中国物理B ›› 2026, Vol. 35 ›› Issue (6): 65201-065201.doi: 10.1088/1674-1056/ae1018

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Noise reduction via dual-grid charge averaging

Haiyun Tan(谭海云)1,2,3, Tianyuan Huang(黄天源)2,3, Peiyu Ji(季佩宇)4, Liang Xu(徐亮)2,3,†, and Xuemei Wu(吴雪梅)2,3,‡   

  1. 1 School of Electronic Information Engineering, Suzhou Polytechnic University, Suzhou 215000, China;
    2 School of Physical Science and Technology & Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou 215006, China;
    3 Key Laboratory of Advanced Optical Manufacturing Technologies of Jiangsu Province & Key Laboratory of Modern Optical Technologies of Education Ministry of China, Soochow University, Suzhou 215006, China;
    4 School of Microelectronics and School of Integrated Circuits, Nantong University, Nantong 226019, China
  • 收稿日期:2025-07-10 修回日期:2025-09-19 接受日期:2025-10-07 发布日期:2026-06-01
  • 通讯作者: Liang Xu, Xuemei Wu E-mail:liangxu@suda.edu.cn;xmwu@suda.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 12405237, 12405293, and 12305284)

Noise reduction via dual-grid charge averaging

Haiyun Tan(谭海云)1,2,3, Tianyuan Huang(黄天源)2,3, Peiyu Ji(季佩宇)4, Liang Xu(徐亮)2,3,†, and Xuemei Wu(吴雪梅)2,3,‡   

  1. 1 School of Electronic Information Engineering, Suzhou Polytechnic University, Suzhou 215000, China;
    2 School of Physical Science and Technology & Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou 215006, China;
    3 Key Laboratory of Advanced Optical Manufacturing Technologies of Jiangsu Province & Key Laboratory of Modern Optical Technologies of Education Ministry of China, Soochow University, Suzhou 215006, China;
    4 School of Microelectronics and School of Integrated Circuits, Nantong University, Nantong 226019, China
  • Received:2025-07-10 Revised:2025-09-19 Accepted:2025-10-07 Published:2026-06-01
  • Contact: Liang Xu, Xuemei Wu E-mail:liangxu@suda.edu.cn;xmwu@suda.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 12405237, 12405293, and 12305284)

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摘要： Numerical heating in particle-in-cell simulations arises primarily from statistical noise during the deposition process, which has long been a critical bottleneck limiting long-term simulation accuracy. This work proposes a dual-grid scheme that enhances sampling accuracy by leveraging complementary spatial information from two staggered grids, thereby reducing statistical noise. Analytical derivations show that, through its distinctive deposition mechanism, the scheme effectively elevates bilinear interpolation to a higher-order formulation. Numerical experiments validate this conclusion: compared to quadratic interpolation, the proposed method achieves comparable noise suppression and mitigation of noise-driven heating, while exhibiting superior capability in controlling grid heating and preserving energy conservation in long-term simulations. Most importantly, phase-space diagnostics confirm that the scheme delivers the highest simulation accuracy among the tested methods. These results demonstrate that the proposed approach provides an effective pathway for advancing noise control in particle-in-cell simulations.

关键词: particle-in-cell, numerical noise, finite-grid-instability

Abstract: Numerical heating in particle-in-cell simulations arises primarily from statistical noise during the deposition process, which has long been a critical bottleneck limiting long-term simulation accuracy. This work proposes a dual-grid scheme that enhances sampling accuracy by leveraging complementary spatial information from two staggered grids, thereby reducing statistical noise. Analytical derivations show that, through its distinctive deposition mechanism, the scheme effectively elevates bilinear interpolation to a higher-order formulation. Numerical experiments validate this conclusion: compared to quadratic interpolation, the proposed method achieves comparable noise suppression and mitigation of noise-driven heating, while exhibiting superior capability in controlling grid heating and preserving energy conservation in long-term simulations. Most importantly, phase-space diagnostics confirm that the scheme delivers the highest simulation accuracy among the tested methods. These results demonstrate that the proposed approach provides an effective pathway for advancing noise control in particle-in-cell simulations.

Key words: particle-in-cell, numerical noise, finite-grid-instability

中图分类号:  (High-frequency and RF discharges)

  • 52.80.Pi
52.27.Aj (Single-component, electron-positive-ion plasmas) 52.65.Rr (Particle-in-cell method)