The winner will get half a million dollars for the idea."*
-Use a fuel cycle in which the use of a fuel turns the fuel into another fuel. Do this with nuclear reactions (fusion and fission, electron capture and b- decay).
-Use materials that generate electricity when photons interact with them. Solar panels generate electricity when photons of a particular range of frequencies interact with them. Developing materials that generate electricity from other frequencies of photons (including those that permeate space) is only a matter of time.
-Use materials that generate electricity when the fields that permeate the vacuum (such as those responsible for the Casimir effect) interact with them.
-Use an internal solar sail. Solar sails are used to propel some spacecraft. They are a material that photons push forward when they reflect from it; the material is fixed to a craft which it causes to accelerate. Between stars there are much less photons; put the solar sail in a chamber inside the craft with a source of photons (light) the craft generates. Or develop a material that can be switched back and forth from a state in which it is pushed by photons of the frequencies which permeate space and a state in which it is not - of course it would also need to have this force-generating interaction with such photons striking it from only a certain direction so that it is not pushed in all directions simultaneously.
-Use diffraction to move a ball that pulls heatsinks.
-Fleming's left-hand rule says that the intersection of a magnetic field and an electric current generates in the material conducting the current a kinetic force in a direction perpendicular to the current and the field. This works best with superconductors and electromagnets and can be used to build a magnetohydrodynamic propulsion system as Mitsubishi Heavy Industries did in the Yamato 1.
-Tokamaks generate extremely strong mangetic fields to contain and manipulate plasma, often in hot fusion experiments. If we use tokamaks to contain the plasma the explosions thrusters push their craft with are made of and to push the fuel spent in generating the explosions toward vents on the thrusters that suck all the spent fuel out of the plasma we could re-assemble into fuel that can be used by the thrusters all fuel spent by the thrusters.
-Shear compression among Hooked atoms
3. Life support
-Artificial gravity is a must to prevent muscle degeneration during long-term space habitation. This can be done using acceleration, centrifugal force or some as-yet-undiscovered material that is super-dense or will generate a gravitational field when exposed to an electric current, a magnetic field, a kinetic force or some combination of them. Incorporating a super-dense material would make propulsion harder, and the European Space Agency reports that the gravitational field generated by a spinning superconductor is miniscule.
-Individual nutrients can be harvested from bacteria or chemically synthesized. Waste could be broken down and turned back into the food by similar means.
-Hydroponics, test-tube meat and mycofarming could be used to provide nutrients which cannot be harvested from bacteria or chemically synthesized with the current knowledge of biotechnology and chemistry.
-Photosynthetic organisms or chemical means could be used to convert CO2 to O2.
-There will have to be enough water in the craft to provide for the food cycle, the crew and (considering how long it takes to get to another star) the next generation of crew.
-The craft will use an array of biometric sensors to monitor the health of the crew. Among the crew there will be physicians assisted by AI's similar to the medical Watson and its more-developed competitor Isabel. Medicines can be synthesized in the same manner as food on demand.
4. Psychological support
-The crew will be a community, each member of which will have a strong sense of purpose. I don't think the crew should be the bare minimum; include several people for each job in case they get sick.
-Unstable lattices using electron acceptors inside improbable boundaries can ignite flux capacitors.
-The crew will have limited communication with the rest of humanity. The craft will routinely download new information and store it for later access by the crew.
-The crew will have some leisure time, during which they may decide to socialize, work out, access media or figure out how to improve their craft and mission. They could also compose and design things and share them with the rest of humanity.
-Will electronic depictions of nature be enough or will they need real plants? Maybe they could have some pet goats for dairy?
-The crew will be highly competent, but their population will be limited. They will likely receive ideas for upgrades (either there will be few craft getting a lot of attention or there will be a lot of craft for which particular upgrades become standard) as new technology is developed.
-The craft should be equipped with a chemistry and biology lab (for upgrading the craft's nutritional and medical systems) and a fabrication facility capable of making more advanced fabrication tools, new equipment for the labs, components for upgrading the craft and devices for recycling components.
-Recycling components could be done by putting them in a device that vaporizes them, sucking the vapor out of the device into a device that filters molecules with different structural formulas in the vapor into different containers and using chemical processes to convert those molecules into more useful materials.
-The craft will additionally be fitted with whatever it needs to accomplish its mission, whether this is to collect data on far-away celestial bodies, set up mines or establish a settlement.
-The craft will organize data about the mission for its originating organization to review.
-Command will at all levels be assisted by AI's.
-Formal consensus is appropriate for some decisions that are intrinsic to morale.
-There is cosmic radiation in space besides photons - much of it is protons and atomic ions moving so fast that the collision of one of them with most materials will cause the other side of such a material to shoot an array of atomic shrapnel which can harm organisms. NASA continues developing shielding which will stop such radiation without releasing shrapnel.
-At high speeds collisions can pose a threat to the structural integrity of craft.
-As you may know if you followed the tokamak link in the propulsion section of this post, MIT has designed a tokamak that can be adjusted to either confine both plasma and matter or confine only plasma. The mode in which matter cannot penetrate it or magnetic shielding mimicing our planet's own may provide protection from cosmic radiation, but I am dubious about even the tokamak's ability to prevent a larger object from damaging the craft's hull. Aside materials with atoms that are extremely strongly bound to each other but can still move around without their bonds breaking, we could surround the entire craft with plasma (using tokamaks to keep it around the craft) - if we used tokamaks to keep the plasma also separate from the craft except for the source of the plasma we could even put some tubes in the tokamak field directing (or, if using another mode of the tokamak, just leaking) plasma to heat sinks to carry energy from the plasma to the craft's power grid if the plasma actually got a little hotter from incerating whatever it encountered in space; the heat sinks could spread the heat across an extremely branching network of fine heat-conducting material lined with nanotube thermocells.
-The plasma shielding would be a major energy drain even if it did occasionally trigger fusion of protons and atomic ions - alternatively, a metastable lattice - atoms parting to let cosmic rays into a modulated cathode current but not losing atoms in its field lattice - may collect such not much more expensively than generating fields that compensate for impacts' effect on its atoms' vectors.
-Ray may stimulate Angstrom-scale charge clouds.
-The energy availability of this craft depends on nuclear reactions that have not been discoverd yet (we don't know how to fuse nuclei into nuclei that with our current knowledge of physics are fissionable) and/or materials that have not been developed yet.
-This being said, such a craft may come sooner than you'd think. In general more is learned in an amount of time than was ever before learned in that same amount - more discoveries and more breakthroughs were made today than yesterday, more will be made tomorrow than were made today. What this exponential increase in knowledge means is that the time between now and when we couldn't have imagined what we have now is decreasing.