Collisionless shock waves in a plasma in a weak magnetic field

The relationship is investigated between laminar and turbulent theories of the structure of a collisionless shock wave. For p e ≫ p i , where p i , p e are the ion and electron pressures, a laminar structure of the shock wave may be constructed in terms of the `solitary' wave with thickness of the order of the Debye length. When p i ≳ p e the principal part within the shock front is played by scattering of ions by small-scale field fluctuations which result from anisotropic instability. The thickness of the front is in order of magnitude Δ ∼ ( c /Ω 0 )( m i / m e )(1/( M -1) 2 ) ( M - 1 < 1), where c is the velocity of light, Ω 0 = 4π ne 2 / m i , m i , m e are the ion and electron masses, and M is the Mach number.