# Self-similar expansion of finite-size non-quasi-neutral plasmas into vacuum: Relation to the problem of ion acceleration

## Abstract

A new self-similar solution is presented which describes nonrelativistic expansion of a finite plasma mass into vacuum with a full account of charge separation effects. The solution exists only when the ratio {lambda}=R/{lambda}{sub D} of the plasma scale length R to the Debye length {lambda}{sub D} is invariant, i.e., under the condition T{sub e}(t){proportional_to}[n{sub e}(t)]{sup 1-2{nu}}, where {nu}=1, 2, and 3 corresponds, respectively, to the planar, cylindrical, and spherical geometries. For {lambda}>>1 the position of the ion front and the maximum energy E{sub i,max} of accelerated ions are calculated analytically: in particular, for {nu}=3 one finds E{sub i,max}=2ZT{sub e0}W({lambda}{sup 2}/2), where T{sub e0} is the initial electron temperature, Z is the ion charge, and W is the Lambert W function. It is argued that, when properly formulated, the results for E{sub i,max} can be applied more generally than the self-similar solution itself. Generalization to a two-temperature electron system reveals the conditions under which the high-energy tail of accelerated ions is determined solely by the hot-electron population.

- Authors:

- Institute of Laser Engineering, Osaka University, Yamada-oka 2-6, Suita, Osaka 565-0871 (Japan)

- Publication Date:

- OSTI Identifier:
- 20782425

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 13; Journal Issue: 1; Other Information: DOI: 10.1063/1.2162527; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ACCELERATION; CYLINDRICAL CONFIGURATION; DEBYE LENGTH; ELECTRON TEMPERATURE; ELECTRONS; FRACTALS; GEOMETRY; ION TEMPERATURE; IONS; MATHEMATICAL SOLUTIONS; PLASMA; PLASMA EXPANSION; PLASMA GUNS

### Citation Formats

```
Murakami, M., and Basko, M.M.
```*Self-similar expansion of finite-size non-quasi-neutral plasmas into vacuum: Relation to the problem of ion acceleration*. United States: N. p., 2006.
Web. doi:10.1063/1.2162527.

```
Murakami, M., & Basko, M.M.
```*Self-similar expansion of finite-size non-quasi-neutral plasmas into vacuum: Relation to the problem of ion acceleration*. United States. doi:10.1063/1.2162527.

```
Murakami, M., and Basko, M.M. Sun .
"Self-similar expansion of finite-size non-quasi-neutral plasmas into vacuum: Relation to the problem of ion acceleration". United States.
doi:10.1063/1.2162527.
```

```
@article{osti_20782425,
```

title = {Self-similar expansion of finite-size non-quasi-neutral plasmas into vacuum: Relation to the problem of ion acceleration},

author = {Murakami, M. and Basko, M.M.},

abstractNote = {A new self-similar solution is presented which describes nonrelativistic expansion of a finite plasma mass into vacuum with a full account of charge separation effects. The solution exists only when the ratio {lambda}=R/{lambda}{sub D} of the plasma scale length R to the Debye length {lambda}{sub D} is invariant, i.e., under the condition T{sub e}(t){proportional_to}[n{sub e}(t)]{sup 1-2{nu}}, where {nu}=1, 2, and 3 corresponds, respectively, to the planar, cylindrical, and spherical geometries. For {lambda}>>1 the position of the ion front and the maximum energy E{sub i,max} of accelerated ions are calculated analytically: in particular, for {nu}=3 one finds E{sub i,max}=2ZT{sub e0}W({lambda}{sup 2}/2), where T{sub e0} is the initial electron temperature, Z is the ion charge, and W is the Lambert W function. It is argued that, when properly formulated, the results for E{sub i,max} can be applied more generally than the self-similar solution itself. Generalization to a two-temperature electron system reveals the conditions under which the high-energy tail of accelerated ions is determined solely by the hot-electron population.},

doi = {10.1063/1.2162527},

journal = {Physics of Plasmas},

number = 1,

volume = 13,

place = {United States},

year = {Sun Jan 15 00:00:00 EST 2006},

month = {Sun Jan 15 00:00:00 EST 2006}

}