Nonlinear interaction of a monochromatic wave with particles in a gravitating system
Abstract
Particle motion in a gravitational field corresponding to a monochromatic vibrational eigenmode of a gravitating collisionless cylinder is studied. It is shown that in the reference frame of a rotating cylinder, the effect of inertial forces on a gravitating particle is analogous to that of a longitudinal magnetic field on a test electric charge. The cylinder particles become magnetized, and their distance from the cylinder's axis is (approximately) conserved as a result. Because of this, the equation of longitudinal particle motion reduces to a mathematicalpendulumtype equation, which is solved in elliptic functions. The nonlinear stage of the gravitational beam instability is examined, the nonlinear evolution of the particle distribution function is investigated, and the particle kineticenergy density averaged over the cylinder's volume is obtained along with the monochromatic wave energy. The time dependence of the nonlinear increment is determined by the energybalance method, and the steadystate oscillation amplitudes are estimated. It is concluded that a nonlinear mechanism for stabilizing a monochromatic density wave may play an important role in gravitating systems.
 Publication:

Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki
 Pub Date:
 July 1977
 Bibcode:
 1977ZhETF..73...20M
 Keywords:

 Gravitational Fields;
 Monochromatic Radiation;
 Nonlinear Equations;
 Particle Interactions;
 Wave Interaction;
 Eigenvalues;
 Elliptic Functions;
 Rotating Cylinders;
 Astrophysics