Particle simulation of Lyapunov exponents in one-component strongly coupled plasmas

Journal Article · Sat Mar 01 04:00:00 EST 1997 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.55.3439· OSTI ID:505236

Ueshima, Y; Nishihara, K ^[1]; Barnett, D M; Tajima, T ^[2]; Furukawa, H ^[3]

---

1. Institute of Laser Engineering, Osaka University, Suita, Osaka 565 (Japan)
2. Fusion Studies, University of Texas at Austin, Austin, Texas 78712 (United States)
3. Institute for Laser Technology, Suita, Osaka 565 (Japan)

The Lyapunov exponents and instantaneous expansion rates in a phase space of Coulomb many-body systems are measured with the use of a three-dimensional particle code SCOPE [K. Nishihara, Kakuyugo Kenkyu {bold 66}, 253 (1991)]. The code calculates particle dynamics determined by Coulomb forces among individual particles. The Lyapunov exponents normalized by plasma frequency are found to be proportional to {Gamma}{sup {minus}2/5} in the range of 1{le}{Gamma}{le}160, where {Gamma} is the Coulomb coupling constant of the ion one-component plasma. There is a large jump of the Lyapunov exponent near {Gamma}{approximately}170, which corresponds to the phase transition from the liquid to the solid state in the one-component plasma. In the solid state, the normalized Lyapunov exponents are proportional to {Gamma}{sup {minus}6/5} for 170{lt}{Gamma}{lt}300. The observed dependence is discussed in analogy to a rigid-body particle system and a weakly nonlinear lattice system for liquid and solid states, respectively. Diffusion coefficients are found to be proportional to the third power of the Lyapunov exponent in the liquid state, that is, for 1{le}{Gamma}{le}160. These results imply that the Lyapunov exponent is in close relation to the transport processes. The instantaneous expansion rate starts from a small value and increases rapidly to a large peak value before declining slowly towards an asymptotic value. This stage is called the Lyapunov transient stage. Products of the transient time and the Lyapunov exponent are found to be 1.5{endash}2. Information of the initial state is lost after the transient time. The chaotic behavior of the instantaneous expansion rate is also shown. {copyright} {ital 1997} {ital The American Physical Society}

• OSTI ID: 505236
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 3 Vol. 55; ISSN PLEEE8; ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
DIFFUSION
LYAPUNOV METHOD
MANY-BODY PROBLEM
PHASE STUDIES
PHASE TRANSFORMATIONS
PLASMA SIMULATION
S CODES
chaos