what causes acceleration of particles when gravity wave frequency is double of larmor frequency acting on it?

I have been through following papers for research:

1)http://cdsads.u-strasbg.fr/cgi-bin/nph-iarticle_query?1990ApJ...362..584M&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf

2)https://arxiv.org/pdf/gr-qc/9905054.pdf

Conclusion of the second paper given above states the following:

"

In this case the

external action (the gravitational wave) amounts to a time variation of the frequency

parameter of the initial system (charged particles in a magnetic field), so that in the

overall system the equilibrium at rest (x

1 = 0) is unstable. Any deviation from this

state, however small, is sufficient to lead to a rapidly increasing displacement along

the peprendicular direction (Landau and Lifshitz 1976). Further analysis shows that,

in any of the above propagation cases, the overall result would be an exponential

increase of the perpendicular energy of the particles involved in this interaction, as a

function of the affine parameter and, hence, of their proper-time as well.

"

From the conclusion I can understand that gravitational blueshift may be the reason for increasing frequency but what could be the reason for perpendicular displacement of particles and exponential increase in perpendicular energy?