Collisionless motion of neutral particles in magnetostatic traps

We present an analytical and numerical analysis of collisionless motion of neutral particles in magnetostatic traps. We treat the example of an idealized Ioffe quadrupole trap, emphasizing that the essential features of coupling between the degrees of freedom are of general relevance for static traps. In common situations the coupling between axial and radial motion predominantly occurs in a regular way. The coupling is weak, in particular, when the frequency of axial oscillations ${\mathrm{\Omega }}_{\mathit{z}}$ is much smaller than the radial frequency ${\mathrm{\Omega }}_{\mathrm{\rho }}$ and the particle energy is much lower than the Zeeman energy in the center of the trap. Then, under an adiabatic change of the potential parameters, the quantity ${\mathit{scrE}}_{\mathit{z}}$/${\mathrm{\Omega }}_{\mathit{z}}$, where ${\mathit{scrE}}_{\mathit{z}}$ is a characteristic axial energy, is an approximate adiabatic invariant. If ${\mathrm{\Omega }}_{\mathit{z}}$ is decreasing and ${\mathrm{\Omega }}_{\mathit{p}}$ is constant, then the characteristic radial energy ${\mathit{scrE}}_{\mathrm{\rho }}$ will remain constant while ${\mathit{scrE}}_{\mathit{z}}$ decreases proportionally to ${\mathrm{\Omega }}_{\mathit{z}}$. This implies one-dimensional adiabatic cooling, which is an interesting option for gravitational studies of light atoms such as hydrogen and antihydrogen.