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Title: 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:
;  [1]
  1. 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}
}
  • Ion acceleration is studied both analytically and numerically. In the analytical model, a new self-similar solution, which can be applied to any geometry (planar, cylindrical, and spherical), is employed to describe non-relativistic expansion of a finite plasma mass into vacuum with a full account of charge separation effects. It turns out that the normalized plasma size {lambda} = R/{lambda}D plays the dominant role in determining the whole ion energy spectrum and thus the maximum ion kinetic energy, where R and {lambda}D are the plasma scale length and the Debye length, respectively. The analytical model is compared with particle simulations andmore » experiments to show excellent agreement. It is argued that, when properly formulated, the analytical results obtained from the present model can be applied more generally than the self-similar solution itself.« less
  • The self-similar solutions are obtained for isothermal expansions of neutral plasmas into a vacuum. The classic solution given by Mora [Phys. Fluids 22, 12 (1979)] corresponds to a special case of our solution. Some special solutions have been pointed out by Gurevich et al. [Phys. Rev. Lett. 42, 769 (1979)] and observed by a lot of experiments. The formulation of ion velocity with respect to the acceleration time is proposed for the general solution, and the numerical result can be obtained easily. The electric field and ion velocity at the ion front have been achieved.
  • A two dimensional planar model is developed for self-similar isothermal expansions of non-quasi-neutral plasmas into a vacuum of solid targets heated by ultraintense laser pulses. The angular ion distribution and the dependence of the maximum ion velocity on laser parameters and target thicknesses are predicted. Considering the self-generated magnetic field of plasma beams as a perturbation, the ion energy on edge at the ion opening angle has an increase of 2% relative to that on the front center. Therefore, the self-generated magnetic field of plasma beams is not large enough to interpret for the ring structures.
  • Shock waves driven by the release of energy at the center of a cold ideal gas sphere of initial density {rho} {proportional_to} r {sup -}{omega} approach a self-similar behavior, with velocity R-dot {proportional_to}R{sup {delta}}, as R {yields} {infinity}. For {omega}>3 the solutions are second-type solutions, i.e., {delta} is determined by the requirement that the flow should include a sonic point. No solution satisfying this requirement exists, however, in the 3 {<=} {omega} {<=} {omega}{sub g}({gamma}) 'gap' ({omega}{sub g} = 3.26 for adiabatic index {gamma} = 5/3). We argue that in general second-type solutions should not be required to include amore » sonic point. Rather, it is sufficient to require the existence of a characteristic line r{sub c} (t), such that the energy in the region r{sub c} (t) < r < R approaches a constant as R {yields} {infinity}, and an asymptotic solution given by the self-similar solution at r{sub c} (t) < r < R and deviating from it at r < r{sub c} may be constructed. The two requirements coincide for {omega}>{omega}{sub g} and the latter identifies {delta} = 0 solutions as the asymptotic solutions for 3 {<=} {omega} {<=} {omega}{sub g} (as suggested by Gruzinov). In these solutions, r{sub c} is a C{sub 0} characteristic. Using numerical solutions of the hydrodynamic equations, it is difficult to check whether the flow indeed approaches a {delta} = 0 self-similar behavior as R {yields} {infinity}, due to the slow convergence to self-similarity for {omega} {approx} 3. We show that in this case the flow may be described by a modified self-similar solution, d ln R-dot/d ln R = {delta} with slowly varying {delta}(R), {eta} {identical_to} d{delta}/dln R << 1, and spatial profiles given by a sum of the self-similar solution corresponding to the instantaneous value of {delta} and a self-similar correction linear in {eta}. The modified self-similar solutions provide an excellent approximation to numerical solutions obtained for {omega} {approx} 3 at large R, with {delta} {yields} 0 (and {eta} {ne} 0) for 3 {<=} {omega} {<=} {omega}{sub g}.« less