  We study heating of motional modes of a single ion and of extended ion
crystals trapped in a linear radio frequency (rf) Paul trap with a precision of
$\Delta \dot{\bar{n}} \approx 0.1 $ phonons s$^{-1}$. Single-ion axial and
radial heating rates are consistent and electric field noise has been stable
over the course of four years. At a secular frequency of
$\omega_\mathrm{sec}=2\pi\times620$ kHz, we measure $\dot{\bar{n}} = 0.77(8)$
phonons s$^{-1}$ per ion for the center-of-mass (com) mode of linear chains of
up to eleven ions and observe no significant heating of the out-of-phase (oop)
modes. By displacing the ions away from the nodal line, inducing excess
micromotion, rf noise heats the com mode by $\dot{\bar{n}}(r)/ r^2 = 0.89(4)$
phonons s$^{-1}$ $\mu$m$^{-2}$ per ion, while the oop mode is protected from rf
heating in linear chains. By changing the quality factor of the resonant rf
circuit from $Q=542$ to $Q=204$, we observe an increase of rf noise by a factor
of up to 3. We show that the rf heating of motional modes of extended crystals
also depends on the symmetry of the crystal and of the mode itself. As an
example, we consider several 2D and 3D crystal configurations. Heating rates of
up to 500 phonons s$^{-1}$ are observed for individual modes, giving rise to a
total kinetic energy increase and thus a fractional time dilation shift of up
to $-0.3\times 10^{-18}$ s$^{-1}$ of the total system. In addition, we detail
on how the excitation probability of the individual ions is reduced and
decoherence is increased due to the Debye-Waller effect.
