Self-similar evolution of the nonlinear magnetic buoyancy instability

Journal Article · Sat Sep 01 04:00:00 EDT 1990 · Physics of Fluids B; (USA)

DOI:https://doi.org/10.1063/1.859420· OSTI ID:6506356

Shibata, K; Tajima, T ^[1]; Matsumoto, R ^[2]

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1. Institute for Fusion Studies, University of Texas at Austin, Austin, TX (USA)
2. Department of Information Science, College of Arts and Sciences, Chiba University, Chiba (Japan)

A new type of self-similar solution of ideal magnetohydrodynamics (MHD) in the nonlinear stage of the undular model ({bold k}{parallel}{bold B}) of the magnetic buoyancy instability (the ballooning instability in fusion plasma physics or the Parker instability in astrophysics) is found through MHD simulation and theory. The linear theory developed agrees well with our simulation in the early (linear) stage. The nonlinear stages of the instability in the simulation show the self-similar evolution. One of the solutions obtained from the nonlinear analysis has the characteristics of nonlinear instability in Lagrangian coordinates; the fluid velocity and the Alfven speed on each magnetic loop increase exponentially with time, because the loop is evacuated by the field-aligned motion of matter resulting from gravitational acceleration. In the later stage of the nonlinear evolution, the solution property changes from exponential to power-law time dependence. The latter corresponds to a force-free expansion solution. The later saturation of the velocity increment is also discussed.

• OSTI ID: 6506356
• Journal Information: Physics of Fluids B; (USA), Journal Name: Physics of Fluids B; (USA) Vol. 2:9; ISSN 0899-8221; ISSN PFBPE
• Country of Publication: United States
• Language: English

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71 CLASSICAL AND QUANTUM MECHANICS
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75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ANALYTICAL SOLUTION
ASTROPHYSICS
ATMOSPHERES
BALLOONING INSTABILITY
CARTESIAN COORDINATES
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NONLINEAR PROBLEMS
ONE-DIMENSIONAL CALCULATIONS
PLASMA
PLASMA INSTABILITY
PLASMA MACROINSTABILITIES
PLASMA SIMULATION
SIMULATION
SOLAR ATMOSPHERE
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TWO-DIMENSIONAL CALCULATIONS