  To understand the properties of a possible cosmic string network requires
knowledge of the structures on long strings, which control the breaking off of
smaller loops. These structures are influenced by backreaction due to
gravitational wave emission. To gain an understanding of this process, we
calculate the effect of gravitational backreaction on the "helical breather":
an infinite cosmic string with a helical standing wave. We do the calculation
analytically to first order in the amplitude of the oscillation. Our results
for the rate of loss of length agree with the total power emitted from this
system as calculated by Sakellariadou. We also find a rotation of the
generators of the string that leads to an advancement of the phase of the
oscillation in addition to that produced by the loss of length.
