Can a charged particle be trapped by a standing EM wave? Can a charged partìcle be trapped between two extreme points (peaks) of a standing wave so because of ite inertia it goes like alternate current stright up and down and so possibly generates its own field?
 A: Though not exactly what you asked, I hope that the case of static electric and magnetic fields mutually perpendicular to each other (the easiest case) provides some useful insight for you.
This case has been discussed in detail by (for example) Griffiths Introduction to Electrodynamics (4th Edition): If you consider placing a charge at rest in an static electric and magnetic fields that are mutually perpendicular to each other what happens? The charge is at rest so there is no magnetic force ($q \bf{v} \times {\bf B}$ with the speed initially zero) and the electric force ($q \bf{E}$) causes the charge to move in the direction of the field. In the attached figure (taken from here) the electric field is in the y direction and the magnetic field is in the z direction.

Note that the charge is pushed along the direction that is perperdicular to the electric force. In fact the motion of the particle is in a direction perpendicular to both the electric and magnetic fields.
As the charge begins to move in the y direction the magnetic force causes it move in a direction perpendicular to its motion, a bit in the x direction and a bit in the negative y direction. Eventually the charge is moving in the opposite direction to the electric field and the electric field acts in a direction to cause the charge to slow down to zero. Then you're back at the beginning: charge in the presence of the electric and magnetic field, though now moving in the x direction. This repeats itself and the resulting motion is called cycloidal motion.
If you know some electromagnetism this won't be too much of a surprise since the Poynting vector, ${\bf S}$, is proportional to ${\bf E} \times {\bf B}$ which is in the x direction.
According to here, the Poynting vector "represents the directional energy flux (the energy transfer per unit area per unit time) of an electromagnetic field".
Your case of interest is a bit more complicated since the electric and magnetic fields, though still mutually perpendicular, now both depend upon both time and space but the general principle holds: the energy flux of the electromagnetic field acts in the direction ${\bf E} \times {\bf B}$.
For the case of a standing wave the motion of the charge will be up and down the resonantor that supports the wave: at times ${\bf E} \times {\bf B}$ will be along the (say) x axis and at other times along the negative x direction.
