Numerical impedance matching via extremum seeking control of single-frequency capacitively coupled plasmas

Chen, Zili; Yu, Shimin; Xu, Jingwen; Cao, Dehen; Chen, Zhipeng; Jiang, Wei; Zhang, Ya

doi:10.1088/1402-4896/ad1f1e

Cited by 4 publications

(4 citation statements)

References 26 publications

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“…Consequently, the obtained solution may exhibit saddle points, indicating the presence of local optimal solutions rather than a global optimum. Our previous work [41,42] has proven the existence of these saddle points. Cao et al [41] proposed a machine learning-based approach to optimize impedance matching in CCP systems.…”

Section: Different Discharge Parametersmentioning

confidence: 82%

“…They observed when the value of   Γ is in a region below a certain threshold, the performance of the parameters in this region becomes consistent and reaches a relatively high level of matching performance. Chen et al [42] proposed a modified gradient descent algorithm (GD) to study the impact of presets on the automatic matching process. The results show multiple extreme points in the IMN parameter space, and the CCP discharge intensity at these extreme points is very close, confirming the existence of many saddle points.…”

Section: Different Discharge Parametersmentioning

confidence: 99%

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Impedance matching design of capacitively coupled plasma with fluid and external circuit coupled model

Zhao,

Yu,

Wang

et al. 2024

Plasma Processes & Polymers

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This paper establishes a fully self‐consistent coupled model of fluid and external circuits. The Kirchhoff equation, the charge conservation equation, and Poisson equation are coupled via boundary conditions and integrated into the fluid model for iterative parameter solution. On the basis of this model, we investigate the influence of impedance matching on single‐frequency capacitively coupled plasma characteristics under different parameters and topological structures. The findings suggest that after several iterations the matching parameters converge. Using different initial circuit parameters, the adjustable capacitance and inductance are eventually adjusted to approximately equal values, resulting in the same optimal matching state, whereas diverse discharge parameters led to different outcomes. Under fixed parameters for two topologies, the power absorption efficiency increases, and the reflection coefficient approaches zero, and the best matching is found. This model can be extended to different fluid programs to investigate the impact of complex external circuits with impedance matching network on plasma discharge while simultaneously seeking best impedance matching.

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Section: Different Discharge Parametersmentioning

confidence: 82%

Section: Different Discharge Parametersmentioning

confidence: 99%

Impedance matching design of capacitively coupled plasma with fluid and external circuit coupled model

Zhao,

Yu,

Wang

et al. 2024

Plasma Processes & Polymers

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“…After 70 years of development, the PIC/MCC approach has been used in various discharge phenomena and plasma sources [2], e.g. the capacitively coupled plasma (CCP) sources [3][4][5][6][7], the inductively coupled plasma (ICP) sources [8][9][10], the magnetrons [11][12][13][14], the ion grid systems [15][16][17], plasma probes [18] and the electric thrusters [19][20][21][22][23][24]. Unlike the fluid approaches including nonlocal closure of the equations as an input, the PIC/MCC method is based on the first principle [25,26].…”

Section: Introductionmentioning

confidence: 99%

A comparative study on the acceleration techniques for solving finite difference discretization poisson’s equation in the PIC/MCC Method

Li,

Wang,

et al. 2024

Phys. Scr.

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A wide variety of plasma phenomena have been investigated during the past decades using the particle-in-cell/Monte Carlo collisions (PIC/MCC) method. As an important component of the PIC/MCC method, solving Poisson’s equation is crucial for the accuracy and efficiency of calculations. Different acceleration techniques for solving finite difference discretization Poisson’s equation are investigated and compared, including direct method, iterative method, multigrid (MG) method, parallel computing and inherited initial value. The charge density distribution with a known analytical solution is used to validate the algorithm and code. The optimal relaxation factor for the successive over-relaxation (SOR) method in 2D Poisson’s equation with unequal grid node numbers in different dimensions is derived, which is only related to the dimension with the largest grid number. Although there will be a “more optimal” relaxation factor deviated from in some simulation cases, selecting the optimal relaxation factor derived always leads to a not slow solving speed. However, when SOR is used in MG for smoothing, the optimal relaxation factor will shift to 0.5-1.2 from the theoretical optimal value derived with the increase of MG levels. By comparing the convergence order under different relaxation factors and MG levels, the suitable MG level is proposed as log2[min(Nx, Ny)]-2. Combining the optimal SOR relaxation factor, MG, parallel computing and inherited initial values, the computational cost may decrease by 5 orders of magnitude than that by the simple Gaussian elimination (GE). Based on the optimal acceleration techniques mentioned above, a benchmark simulation case electron cyclotron drift instability (ECDI) in magnetized plasmas was run to further validate the developed PIC/MCC code. The distributions of electric field in the x-direction, electron density and electron temperature are all consistent with the literatures. This paper provides a reference for the acceleration strategy selection for solving Poisson's equation quickly in plasma simulations.

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“…SF-CCPs usually adopt L-type matching networks, which can even be designed by numerical simulations: Yu et al studied the impedance matching design method for SF-CCPs in detail [32], in which the matching was achieved by iterative adjustment of the variable elements of the impedance matching network (IMN). Recently, Cao et al [33] and Chen et al [34] also achieve impedance matching by machine learning and extreme value search methods for SF-CCPs, respectively.…”

Section: Introductionmentioning

confidence: 99%

Kinetic simulations of capacitively coupled plasmas driven by tailored voltage waveforms with multi-frequency matching

Yu,

Wu,

Yang

et al. 2024

Plasma Sources Sci. Technol.

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Impedance matching is crucial for optimizing plasma generation and reducing power reflection in capacitively coupled plasmas (CCP). Designing these matchings is challenging due to the varying and typically unknown impedance of the plasma, especially in the presence of multiple driving frequencies. Here, a computational design method for impedance matching networks (IMNs) for CCPs is proposed and applied to discharges driven by tailored voltage waveforms (TVW). This method is based on a self-consistent combination of particle in cell/Monte Carlo collision simulations of the plasma with Kirchhoff’s equations to describe the external electrical circuit. Two Foster second-form networks with the same structure are used to constitute an L-type matching network, and the matching capability is optimized by iteratively updating the values of variable capacitors inside the IMN. The results show that the plasma density and the power absorbed by the plasma continuously increase in the frame of this iterative process of adjusting the matching parameters until an excellent impedance matching capability is finally achieved. Impedance matching is found to affect the DC self-bias voltage, whose absolute value is maximized when the best matching is achieved. Additionally, a change in the quality of the impedance matching is found to cause an electron heating mode transition. Poor impedance matching results in a heating mode where electron power absorption in the plasma bulk by drift electric fields plays an important role, while good matching results in the classical α-mode operation, where electron power absorption by ambipolar electric fields at the sheath edges dominates. The method proposed in this work is expected to be of great significance in promoting TVW plasma sources from theory to industrial application, since it allows designing the required complex multi-frequency IMNs.

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Numerical impedance matching via extremum seeking control of single-frequency capacitively coupled plasmas

Cited by 4 publications

References 26 publications

Impedance matching design of capacitively coupled plasma with fluid and external circuit coupled model

Impedance matching design of capacitively coupled plasma with fluid and external circuit coupled model

A comparative study on the acceleration techniques for solving finite difference discretization poisson’s equation in the PIC/MCC Method

Kinetic simulations of capacitively coupled plasmas driven by tailored voltage waveforms with multi-frequency matching

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