The solitary hydromagnetic wave revisited: A demonstration of the force in a collisionless plasma

An early paper on a solitary wave in a collision-free plasma, namely, a hydromagnetic wave propagating at right angles to a magnetic field, is further examined. The trajectories of both ions and electrons have been calculated for different wave velocities, up to the limiting value of twice the Alfvén velocity. The study clearly illustrates the fact that the positive ions move under the action of an electrostatic field, and the magnetic force has a negligible effect on their trajectories. The investigation shows that the macroscopic j x B force, i.e., that acting on the whole plasma, is transmitted to the ions via an electrostatic field.