  Relating in situ measurements of relativistic solar particles to their parent
activity in the corona requires understanding the magnetic structures that
guide them from their acceleration site to the Earth. Relativistic particle
events are observed at times of high solar activity, when transient magnetic
structures such as Interplanetary Coronal Mass Ejections (ICMEs) often shape
the interplanetary magnetic field (IMF). They may introduce interplanetary
paths that are longer than nominal, and magnetic connections rooted far from
the nominal Parker spiral. We present a detailed study of the IMF
configurations during ten relativistic solar particle events of the 23rd
activity cycle to elucidate the actual IMF configuration guiding the particles
to Earth, where they are measured by neutron monitors. We use magnetic field
(MAG) and plasma parameter measurements (SWEPAM) from ACE, and determine
interplanetary path lengths of energetic particles through a modified version
of the velocity dispersion analysis based on energetic particle measurements
with SoHO/ERNE. We find that the majority (7/10) of the events is detected in
the vicinity of an ICME. Their interplanetary path lengths are found to be
longer (1.5-2.6 AU) than those of the two events propagating in the slow solar
wind (1.3 AU). The largest apparent path length is found in an event within the
fast solar wind, probably due to enhanced pitch angle scattering. The derived
path lengths imply that the first energetic and relativistic protons are
released at the Sun at the same time as electron beams emitting type III radio
bursts. The timing of the first high-energy particle arrival at Earth is
dominantly determined by the type of IMF in which the particles propagate.
Initial arrival times are as expected from Parker's model in the slow solar
wind, and significantly larger in or near transient structures such as ICMEs.
