  Using a fluxonium qubit with in situ tunability of its Josephson energy, we
characterize its energy relaxation at different flux biases as well as
different Josephson energy values. The relaxation rate at qubit energy values,
ranging more than one order of magnitude around the thermal energy $k_B T$, can
be quantitatively explained by a combination of dielectric loss and $1/f$ flux
noise with a crossover point. The amplitude of the $1/f$ flux noise is
consistent with that extracted from the qubit dephasing measurements at the
flux sensitive points. In the dielectric loss dominant regime, the loss is
consistent with that arises from the electric dipole interaction with
two-level-system (TLS) defects. In particular, as increasing Josephson energy
thus decreasing qubit frequency at the flux insensitive spot, we find that the
qubit exhibits increasingly weaker coupling to TLS defects thus desirable for
high-fidelity quantum operations.
