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33.8 tons payload size with the single 1000 ton Mars engine is more practical and fitting your specifications and converting 1 ton of propellant fuel to the required energy.
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Since the total mass of the ship including propellant mass is constantly decreasing, are you varying Ve or q or both to maintain acceleration at one g? How many kg/sec of propellant is actually being discharged (if variable, on average)? What material is actually being discharged? What is the ratio of mass loss to energy conversion to that of the actually expelled propellant?
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Interstellar space is mostly empty as particle mass collects in stars gravity wells and I am traveling at a very small fraction of light speed in those wells so steer away from the asteroids and ort cloud of comets. Well outside those wells I am traveling at light speed and beyond and the probability of collision decreases when velocity increases so the probability of me colliding with any mass at light speed and beyond is insignificant if not zero.
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Indeed it is mostly empty, but only mostly. The center of the Oort cloud, radially speaking, is about one light year away; how fast do you plan to go through it. We can not be sure that the intragalactic density of Oort-cloud-like-stuff is insignificant. Caution is advised. It is not unreasonable to expect a cloud similar to the Oort around most stellar systems.
Why do you think going fast reduces the chances of collision? My guess is that stellar systems are slingshotting projectiles into individual galactic orbits from time to time thereby keeping intragalactic space well stocked with things to run into. Have you considered what limits to put on the radius of curvature of course changes required to avoid obstacles as a function of ship velocity? Even relatively small changes in direction at velocities near light speed can generate very strong g-forces perhaps sending you and other loosely anchored objects through the side of the ship if not ripping off the engines. Also, as you approach 0.5c radar-type detection of objects won't return data in time to initiate a successful maneuver.