This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: 17. Hydromagnetic shock waves Reading: Shu, Vol.II, Ch. 25 17.1 The jump conditions A magnetized and electrically conducting plasma can carry different types of small-amplitude waves, depending on the angle between the large-scale magnetic field and their direction of propagation or on the values of the Alfv´ en velocity and the sound speed. We can therefore expect to also find different classes of hydromagnetic shocks. Let us again consider a steady-state plane-parallel shock in its rest frame in the absence of an external force. Let us further assume ideal MHD, i.e. the conductivity in infinitely large. Then the MHD equations read in Einstein convention ∂ ∂x k ( ρ V k ) = 0 (17 . 1) ∂ ∂x k ρ V i V k + P δ ik- 1 4 π B i B k- 1 2 | ~ B 2 | δ ik = 0 (17 . 2) ∂ ∂x k " V k ρ 2 V 2 + γ γ- 1 P ! + 1 4 π ( ~ B × ~ V ) × ~ B # = 0 (17 . 3) ∂ ∂x k B k = 0 (17 . 4) ~ ∇ × ( ~ B × ~ V ) = 0 (17 . 5) Calculations show that it is possible to choose a coordinate system, the de Hoffmann-Teller frame, in which the velocity vector...
View Full Document
This note was uploaded on 02/29/2012 for the course PHYS 227 taught by Professor Rabe during the Fall '08 term at Rutgers.
- Fall '08