The Heavy-Ion Approximation for Ambipolar Diffusion Calcuations for Weakly Ionized Plasmas

Journal Article · Thu Jul 27 04:00:00 EDT 2006 · Astrophysical Journal

OSTI ID:943821

Li, P; McKee, C; Klein, R

Ambipolar diffusion redistributes magnetic flux in weakly ionized plasmas and plays a critical role in star formation. Simulations of ambipolar diffusion using explicit MHD codes are prohibitively expensive for the level of ionization observed in molecular clouds ({approx}< 10{sup -6}) since an enormous number of time steps is required to represent the dynamics of the dominant neutral component with a time step determined by the trace ion component. Here we show that ambipolar diffusion calculations can be significantly accelerated by the 'heavy-ion approximation', in which the mass density of the ions is increased and the collisional coupling constant with the neutrals decreased such that the product remains constant. In this approximation, the ambipolar diffusion time and the ambipolar magnetic Reynolds number remain unchanged. We present three tests of the heavy-ion approximation: C-type shocks, the Wardle instability, and the 1D collapse of a magnetized slab. We show that this approximation is quite accurate provided that (1) the square of the Alfven Mach number is small compared to the ambipolar diffusion Reynolds number for dynamical problems, and that (2) the ion mass density is negligible for quasi-static problems; a specific criterion is given for the magnetized slab problem. The first condition can be very stringent for turbulent flows with large density fluctuations.

• Research Organization: Lawrence Livermore National Laboratory (LLNL), Livermore, CA
• Sponsoring Organization: USDOE
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 943821
• Report Number(s): UCRL-JRNL-223245
• Journal Information: Astrophysical Journal, Journal Name: Astrophysical Journal Journal Issue: 2 Vol. 653; ISSN ASJOAB; ISSN 0004-637X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
AMBIPOLAR DIFFUSION
APPROXIMATIONS
CLOUDS
COUPLING CONSTANTS
FLUCTUATIONS
INSTABILITY
IONIZATION
MACH NUMBER
MAGNETIC FLUX
MAGNETIC REYNOLDS NUMBER
REYNOLDS NUMBER
STARS
TURBULENT FLOW