Bernstein-Greene-Kruskal solitary waves in three-dimensional magnetized plasma

We study the width-amplitude relation for three-dimensional Bernstein-Greene-Kruskal (BGK) electrostatic solitary waves in magnetized plasmas, taking into account the dynamics of both electrons and ions. We obtain two coupled inequalities that constrain the amplitude and the widths parallel and perpendicular to the magnetic field for a Gaussian potential, and demonstrate how the solution space is further constrained by the finite temperature ratio between electrons and ions. The description is valid for both the electron and ion mode solitary waves. Our results provide a quantitative basis for understanding the ubiquity of BGK waves in widely different classes of collisionless plasmas.