  On the basis of the condition for nuclear burning wave existence in the
neutron-multiplicating media (U-Pu and Th-U cycles) we show the possibility of
surmounting the so-called dpa-parameter problem, and suggest an algorithm of
the optimal nuclear burning wave mode adjustment, which is supposed to yield
the wave parameters (fluence/neutron flux, width and speed of nuclear burning
wave) that satisfy the dpa-condition associated with the tolerable level of the
reactor materials radioactive stability, in particular that of the cladding
materials.
  It is shown for the first time that the capture and fission cross-sections of
$^{238}$U and $^{239}$Pu increase with temperature within 1000-3000K range,
which under certain conditions may lead to a global loss of the nuclear burning
wave stability. Some variants of the possible stability loss due to the
so-called blow-up modes (anomalous nuclear fuel temperature and neutron flow
evolution) are discussed and are found to possibly become a reason for a
trivial violation of the traveling wave reactor internal safety.

Nuclear Theory;Nuclear Experiment