Ideal MHD equations in terms of compressive Elsässer variables

By the help of the so‐called Elsässer variables, if adopted to the situation of a compressible plasma, the equations of ideal magnetohydrodynamics can be rewritten in a new form. This appears to be particularly suitable to describe the situation of compressive MHD turbulence. After having derived the basic equations of motion, the conservation equations for energy and cross‐helicity are rephrased in terms of Elsässer variables. The sinks and sources of cross‐helicity associated with the compressibility of the plasma are elucidated. A standard normal mode analysis, performed in terms of Elsässer variables, emphasizes their usefulness in treating hydrodynamic waves. In the conclusions some possible future, more sophisticated applications are outlined.