# Relativistic current collection by a cylindrical Langmuir probe

## Abstract

The current I to a cylindrical Langmuir probe with a bias {Phi}{sub p} satisfying {beta}{identical_to}e{Phi}{sub p}/m{sub e}c{sup 2}{approx}O(1) is discussed. The probe is considered at rest in an unmagnetized plasma composed of electrons and ions with temperatures kT{sub e}{approx}kT{sub i} Much-Less-Than m{sub e}c{sup 2}. For small enough radius, the probe collects the relativistic orbital-motion-limited (OML) current I{sub OML}, which is shown to be larger than the non-relativistic result; the OML current is proportional to {beta}{sup 1/2} and {beta}{sup 3/2} in the limits {beta} Much-Less-Than 1 and {beta} Much-Greater-Than 1, respectively. Unlike the non-relativistic case, the electron density can exceed the unperturbed density value. An asymptotic theory allowed to compute the maximum radius of the probe to collect OML current, the sheath radius for probe radius well below maximum and how the ratio I/I{sub OML} drops below unity when the maximum radius is exceeded. A numerical algorithm that solves the Vlasov-Poisson system was implemented and density and potential profiles presented. The results and their implications in a possible mission to Jupiter with electrodynamic bare tethers are discussed.

- Authors:

- Departamento de Fisica Aplicada, Escuela Tecnica Superior de Ingenieros Aeronauticos, Universidad Politecnica de Madrid, Plaza de Cardenal Cisneros 3, 28040 Madrid (Spain)

- Publication Date:

- OSTI Identifier:
- 22072504

- Resource Type:
- Journal Article

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 19; Journal Issue: 6; Other Information: (c) 2012 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-664X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ALGORITHMS; ASYMPTOTIC SOLUTIONS; BOLTZMANN-VLASOV EQUATION; CURRENTS; CYLINDRICAL CONFIGURATION; ELECTRON DENSITY; ELECTRON TEMPERATURE; ION TEMPERATURE; JUPITER PLANET; LANGMUIR PROBE; PLASMA SHEATH; POISSON EQUATION; RELATIVISTIC RANGE

### Citation Formats

```
Sanchez-Arriaga, G., and Sanmartin, J. R.
```*Relativistic current collection by a cylindrical Langmuir probe*. United States: N. p., 2012.
Web. doi:10.1063/1.4729662.

```
Sanchez-Arriaga, G., & Sanmartin, J. R.
```*Relativistic current collection by a cylindrical Langmuir probe*. United States. doi:10.1063/1.4729662.

```
Sanchez-Arriaga, G., and Sanmartin, J. R. Fri .
"Relativistic current collection by a cylindrical Langmuir probe". United States. doi:10.1063/1.4729662.
```

```
@article{osti_22072504,
```

title = {Relativistic current collection by a cylindrical Langmuir probe},

author = {Sanchez-Arriaga, G. and Sanmartin, J. R.},

abstractNote = {The current I to a cylindrical Langmuir probe with a bias {Phi}{sub p} satisfying {beta}{identical_to}e{Phi}{sub p}/m{sub e}c{sup 2}{approx}O(1) is discussed. The probe is considered at rest in an unmagnetized plasma composed of electrons and ions with temperatures kT{sub e}{approx}kT{sub i} Much-Less-Than m{sub e}c{sup 2}. For small enough radius, the probe collects the relativistic orbital-motion-limited (OML) current I{sub OML}, which is shown to be larger than the non-relativistic result; the OML current is proportional to {beta}{sup 1/2} and {beta}{sup 3/2} in the limits {beta} Much-Less-Than 1 and {beta} Much-Greater-Than 1, respectively. Unlike the non-relativistic case, the electron density can exceed the unperturbed density value. An asymptotic theory allowed to compute the maximum radius of the probe to collect OML current, the sheath radius for probe radius well below maximum and how the ratio I/I{sub OML} drops below unity when the maximum radius is exceeded. A numerical algorithm that solves the Vlasov-Poisson system was implemented and density and potential profiles presented. The results and their implications in a possible mission to Jupiter with electrodynamic bare tethers are discussed.},

doi = {10.1063/1.4729662},

journal = {Physics of Plasmas},

issn = {1070-664X},

number = 6,

volume = 19,

place = {United States},

year = {2012},

month = {6}

}