Weak waves in a magnetized Synge gas mixture

In the present paper the development of weak discontinuities of a magnetized neutral Synge gas composed of protons, electrons and photons is examined within the framework of special relativity supposing that the pair production may be neglected. The main system of the problem contains the equations of continuity, the equation of motion, the Maxwell equation of an ideal plasma and the equations of state of the mixture. The authors first task is to compute the propagation velocities of the wave front Φ (across which the quantities are continuous, but their derivatives undergo finite jumps) making use of the compatibility conditions found by Maugin. After this the authors differentiate the main system and take jumps across Φ stipulating that the medium is perturbed in front of the discontinuity. Two special modes are discussed. At first they consider an Alfven discontinuity in which the magnetic field is normal to the wave front. It is shown that the amplitude of weak discontinuity remains unchanged in this case. Their main purpose is to examine the growth of compressive magnetoacoustic weak waves in which the magnetic field is tangential to the hypersurface Φ. The growth equation of discontinuities if of Bernoulli type, it contains three parameters (besides the principal curvatures of Φ): the electron temperature (1/x1), the relative number density of photons (ρ) and the pressure number (ratio of magnetic and hydrodynamic pressure, h)