Particle-in-cell simulations aimed at improving the coupling efficiency of input laser energy deposited to a compressed core by using a double cone are described. It is found that the number of high-energy electrons escaping from the sides of the cone is greatly reduced by the vacuum gap inside the wing of the double cone. Two main mechanisms to confine high-energy electrons are found. These mechanisms are the sheath electric field at the rear of the inner cone wing and the quasistatic magnetic field inside the vacuum gap. The generation mechanism for the quasistatic magnetic fields is discussed in detail. It is found that the quasistatic fields continue to confine the high-energy electrons for longer than a few picoseconds. The double cones provide confinement and focusing of about 15% of the input energy for deposition in the compressed core.