Context : 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 .

Aims : 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 .

Methods : 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 .

Results : 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 .

Conclusions : 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 .