# On modified finite difference method to obtain the electron energy distribution functions in Langmuir probes

## Abstract

A modified central difference method (MCDM) is proposed to obtain the electron energy distribution functions (EEDFs) in single Langmuir probes. Numerical calculation of the EEDF with MCDM is simple and has less noise. This method provides the second derivatives at a given point as the weighted average of second order central difference derivatives calculated at different voltage intervals, weighting each by the square of the interval. In this paper, the EEDFs obtained from MCDM are compared to those calculated via the averaged central difference method. It is found that MCDM effectively suppresses the noises in the EEDF, while the same number of points are used to calculate of the second derivative.

- Authors:

- Department of Electrical Engineering, Hanyang University, 222, Wangsimni-ro, Seongdong-gu, Seoul 133-791 (Korea, Republic of)
- Seoul Science High School, 63, Hyehwa-ro, Jongno-gu, Seoul 110-530 (Korea, Republic of)

- Publication Date:

- OSTI Identifier:
- 22600149

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 23; Journal Issue: 6; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; COMPARATIVE EVALUATIONS; DISTRIBUTION FUNCTIONS; ELECTRIC POTENTIAL; ELECTRONS; ENERGY SPECTRA; FINITE DIFFERENCE METHOD; LANGMUIR PROBE; NOISE; WEIGHT

### Citation Formats

```
Kang, Hyun-Ju, Chung, Chin-Wook, E-mail: joykang@hanyang.ac.kr, Choi, Hyeok, Kim, Jae-Hyun, Lee, Se-Hun, and Yoo, Tae-Ho.
```*On modified finite difference method to obtain the electron energy distribution functions in Langmuir probes*. United States: N. p., 2016.
Web. doi:10.1063/1.4951020.

```
Kang, Hyun-Ju, Chung, Chin-Wook, E-mail: joykang@hanyang.ac.kr, Choi, Hyeok, Kim, Jae-Hyun, Lee, Se-Hun, & Yoo, Tae-Ho.
```*On modified finite difference method to obtain the electron energy distribution functions in Langmuir probes*. United States. doi:10.1063/1.4951020.

```
Kang, Hyun-Ju, Chung, Chin-Wook, E-mail: joykang@hanyang.ac.kr, Choi, Hyeok, Kim, Jae-Hyun, Lee, Se-Hun, and Yoo, Tae-Ho. Wed .
"On modified finite difference method to obtain the electron energy distribution functions in Langmuir probes". United States.
doi:10.1063/1.4951020.
```

```
@article{osti_22600149,
```

title = {On modified finite difference method to obtain the electron energy distribution functions in Langmuir probes},

author = {Kang, Hyun-Ju and Chung, Chin-Wook, E-mail: joykang@hanyang.ac.kr and Choi, Hyeok and Kim, Jae-Hyun and Lee, Se-Hun and Yoo, Tae-Ho},

abstractNote = {A modified central difference method (MCDM) is proposed to obtain the electron energy distribution functions (EEDFs) in single Langmuir probes. Numerical calculation of the EEDF with MCDM is simple and has less noise. This method provides the second derivatives at a given point as the weighted average of second order central difference derivatives calculated at different voltage intervals, weighting each by the square of the interval. In this paper, the EEDFs obtained from MCDM are compared to those calculated via the averaged central difference method. It is found that MCDM effectively suppresses the noises in the EEDF, while the same number of points are used to calculate of the second derivative.},

doi = {10.1063/1.4951020},

journal = {Physics of Plasmas},

number = 6,

volume = 23,

place = {United States},

year = {Wed Jun 15 00:00:00 EDT 2016},

month = {Wed Jun 15 00:00:00 EDT 2016}

}

DOI: 10.1063/1.4951020

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