A method of operating a nuclear fission reactor, the method comprising: providing a nuclear fission reactor having a reactor vessel, the reactor vessel having a fission region and a fertile blanket region, wherein the fission region is separate from and interior to the fertile blanket region, and the fertile blanket region is between the fission region and a wall of the reactor vessel; receiving a solution in the fission region and the fertile blanket region of the reactor vessel of the nuclear fission reactor, the solution including a neutronically translucent liquid carrier material and a first fissile nuclear fission fuel material, the first fissile nuclear fission fuel material being dissolved in the neutronically translucent liquid carrier material; disposing an undissolved fertile nuclear fission fuel material in a foam form or a granular form or a plate form or a wire form in the fertile blanket region of the reactor vessel and in direct physical contact with the solution; exposing the undissolved fertile nuclear fission fuel material to a neutron flux of the nuclear fission reactor to transmute a portion of the undissolved fertile nuclear fission fuel material into a second fissile nuclear fission fuel material; and receiving the solution in the fission region and the fertile blanket region of the reactor vessel of the nuclear fission rector, the solution including the neutronically translucent liquid carrier material, the first fissile nuclear fission fuel material, and the second fissile nuclear fission fuel material, the first and second fissile nuclear fuel materials being dissolved in the neutronically translucent liquid carrier material. providing a nuclear fission reactor having a reactor vessel, the reactor vessel having a fission region and a fertile blanket region, wherein the fission region is separate from and interior to the fertile blanket region, and the fertile blanket region is between the fission region and a wall of the reactor vessel; receiving a solution in the fission region and the fertile blanket region of the reactor vessel of the nuclear fission reactor, the solution including a neutronically translucent liquid carrier material and a first fissile nuclear fission fuel material, the first fissile nuclear fission fuel material being dissolved in the neutronically translucent liquid carrier material; disposing an undissolved fertile nuclear fission fuel material in a foam form or a granular form or a plate form or a wire form in the fertile blanket region of the reactor vessel and in direct physical contact with the solution; exposing the undissolved fertile nuclear fission fuel material to a neutron flux of the nuclear fission reactor to transmute a portion of the undissolved fertile nuclear fission fuel material into a second fissile nuclear fission fuel material; and receiving the solution in the fission region and the fertile blanket region of the reactor vessel of the nuclear fission rector, the solution including the neutronically translucent liquid carrier material, the first fissile nuclear fission fuel material, and the second fissile nuclear fission fuel material, the first and second fissile nuclear fuel materials being dissolved in the neutronically translucent liquid carrier material.