  Studies of the fragmentation of jets into charged particles in heavy-ion
collisions can provide information about the mechanism of jet-quenching by the
hot and dense QCD matter created in such collisions, the quark-gluon plasma.
This paper presents a measurement of the angular distribution of charged
particles around the jet axis in $\sqrt{s_{\mathrm{NN}}}=$ 5.02 TeV Pb+Pb and
$pp$ collisions, using the ATLAS detector at the LHC. The Pb+Pb and $pp$ data
sets have integrated luminosities of 0.49 nb$^{-1}$ and 25 pb$^{-1}$,
respectively. The measurement is performed for jets reconstructed with the
anti-$k_{t}$ algorithm with radius parameter $R = 0.4$ and is extended to an
angular distance of $r= 0.8$ from the jet axis. Results are presented as a
function of Pb+Pb collision centrality and distance from the jet axis for
charged particles with transverse momenta in the 1$-$63 GeV range, matched to
jets with transverse momenta in the 126$-$316 GeV range and an absolute value
of jet rapidity of less than 1.7. Modifications to the measured distributions
are quantified by taking a ratio to the measurements in $pp$ collisions. Yields
of charged particles with transverse momenta below 4 GeV are observed to be
increasingly enhanced as a function of angular distance from the jet axis,
reaching a maximum at $r=0.6$. Charged particles with transverse momenta above
4 GeV have an enhanced yield in Pb+Pb collisions in the jet core for angular
distances up to $r = 0.05$ from the jet axis, with a suppression at larger
distances.
