Fusion Energy Research

The physical goal of fusion energy research is to confine fusion fuel in a certain way so that the energy released from fusion exceeds the energy consumed to sustain the fusion process, thereby achieving economically viable energy production. Based on fundamental physics, this book focuses on the physics of the core region in fusion energy reactors, discussing the relevant limiting factors and parameter ranges. By examining the zeroth-order quantity system of the fundamental principles of fusion ignition, we review the current progress and challenges in fusion energy research. These challenges encompass various aspects such as physics, engineering, materials, and economics, providing better insights for the future development of fusion as an energy source. [This English version is primarily a translation generated using ChatGPT based on the original Chinese book, and can be cited as "Huasheng Xie, Introduction to Fusion Ignition Principles, USTC press, Hefei, 2023." For any inaccuracies or ambiguities, please refer to the original Chinese version for clarification.]

physics.plasm-ph↗

arXiv2024

Rapid Computation of the Plasma Dispersion Function: Rational and Multi-pole Approximation, and Improved Accuracy

The plasma dispersion function $Z(s)$ is a fundamental complex special integral function widely used in the field of plasma physics. The simplest and most rapid, yet accurate, approach to calculating it is through rational or equivalent multi-pole expansions. In this work, we summarize the numerical coefficients that are practically useful to the community. Besides the Pade approximation to obtain coefficients, which are accurate for both small and large arguments, we also employ optimization methods to enhance the accuracy of the approximation for the intermediate range. The best coefficients provided here for calculating $Z(s)$ can deliver twelve significant decimal digits. This work serves as a foundational database for the community for further applications.

physics.plasm-ph↗

arXiv2023

A linear parameters study of ion cyclotron emission using drift ring beam distribution

Ion cyclotron emission (ICE) holds great potential as a diagnostic tool for fast ions in fusion devices. The theory of magnetoacoustic cyclotron instability (MCI), as an emission mechanism for ICE, states that MCI is driven by a velocity distribution of fast ions that approximates a drift ring beam. The influence of key parameters on the linear MCI is systematically investigated using the linear kinetic dispersion relation solver BO (Xie H. 2019 Comput. Phys. Comm. 244 343). The computational spectra region considered extends up to 40 times the ion cyclotron frequency. By examining the influence of these key parameters on MCI, several novel results have been obtained. In the case of MCI excited by super-Alfvénic fast ions, the parallel velocity spread significantly affects the bandwidth of harmonics and the continuous spectrum, while the perpendicular velocity spread has a decisive effect on the MCI growth rate. As the velocity spread increases, the linear relationship between the MCI growth rate and the square root of the number density ratio transitions to a linear relationship between the MCI growth rate and the number density ratio. This finding provides a linear perspective explanation for the observed linear relation between fast ion number density and ICE intensity in JET. Furthermore, high harmonics are more sensitive to changes in propagation angle than low harmonics because a decrease in the propagation angle alters the dispersion relation of the fast Alfvén wave. In the case of MCI excited by sub-Alfvénic fast ions, a significant growth rate increase occurs at high harmonics due to the transition of sub-Alfvénic fast ions to super-Alfvénic fast ions.

physics.plasm-ph↗

arXiv2023

A Simple and Fast Approach for Computing the Fusion Reactivities with Arbitrary Ion Velocity Distributions

Calculating fusion reactivity involves a complex six-dimensional integral of the fusion cross section and ion velocity distributions of two reactants. We demonstrate a simple Monte Carlo approach that efficiently computes this integral for arbitrary ion velocity distributions with a time complexity of $O(N)$, where $N$ is the number of samples. This approach generates random numbers that satisfy the reactant velocity distributions. In cases where these numbers are not readily available, we propose using Gaussian random numbers with weighted factors. For cases where only a small number of $N$ samples are available, a $O(N^2)$ method can be used. We benchmarked this approach against analytical results for drift bi-Maxwellian distributions and provided examples of drift ring beam and slowing down distributions. Our results show that the error can be less than 1\% with $N\sim10^4$ samples for our standard approach.

physics.comp-ph↗

arXiv2023

Enhancement of Fusion Reactivity under Non-Maxwellian Distributions: Effects of Drift-Ring-Beam, Slowing-Down, and Kappa Super-Thermal Distributions

Non-Maxwellian distributions of particles are commonly observed in fusion studies, especially for magnetic confinement fusion plasmas. The particle distribution has a direct effect on fusion reactivity, which is the focus of this study. We investigate the effects of three types of non-Maxwellian distributions, namely drift-ring-beam, slowing-down, and kappa super-thermal distributions, on the fusion reactivities of D-T (Deuterium-Trillium) and p-B11 (proton-Boron) using a newly developed program, where the enhancement of fusion reactivity relative to the Maxwellian distribution is computed while keeping the total kinetic energy constant. The calculation results show that for the temperature ranges of interest to us, namely 5-50 keV for D-T and 100-500 keV for p-B11, these non-Maxwellian distributions can enhance the fusion reactivities. In the case of the drift-ring-beam distribution, the enhancement factors for both reactions are affected by the perpendicular ring beam velocity, leading to decreased enhancement in low temperature range and increased enhancement in high temperature range. However, this effect is favorable for p-B11 fusion reaction and unfavorable for D-T fusion reaction. In the slowing-down distribution, the birth speed plays a crucial role in both reactions, and increasing birth speed leads to a shift in the enhancement ranges towards lower temperatures, which is beneficial for both reactions. Finally, the kappa super-thermal distribution results in a relatively large enhancement in the low temperature range with a small high energy power-law index κ. Overall, this study provides insight into the effects of non-Maxwellian distributions on fusion reactivity and highlights potential opportunities for enhancing fusion efficiency.

physics.plasm-ph↗

arXiv2023

MAS: A versatile Landau-fluid eigenvalue code for plasma stability analysis in general geometry

We have developed a new global eigenvalue code, Multiscale Analysis for plasma Stabilities (MAS), for studying plasma problems with wave toroidal mode number n and frequency omega in a broad range of interest in general tokamak geometry, based on a five-field Landau-fluid description of thermal plasmas. Beyond keeping the necessary plasma fluid response, we further retain the important kinetic effects including diamagnetic drift, ion finite Larmor radius, finite parallel electric field, ion and electron Landau resonances in a self-consistent and non-perturbative manner without sacrificing the attractive efficiency in computation. The physical capabilities of the code are evaluated and examined in the aspects of both theory and simulation. In theory, the comprehensive Landau-fluid model implemented in MAS can be reduced to the well-known ideal MHD model, electrostatic ion-fluid model, and drift-kinetic model in various limits, which clearly delineates the physics validity regime. In simulation, MAS has been well benchmarked with theory and other gyrokinetic and kinetic-MHD hybrid codes in a manner of adopting the unified physical and numerical framework, which covers the kinetic Alfven wave, ion sound wave, low-n kink, high-n ion temperature gradient mode and kinetic ballooning mode. Moreover, MAS is successfully applied to model the Alfven eigenmode (AE) activities in DIII-D discharge #159243, which faithfully captures the frequency sweeping of RSAE, the tunneling damping of TAE, as well as the polarization characteristics of KBAE and BAAE being consistent with former gyrokinetic theory and simulation. With respect to the key progress contributed to the community, MAS has the advantage of combining rich physics ingredients, realistic global geometry and high computation efficiency together for plasma stability analysis in linear regime.

physics.plasm-ph↗

arXiv2023

Fusion Reactivities with Drift bi-Maxwellian Ion Velocity Distributions

The calculation of fusion reactivity involves a complex six-dimensional integral that takes into account the fusion cross-section and velocity distributions of two reactants. However, a more simplified one-dimensional integral form can be useful in certain cases, such as for studying fusion yield or diagnosing ion energy spectra. This simpler form has been derived in a few special cases, such as for a combination of two Maxwellian distributions, a beam-Maxwellian combination, and a beam-target combination, and can greatly reduce computational costs. In this study, it is shown that the reactivity for two drift bi-Maxwellian reactants with different drift velocities, temperatures, and anisotropies can also be reduced to a one-dimensional form, unifying existing derivations into a single expression. This result is used to investigate the potential enhancement of fusion reactivity due to the combination of beam and temperature anisotropies. For relevant parameters in fusion energy, the enhancement factor can be larger than 20\%, which is particularly significant for proton-boron (p-B11) fusion, as this factor can have a significant impact on the Lawson fusion gain criteria.

physics.plasm-ph↗

arXiv2022

Alpha-particle generation from H-11B fusion initiated by laser-accelerated boron ions

Here we report the generation of MeV alpha-particles from H-11B fusion initiated by laser-accelerated boron ions. Boron ions with maximum energy of 6MeV and fluence of 10^9/MeV/sr@5MeV were generated from 60-nm-thick self-supporting boron nanofoils irradiated by 1J femtosecond pulses at an intensity of 10^19W/cm^2. By bombarding secondary hydrogenous targets with the boron ions, 3*10^5/sr alpha-particles from H-11B fusion were registered, which is consistent with the theoretical yield calculated from the measured boron energy spectra. Our results demonstrate an alternative way toward ultrashort MeV alpha-particle sources employing compact femtosecond lasers. The ion acceleration and product measurement scheme are referential for the studies on the ion stopping power and cross-section of the H-11B reaction in solid or plasma.

physics.plasm-ph↗

arXiv2022

A study of the requirements of p-11B fusion reactor by tokamak system code

Most tokamak devices including ITER exploit the D-T reaction due to its high reactivity, but the wall loading caused by the associated 14MeV neutrons will limit the further development of fusion performance at high beta. To explore p-11B fusion cycle, a tokamak system code is extended to incorporate the relativistic bremsstrahlung since the temperature of electrons is approaching the rest energy of electron. By choosing an optimum p-11B mix and ion temperature, some representative sets of parameters of p-11B tokamak reactor, whose fusion gain exceeds 1, have been found under the thermal wall loading limit and beta limit when synchrotron radiation loss is neglected. However, the fusion gain greatly decreases when the effect of synchrotron radiation loss is considered. Helium ash also plays an important role in the fusion performance, and we have found that the helium confinement time must be below the energy confinement time to keep the helium concentration ratio in an acceptable range.

physics.plasm-ph↗

arXiv2021

Experimental study on edge energetic electrons in EXL-50 spherical torus

A significant number of confined energetic electrons have been observed outside the Last Closed Flux Surface (LCFS) of the solenoid-free, ECRH sustained plasmas in the EXL-50 spherical torus. Several diagnostics have been applied, for the first time, to investigate the key characters of energetic electrons. Experiments reveal the existence of high-temperature low density electrons, which can carry relatively a large amount of the stored energy. The boundary between the thermal plasma and the energetic electron fluid appears to be clearly separated and the distance between the two boundaries can reach tens of centimeters (around the size of the minor radius of the thermal plasma). This implies that the Grad-Shafranov equilibrium is not suitable to describe the equilibrium of the EXL-50 plasma and a multi-fluid model is required. Particle dynamics simulations of full orbits show that energetic electrons can be well confined outside the LCFS. This is consistent with the experimental observations.

physics.plasm-ph↗

arXiv2021

Plasma Waves Accessibility Diagrams: A Tutorial to Include the Fluid and Kinetic Thermal Effects

Although the accurate description of the wave propagation and absorption in plasmas requires complicated full wave solutions or kinetic simulations, the local dispersion analysis can still be helpful to capture the main physics of wave properties. Plasma wave accessibility informs that whether a wave can propagate to a region, which usually depends on the wave frequency, wave vector, and the local plasma density and magnetic field. In this tutorial paper, we describe the wave accessibility beyond usual textbooks and especially highlight the warm plasma effects. Useful numerical models and methods are provided, which can be used to obtain a quick view of the wave accessibility parameters space. The thermal effects are modeled by both multi-fluid model with isotropic pressure term and kinetic model with Maxwellian velocity distribution function. All cold plasma waves from high frequency electron cyclotron waves, intermediate frequency low hybrid waves to low frequency ion cyclotron waves, as well as kinetic ion and electron Bernstein waves, are presented. The questions that how many plasma wave modes exist and how to find the solutions are also discussed. It is interesting to find that the warm multi-fluid model, though incapable of reproducing the Bernstein modes, can provide a quick way to determine whether the thermal effects are important. To show the kinetic thermal effects, the ray tracing calculations of the mode conversion from cold plasma waves to kinetic waves are also provided, i.e., from the slow X electron cyclotron wave to electron Bernstein wave and from the ion cyclotron fast wave to ion Bernstein wave.

physics.plasm-ph↗