  The Alcubierre warp drive allows a spaceship to travel at an arbitrarily
large global velocity by deforming the spacetime in a bubble around the
spaceship. Little is known about the interactions between massive particles and
the Alcubierre warp drive, or the effects of an accelerating or decelerating
warp bubble. We examine geodesics representative of the paths of null and
massive particles with a range of initial velocities from -c to c interacting
with an Alcubierre warp bubble travelling at a range of globally subluminal and
superluminal velocities on both constant and variable velocity paths. The key
results for null particles match what would be expected of massive test
particles as they approach +/- c. The increase in energy for massive and null
particles is calculated in terms of v_s, the global ship velocity, and v_p, the
initial velocity of the particle with respect to the rest frame of the
origin/destination of the ship. Particles with positive v_p obtain extremely
high energy and velocity and become "time locked" for the duration of their
time in the bubble, experiencing very little proper time between entering and
eventually leaving the bubble. When interacting with an accelerating bubble,
any particles within the bubble at the time receive a velocity boost that
increases or decreases the magnitude of their velocity if the particle is
moving towards the front or rear of the bubble respectively. If the bubble is
decelerating, the opposite effect is observed. Thus Eulerian matter is
unaffected by bubble accelerations/decelerations. The magnitude of the velocity
boosts scales with the magnitude of the bubble acceleration/deceleration.
