Shock Wave and Solitary Wave Structure in a Plasma

Journal Article · Fri Jan 01 04:00:00 EST 1960 · Physics of Fluids (New York)

DOI:https://doi.org/10.1063/1.1706124· OSTI ID:4130045

Greenberg, O. W.; Trève, Y. M.

Plane steady shock waves and solitary waves in a hydrogen plasma without external magnetic fields were studied using a simple kinetic-theory model to describe the plasma. This model uses a Mott-Smith distribution for the protons and a local Maxwellian distribution for the electrons. Charge separations occurred inside the shock front because of the proton-electron mass difference. The proton and electron densities and the electric field had an oscillatory fine structure with characteristic length approximately 10 M lambda /sub D/, where M is the Mach number and lambda /sub D/ the Debye length, going through the shock. In these oscillations, the densities overshot their final Rankine-Hugoniot condition values. The distance in which the oscillations decayed to 1/e, which can be taken as the shock width, was approximately 4 lambda , where lambda is the mean free path in the unshocked gas, in the range of Mach numbers considered. There were no continuous solutions for this model above Mach 2.19. The peak electric fields inside the shock were large. In a plasma of lambda / lambda /sub D/ = 2 x 10/sup 4/, the electric field reached 2.2 x 10/sup 6/ v/cm in a Mach 2.1 shock. The large-amplitude solitary waves, which were the basic ingredient of the fine structure of the shock, were studied separately, and a heuristic picture is presented of the growth of these solitary waves, which was due to the coupling between the bulk flow of the plasma and the internal electric fields generated by charge separation. The rate of decay of these solitary waves was estimated.

• Research Organization: Air Force Cambridge Research Center, Bedford, Mass.
• Sponsoring Organization: USDOE
• NSA Number: NSA-14-026362
• OSTI ID: 4130045
• Journal Information: Physics of Fluids (New York), Journal Name: Physics of Fluids (New York) Journal Issue: 5 Vol. 3; ISSN 0031-9171; ISSN PFLDAS
• Publisher: American Institute of Physics
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

CHARGED PARTICLES
DEBYE LENGTH
DENSITY
DISTRIBUTION
ELECTRIC CHARGES
ELECTRIC FIELDS
ELECTRONS
HUGONIOT CURVE
HYDROGEN
MACH NUMBER
MASS
MEAN FREE PATH
OSCILLATIONS
PHYSICS
PLASMA
PLASMA WAVES
PROTONS
SHIELDING
SHOCK WAVES
THICKNESS
VELOCITY