E{lost}= (4π(d + l2 ) / cω) n
E{los}t= (4π(d + l2 ) / cω) ((A((mv) / (2tAρ1)[1/4] / (256m{e}[1/4]))) e[2] / 6πε{0}m{e}c[3] )

Where n denotes the number of complete oscillations the electron plasma will have gone through since the initial impact. The energy Eincident results in a massive radiative force on the plasma and contained projectile. The total energy of the plasma contained within the parallel bounds of emission region a now becomes:

E{final} = E{app} - E{lost} + E{incident}
E{final} = ((½ mv[2] ) + (npaTS ) s(x)l ((A((mv) / (2tAρ1)[1/4] )/ (256m{e}[1/4]))) e[2] - (4π(d + l2 ) / cω) ((A((mv) / (2tAρ1)[1/4] / (256m{e}[1/4]))) e[2] / 6πε{0}m{e}c[3] )

However, because the base energy of the plasma was defined as E = 0, the plasma must somehow loose this energy to return to its base energy state. This will be in the form of electromagnetic radiation emitted from the plasma. The great majority of this radiation will me emitted along the vector –v'', parallel to the initial projectile's path but opposite in direction. The radiation pressure on the projectile can be determined using a pointing vector relation, for cross-sectional area of the projectile a,

S = (1/a)(dU/dt) = ε{0} cE[2]
P= ((R + 1) ε{0} cE[2] ) / c

Where R is the reflectivity of the projectile. Here E will be the energy delivered to the projectile, equal to the portion of the radiative discharge that is directed in the –v'' direction. This is, incidentally, simply the value Eincident, as this radiation is already coherent and directed in the correct direction. Elost will contribute a small amount to the final energy, but this will be ignored due to its infinitesimal magnitude for simplicity. The energy Ereturn, the energy imparted on the projectile opposite to its kinetic energy vector, is therefore Eincident. Hence the radiation pressure has magnitude-

P= ((R + 1) ε{0} c E{incident} [2] ) / c
P= ((R + 1) ε{0} c ((npaTS ) s(x)l ((A((mv) / (2tAρ1)[1/4] / (256m{e}[1/4]))) e[2] / 6πε{0}m{e}c[3] ))[2] ) / c

Because P= F/a, the force on the projectile is:

F{return} = ((R + 1) ε{0} c E{incident}[2] )a / c

A quick check on the ratio of F{return} and F{app} shows that F{return} > F{app}. Quite simply, this will impart an acceleration on the projectile,

Acceleration = ((R + 1) ε{0} c E{incident}[2] )a / m{p}c

With m{p} being the mass of the projectile. The direction of acceleration will again be opposite to the projectile's initial kinetic vector. Because F{return} > F{app} , the projectile will be either stopped or reflected.
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Damn that hurt.

To those of you that are diehard that shields are "Modulated Electromagnetic Fields", I've produced this: A model of that described above, using only EM fields. Hooray.

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