  The Inert Doublet Model (IDM) is one of the simplest extensions of the
Standard Model (SM), providing a dark matter candidate. It is a two Higgs
doublet model with a discrete $Z_2$ symmetry, that prevents the scalars of the
second doublet (inert scalars) from coupling to the SM fermions and makes the
lightest of them stable. We study a large number of IDM scenarios, which are
consistent with current constraints on direct detection and relic density of
dark matter, as well as with all collider and low-energy limits. We propose a
set of benchmark points with different kinematic features, that promise
detectable signals at future $e^+e^-$ colliders. Two inert scalar
pair-production processes are considered, $e^+e^- \to A~H $ and $e^+e^- \to
H^+H^-$, followed by decays of $A$ and $H^\pm$ into final states which always
include the lightest and stable neutral scalar dark matter candidate $H$.
Significance of the expected observations is studied for different benchmark
models and different running scenarios, for centre-of-mass energies from 250
GeV up to 3 TeV. For low mass scenarios, high significance can be obtained for
the signal signatures with two muons or an electron and a muon in the final
state. For high mass scenarios, which are only accessible at high energy stages
of CLIC, the significance is too low for the leptonic signature and the
semi-leptonic final state has to be used as the discovery channel. Results
presented for this channel are based on the fast simulation of the CLIC
detector response with the DELPHES package.
