  We have used inelastic neutron scattering to examine the magnetic
fluctuations at intermediate frequencies in the simplest high temperature
superconductor, La_{2-x}Sr_{x}Cu_{4}. The suppression of the low energy
magnetic response in the superconducting state is accompanied by an increase in
the response at higher energies. Just above a threshold energy of ~7 meV there
is additional scattering present below T_{c} which is characterised by an
extraordinarily long coherence length, in excess of 50 \AA.
