  The knowledge of physical conditions in young radio sources is important for
defining the framework of models describing radio source evolution. We
investigate whether young radio sources are in equipartition (i.e. minimum
energy) conditions by comparing the equipartition magnetic fields of 5 High
Frequency Peakers (HFP) with values directly inferred from the spectral peak
assumed to be produced by synchrotron self absorption. Multi-frequency VLBA
observations of 5 HFPs were carried out in both the optically thick and thin
part of the spectrum to determine the spectral shape and angular size of the
components for which individual radio spectra were obtained. We find that the
magnetic fields measured using observations agree well with those obtained by
assuming equipartition, which implies that these sources are in minimum energy
condition and the turnover in their spectra is due probably to SSA. In two
source components, we found that the peak of the spectrum is caused by
absorption of a thermal plasma instead of being due to SSA. The magnetic fields
found in the various components range from 10 to 100 mG. In the presence of
such high magnetic fields, electron populations with rather low $\gamma$ emit
in the GHz-regime. In one source, we detect low-surface brightness extended
emission at low frequency located ~30 mas (~50 pc) from the main source. This
feature may be related to either an earlier episode of radio activity or a
discontinuous start of the radio activity (sputtering). By comparing our data
with previous VLBA observations, we estimate the hotspot advance speed to be in
the range 0.1-0.7c and kinematic ages of a few hundred years.
