I tried contacting the authors but didn’t manage to reach them.

Pfeiffer et al describes transfer of a constant velocity:

…the block accelerates away from the beam source while it is traversed by the leading edge of the beam, then continues to travel away from the source at constant velocity while the beam is turned on. When the beam is turned off, traversal of the trailing edge restores the block to rest

Masud Mansuripur describes a similar transfer of a constant momentum, and derives the equation:

MV = ¼εo(ε – 1)Eo2 A∆T.

Both agree that acceleration is not indefinite, but that a certain velocity (or momentum) will be imposed. In essence my question is then: What is ∆T?

To clarify the question with another question;

Does the block stop accelerating when the beam reaches the other side of the block, or does it continue to accelerate (due to inertia) until the imposed velocity/momentum is reached?

My first take is that acceleration will be very short as the beam traverses the block, because it must also stop the block when it completely exits.

(If it doesn't stop the block, then momentum is transfered, and the beam must lose energy.)

I have some problems with my take on it though and I would like to hear other opinions.

Thank you kindly if you have a response to offer.

REF:

1. Masud Mansuripur, (2004), Radiation pressure and the linear momentum

of the electromagnetic field, Article Radiation pressure and the linear momentum of the electromag...

2. Robert N. C. Pfeifer, Timo A. Nieminen, Norman R. Heckenberg, Halina Rubinsztein-Dunlop, (Oct 2007), Momentum of an electromagnetic wave in dielectric media, Article Colloquium: Momentum of an electromagnetic wave in dielectric media